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1. A remark on inverse problems for nonlinear magnetic Schrödinger equations on complex manifolds

   https://doi.org/10.1090/proc/16060  

   Krupchyk, Katya; Uhlmann, Gunther; Yan, Lili (April 2024, Proceedings of the American Mathematical Society)

   We show that the knowledge of the Dirichlet–to–Neumann map for a nonlinear magnetic Schrödinger operator on the boundary of a compact complex manifold, equipped with a Kähler metric and admitting sufficiently many global holomorphic functions, determines the nonlinear magnetic and electric potentials uniquely. 

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2. Recovery of a time-dependent potential in hyperbolic equations on conformally transversally anisotropic manifolds

   https://doi.org/10.4171/jst/547  

   Liu, Boya; Saksala, Teemu; Yan, Lili (March 2025, Journal of Spectral Theory)

   We study an inverse problem of determining a time-dependent potential appearing in the wave equation on conformally transversally anisotropic manifolds of dimension three or higher. These are compact Riemannian manifolds with boundary that are conformally embedded in a product of the real line and a transversal manifold. Under the assumption of the attenuated geodesic ray transform being injective on the transversal manifold, we prove the unique determination of time-dependent potentials from the knowledge of a certain partial Cauchy data set. 

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3. Inverting the local geodesic ray transform of higher rank tensors

   https://doi.org/10.1088/1361-6420/ab1ace  

   de Hoop, Maarten V; Uhlmann, Gunther; Zhai, Jian (January 2018, Inverse Problems)

   Consider a Riemannian manifold in dimension n ≥ 3 with strictly convex boundary. We prove the local invertibility, up to potential fields, of the geodesic ray transform on tensor fields of rank four near a boundary point. This problem is closely related with elastic qP-wave tomography. Under the condition that the manifold can be foliated with a continuous family of strictly convex hypersurfaces, the local invertibility implies a global result. One can straightforwardly adapt the proof to show similar results for tensor fields of arbitrary rank. 

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4. High-resolution particle-in-cell simulations of two-dimensional Bernstein–Greene–Kruskal modes

   https://doi.org/10.1063/5.0187853  

   McClung, J.; Franciscovich, M_T; Germaschewski, K.; Ng, C_S (April 2024, Physics of Plasmas)

   We present two-dimensional (2D) particle-in-cell (PIC) simulations of 2D Bernstein–Greene–Kruskal modes, which are exact nonlinear steady-state solutions of the Vlasov–Poisson equations, on a 2D plane perpendicular to a background magnetic field, with a cylindrically symmetric electric potential localized on the plane. PIC simulations are initialized using analytic electron distributions and electric potentials from the theory. We confirm the validity of such solutions using high-resolutions up to a 20482 grid. We show that the solutions are dynamically stable for a stronger background magnetic field, while keeping other parameters of the model fixed, but become unstable when the field strength is weaker than a certain value. When a mode becomes unstable, we observe that the instability begins with the excitation of azimuthal electrostatic waves that ends with a spiral pattern. 

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5. Changes in the Magnetic Field Topology and the Dayside/Nightside Reconnection Rates in Response to a Solar Wind Dynamic Pressure Front: A Case Study

   https://doi.org/10.1029/2020JA028768  

   Boudouridis, A.; Connor, H. K.; Lummerzheim, D.; Ridley, A. J.; Zesta, E. (July 2021, Journal of Geophysical Research: Space Physics)

   Abstract One of the most significant observations associated with a sharp enhancement in solar wind dynamic pressure,, is the poleward expansion of the auroral oval and the closing of the polar cap. The polar cap shrinking over a wide range of magnetic local times (MLTs), in connection with an observed increase in ionospheric convection and the transpolar potential, led to the conclusion that the nightside reconnection rate is significantly enhanced after a pressure front impact. However, this enhanced tail reconnection has never been directly measured. We demonstrate the effect of a solar wind dynamic pressure front on the polar cap closure, and for the first time, measure the enhanced reconnection rate in the magnetotail, for a case occurring during southward background Interplanetary Magnetic Field (IMF) conditions. We use Polar Ultra‐Violet Imager (UVI) measurements to detect the location of the open‐closed field line boundary, and combine them with Assimilative Mapping of Ionospheric Electrodynamics (AMIE) potentials to calculate the ionospheric electric field along the polar cap boundary, and thus evaluate the variation of the dayside/nightside reconnection rates. We find a strong response of the polar cap boundary at all available MLTs, exhibiting a significant reduction of the open flux content. We also observe an immediate response of the dayside reconnection rate, plus a phased response, delayed by ∼15–20 min, of the nightside reconnection rate. Finally, we provide comparison of the observations with the results of the Open Geospace General Circulation Model (OpenGGCM), elucidating significant agreements and disagreements. 

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