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1. Recent developments in mathematical aspects of relativistic fluids

   https://doi.org/10.1007/s41114-024-00052-x  

   Disconzi, Marcelo (October 2024, Living Reviews in Relativity)

   Abstract We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs’ main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research. 

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2. Relativistic Electron Precipitation Driven by Mesoscale Transients, Inferred From Ground and Multi‐Spacecraft Platforms

   https://doi.org/10.1029/2023JA032287  

   Artemyev, A. V.; Zhang, X.‐J.; Demekhov, A. G.; Meng, X.; Angelopoulos, V.; Fedorenko, Yu. V. (February 2024, Journal of Geophysical Research: Space Physics)

   Abstract Precipitation of relativistic electrons into the Earth's atmosphere regulates the outer radiation belt fluxes and contributes to magnetosphere‐atmosphere coupling. One of the main drivers of such precipitation is electron scattering by whistler‐mode waves. Such waves typically originate at the equator, where they can resonate with and scatter sub‐relativistic (tens to a few hundred keV) electrons. However, they can occasionally propagate far away from the equator along field lines, reaching middle latitudes, where they can resonate with and scatter relativistic (>500 keV) electrons. Such a propagation is typical for the dayside, but statistically has not been found on the nightside where the waves are quickly damped along their propagation due to Landau damping. Here we explore two events of relativistic electron precipitation from low‐altitude observations on the nightside. Combining measurements of whistler‐mode waves from ground observatories, relativistic electron precipitation from low‐altitude satellites, total electron content maps from GPS receivers, and magnetic field and electron flux from equatorial satellites, we show wave ducting by plasma density gradients is the possible channel that allows the waves to reach middle latitudes and scatter relativistic electrons. We suggest that both whistler‐mode wave generation and ducting can be driven by equatorial mesoscale (with spatial scales of about one Earth radius) transient structures during nightside injections. We also compare these nightside events with observations of ducted waves and relativistic electron precipitation at the dayside, where wave generation and ducting are driven by ultra‐low‐frequency waves. This study demonstrates the potential importance of mesoscale transients in relativistic electron precipitation, but does not however unequivocally establish that ducted whistler‐mode waves are the primary cause of the observed electron precipitation. 

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3. Weak Alfvénic turbulence in relativistic plasmas. Part 1. Dynamical equations and basic dynamics of interacting resonant triads

   https://doi.org/10.1017/S002237782100115X  

   TenBarge, J.M.; Ripperda, B.; Chernoglazov, A.; Bhattacharjee, A.; Mahlmann, J.F.; Most, E.R.; Juno, J.; Yuan, Y.; Philippov, A.A. (December 2021, Journal of Plasma Physics)

   Alfvén wave collisions are the primary building blocks of the non-relativistic turbulence that permeates the heliosphere and low- to moderate-energy astrophysical systems. However, many astrophysical systems such as gamma-ray bursts, pulsar and magnetar magnetospheres and active galactic nuclei have relativistic flows or energy densities. To better understand these high-energy systems, we derive reduced relativistic magnetohydrodynamics equations and employ them to examine weak Alfvénic turbulence, dominated by three-wave interactions, in reduced relativistic magnetohydrodynamics, including the force-free, infinitely magnetized limit. We compare both numerical and analytical solutions to demonstrate that many of the findings from non-relativistic weak turbulence are retained in relativistic systems. But, an important distinction in the relativistic limit is the inapplicability of a formally incompressible limit, i.e. there exists finite coupling to the compressible fast mode regardless of the strength of the magnetic field. Since fast modes can propagate across field lines, this mechanism provides a route for energy to escape strongly magnetized systems, e.g. magnetar magnetospheres. However, we find that the fast-Alfvén coupling is diminished in the limit of oblique propagation. 

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4. Chapter Two - Localized Relativistic Two-Component Methods for Ground and Excited State Calculations

   Zhang, Tianyuan; Kasper, Joseph M.; Li, Xiaosong (September 2020, Annual reports in computational chemistry)

   null (Ed.)

   Scientists are extending the computational application of relativistic methods to ever-increasing sizes of molecular systems. To this end, reduction of the computational cost of relativistic methods through modest approximations is a welcome effort. In this work, we review several localized two-component approximations and introduce a maximally localized variant. We also extend the focus of local relativistic approximations from the ground state to excited states. Benchmark calculations on both valence and core electron absorption spectra are carried out to analyze the error incurred by using the relativistic local approximations for excited state computations. 

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5. Kinetic description of stable white dwarfs

   https://doi.org/10.3934/krm.2021033  

   Jang, Juhi; Seok, Jinmyoung (January 2022, Kinetic and Related Models)

   In this paper, we study fermion ground states of the relativistic Vlasov-Poisson system arising in the semiclassical limit from relativistic quantum theory of white dwarfs. We show that fermion ground states of the three dimensional relativistic Vlasov-Poisson system exist for subcritical mass, the mass density of such fermion ground states satisfies the Chandrasekhar equation for white dwarfs, and that they are orbitally stable as long as solutions exist. 

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