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1. A duality between scattering poles and transmission eigenvalues in scattering theory

   https://doi.org/10.1098/rspa.2020.0612  

   Cakoni, Fioralba; Colton, David; Haddar, Houssem (December 2020, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   null (Ed.)

   In this paper, we develop a conceptually unified approach for characterizing and determining scattering poles and interior eigenvalues for a given scattering problem. Our approach explores a duality stemming from interchanging the roles of incident and scattered fields in our analysis. Both sets are related to the kernel of the relative scattering operator mapping incident fields to scattered fields, corresponding to the exterior scattering problem for the interior eigenvalues and the interior scattering problem for scattering poles. Our discussion includes the scattering problem for a Dirichlet obstacle where duality is between scattering poles and Dirichlet eigenvalues, and the inhomogeneous scattering problem where the duality is between scattering poles and transmission eigenvalues. Our new characterization of the scattering poles suggests a numerical method for their computation in terms of scattering data for the corresponding interior scattering problem. 

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2. Multiple-scattering frequency-time hybrid solver for the wave equation in interior domains

   https://doi.org/10.1090/mcom/3872  

   Bruno, Oscar; Yin, Tao (March 2024, Mathematics of Computation)

   Brenner, Susan (Ed.)

   This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensionalinterior spatial domains. The approach relies on four main elements, namely, (1) A multiple scattering strategy that decomposes a giveninteriortime-domain problem into a sequence oflimited-durationtime-domain problems of scattering by overlapping open arcs, each one of which is reduced (by means of the Fourier transform) to a sequence ofHelmholtz frequency-domain problems; (2) Boundary integral equations on overlapping boundary patches for the solution of the frequency-domain problems in point (1); (3) A smooth“Time-windowing and recentering”methodology that enables both treatment of incident signals of long duration and long time simulation; and, (4) A Fourier transform algorithm that delivers numerically dispersionless,spectrally-accurate time evolutionfor given incident fields. By recasting the interior time-domain problem in terms of a sequence of open-arc multiple scattering events, the proposed approach regularizes the full interior frequency domain problem—which, if obtained by either Fourier or Laplace transformation of the corresponding interior time-domain problem, must encapsulate infinitely many scattering events, giving rise to non-uniqueness and eigenfunctions in the Fourier case, and ill conditioning in the Laplace case. Numerical examples are included which demonstrate the accuracy and efficiency of the proposed methodology. 

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3. Calculating the High‐Latitude Ionospheric Electrodynamics Using a Machine Learning‐Based Field‐Aligned Current Model

   https://doi.org/10.1029/2023SW003683  

   Gowtam, V. Sai; Connor, Hyunju; Kunduri, Bharat S. R.; Raeder, Joachim; Laundal, Karl M.; Tulasi Ram, S.; Ozturk, Dogacan S.; Hampton, Donald; Chakraborty, Shibaji; Owolabi, Charles; et al (April 2024, Space Weather)

   Abstract We introduce a new framework called Machine Learning (ML) based Auroral Ionospheric electrodynamics Model (ML‐AIM). ML‐AIM solves a current continuity equation by utilizing the ML model of Field Aligned Currents of Kunduri et al. (2020,https://doi.org/10.1029/2020JA027908), the FAC‐derived auroral conductance model of Robinson et al. (2020,https://doi.org/10.1029/2020JA028008), and the solar irradiance conductance model of Moen and Brekke (1993,https://doi.org/10.1029/92gl02109). The ML‐AIM inputs are 60‐min time histories of solar wind plasma, interplanetary magnetic fields (IMF), and geomagnetic indices, and its outputs are ionospheric electric potential, electric fields, Pedersen/Hall currents, and Joule Heating. We conduct two ML‐AIM simulations for a weak geomagnetic activity interval on 14 May 2013 and a geomagnetic storm on 7–8 September 2017. ML‐AIM produces physically accurate ionospheric potential patterns such as the two‐cell convection pattern and the enhancement of electric potentials during active times. The cross polar cap potentials (Φ_PC) from ML‐AIM, the Weimer (2005,https://doi.org/10.1029/2004ja010884) model, and the Super Dual Auroral Radar Network (SuperDARN) data‐assimilated potentials, are compared to the ones from 3204 polar crossings of the Defense Meteorological Satellite Program F17 satellite, showing better performance of ML‐AIM than others. ML‐AIM is unique and innovative because it predicts ionospheric responses to the time‐varying solar wind and geomagnetic conditions, while the other traditional empirical models like Weimer (2005,https://doi.org/10.1029/2004ja010884) designed to provide a quasi‐static ionospheric condition under quasi‐steady solar wind/IMF conditions. Plans are underway to improve ML‐AIM performance by including a fully ML network of models of aurora precipitation and ionospheric conductance, targeting its characterization of geomagnetically active times. 

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4. Mountaintop Gamma Ray Observations of Three Terrestrial Gamma‐Ray Flashes at the Säntis Tower, Switzerland With Coincident Radio Waveforms

   https://doi.org/10.1029/2023JD039761  

   Chaffin, Jeffrey M.; Smith, David M.; Lapierre, Jeff; Cummer, Steve; Ortberg, John; Sunjerga, Antonio; Mostajabi, Amirhossein; Rubinstein, Marcos; Rachidi, Farhad (January 2024, Journal of Geophysical Research: Atmospheres)

   Abstract We report on the mountain top observation of three terrestrial gamma‐ray flashes (TGFs) that occurred during the summer storm season of 2021. To our knowledge, these are the first TGFs observed in a mountaintop environment and the first published European TGFs observed from the ground. A gamma‐ray sensitive detector was located at the base of the Säntis Tower in Switzerland and observed three unique TGF events with coincident radio sferic data characteristic of TGFs seen from space. We will show an example of a “slow pulse” radio signature (Cummer et al., 2011,https://doi.org/10.1029/2011GL048099; Lu et al., 2011,https://doi.org/10.1029/2010JA016141; Pu et al., 2019,https://doi.org/10.1029/2019GL082743; Pu et al., 2020,https://doi.org/10.1029/2020GL089427), a −EIP (Lyu et al., 2016,https://doi.org/10.1002/2016GL070154; Lyu et al., 2021,https://doi.org/10.1029/2021GL093627; Wada et al., 2020,https://doi.org/10.1029/2019JD031730), and a double peak TGF associated with an extraordinarily powerful and complicated positive‐polarity sferic, where each TGF peak is possibly preceded by a short burst of stepped leader emission. 

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5. A spectral target signature for thin surfaces with higher order jump conditions

   https://doi.org/10.3934/ipi.2022020  

   Cakoni, Fioralba; Lee, Heejin; Monk, Peter; Zhang, Yangwen (January 2022, Inverse Problems and Imaging)

   In this paper we consider the inverse problem of determining structural properties of a thin anisotropic and dissipative inhomogeneity in \begin{document}$$ {\mathbb R}^m $$\end{document}, \begin{document}$ m = 2, 3 $$\end{document} from scattering data. In the asymptotic limit as the thickness goes to zero, the thin inhomogeneity is modeled by an open \begin{document}$$ m-1 $$\end{document}$ dimensional manifold (here referred to as screen), and the field inside is replaced by jump conditions on the total field involving a second order surface differential operator. We show that all the surface coefficients (possibly matrix valued and complex) are uniquely determined from far field patterns of the scattered fields due to infinitely many incident plane waves at a fixed frequency. Then we introduce a target signature characterized by a novel eigenvalue problem such that the eigenvalues can be determined from measured scattering data, adapting the approach in [20]. Changes in the measured eigenvalues are used to identified changes in the coefficients without making use of the governing equations that model the healthy screen. In our investigation the shape of the screen is known, since it represents the object being evaluated. We present some preliminary numerical results indicating the validity of our inversion approach 

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