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The authors of this report met on 28-30 March 2018 at the New Jersey Institute of Technology, Newark, New Jersey, for a 3-day workshop that brought together a group of data providers, expert modelers, and computer and data scientists, in the solar discipline. Their objective was to identify challenges in the path towards building an effective framework to achieve transformative advances in the understanding and forecasting of the Sun-Earth system from the upper convection zone of the Sun to the Earth's magnetosphere. The workshop aimed to develop a research roadmap that targets the scientific challenge of coupling observations and modeling with emerging data-science research to extract knowledge from the large volumes of data (observed and simulated) while stimulating computer science with new research applications. The desire among the attendees was to promote future trans-disciplinary collaborations and identify areas of convergence across disciplines. The workshop combined a set of plenary sessions featuring invited introductory talks and workshop progress reports, interleaved with a set of breakout sessions focused on specific topics of interest. Each breakout group generated short documents, listing the challenges identified during their discussions in addition to possible ways of attacking them collectively. These documents were combined into this report-wherein a list of prioritized activities have been collated, shared and endorsed., Comment: Workshop Report

The shape of the solar wind bubble within the interstellar medium, the so-called heliosphere, has been explored over six decades. As the Sun moves through the surrounding partially-ionized medium, neutral hydrogen atoms penetrate the heliosphere, and through charge-exchange with the supersonic solar wind, create a population of hot pick-up ions (PUIs). The Termination Shock (TS) crossing by Voyager 2 (V2) data demonstrated that the heliosheath (HS) (the region of shocked solar wind) pressure is dominated by suprathermal particles. Here we use a novel magnetohydrodynamic model that treats the freshly ionized PUIs as a separate fluid from the thermal component of the solar wind. Unlike previous models, the new model reproduces the properties of the PUIs and solar wind ions based on the New Horizon and V2 spacecraft observations. The PUIs charge exchange with the cold neutral H atoms of the ISM in the HS and are quickly depleted. The depletion of PUIs cools the heliosphere downstream of the TS, "deflating" it and leading to a narrower HS and a smaller and rounder shape, in agreement with energetic neutral atom observations by the Cassini spacecraft. The new model, with interstellar magnetic field orientation constrained by the IBEX ribbon, reproduces the magnetic field data outside the HP at Voyager 1(V1). We present the predictions for the magnetic field outside the HP at V2., Comment: submitted to publication - new version after review

The Energy Conserving Semi-Implicit Method (ECSIM) introduced by Lapenta (2017) has many advantageous properties compared to the classical semi-implicit and explicit PIC methods. Most importantly, energy conservation eliminates the growth of the finite grid instability. We have implemented ECSIM in a different and more efficient manner than the original approach. More importantly, we have addressed two major shortcomings of the original ECSIM algorithm: there is no mechanism to enforce Gauss's law and there is no mechanism to reduce the numerical oscillations of the electric field. A classical approach to satisfy Gauss's law is to modify the electric field and its divergence using either an elliptic or a parabolic/hyperbolic correction based on the Generalized Lagrange Multiplier method. This correction, however, violates the energy conservation property, and the oscillations related to the finite grid instability reappear in the modified ECSIM scheme. We invented a new alternative approach: the particle positions are modified instead of the electric field in the correction step. Displacing the particles slightly does not change the energy conservation property, while it can satisfy Gauss's law by changing the charge density. We found that the new Gauss's Law satisfying Energy Conserving Semi-Implicit Method (GL-ECSIM) produces superior results compared to the original ECSIM algorithm. In some simulations, however, there are still some numerical oscillations present in the electric field. We attribute this to the simple finite difference discretization of the energy conserving implicit electric field solver. We modified the spatial discretization of the field solver to reduce these oscillations while only slightly violating the energy conservation properties. We demonstrate the improved quality of the GL-ECSIM method with several tests.

We discuss a Curie-Weiss model with two groups in the critical regime. This is the region where the central limit theorem does not hold any more but the mean magnetization still goes to zero as the number of spins grows. We show that the total magnetization normalized by $N^{3/4}$ converges to a non-trivial distribution which is not Gaussian, just as in the single-group Curie-Weiss model., Comment: 16 pages

We discuss a Curie-Weiss model with two groups with different coupling constants within and between groups. For the total magnetisations in each group, we show bivariate laws of large numbers and a central limit theorem which is valid in the high temperature regime. In the critical regime, the total magnetisation normalised by $N^{3/4}$ converges to a non-trivial distribution which is not Gaussian, just as in the single-group Curie-Weiss model. Finally, we prove a kind of a `law of large numbers' in the low temperature regime, more precisely we prove that the empirical magnetisation converges in distribution to a mixture of two Dirac measures., Comment: The third version contains some new results as well as the critical regime results from arXiv:1807.05020

In this Letter, we make use of sophisticated 3D numerical simulations to assess the extent of atmospheric ion and photochemical losses from Mars over time. We demonstrate that the atmospheric ion escape rates were significantly higher (by more than two orders of magnitude) in the past at $\sim 4$ Ga compared to the present-day value owing to the stronger solar wind and higher ultraviolet fluxes from the young Sun. We found that the photochemical loss of atomic hot oxygen dominates over the total ion loss at the current epoch whilst the atmospheric ion loss is likely much more important at ancient times. We briefly discuss the ensuing implications of high atmospheric ion escape rates in the context of ancient Mars, and exoplanets with similar atmospheric compositions around young solar-type stars and M-dwarfs., Comment: 6 pages, 4 figures, 1 table, accepted for publication in ApJ Letters

We study roles of the thermosphere and exosphere on the Martian ionospheric structure and ion escape rates in the process of the solar wind-Mars interaction. We employ a four-species multifluid MHD (MF-MHD) model to simulate the Martian ionosphere and magnetosphere. The $cold$ thermosphere background is taken from the Mars Global Ionosphere Thermosphere Model (M-GITM) and the $hot$ oxygen exosphere is adopted from the Mars exosphere Monte Carlo model - Adaptive Mesh Particle Simulator (AMPS). A total of four cases with the combination of 1D (globally averaged) and 3D thermospheres and exospheres are studied. The ion escape rates calculated by adopting 1D and 3D atmospheres are similar; however, the latter are required to adequately reproduce MAVEN ionospheric observations. In addition, our simulations show that the 3D hot oxygen corona plays an important role in preventing planetary molecular ions (O$_2^+$ and CO$_2^+$) escaping from Mars, mainly resulting from the mass loading of the high-altitude exospheric O$^+$ ions. The $cold$ thermospheric oxygen atom, however, is demonstrated to be the primary neutral source for O$^+$ ion escape during the relatively weak solar cycle 24., Comment: 21 pages, 10 figures, 4 tables, accepted for publication in Journal of Geophysical Research-Space Physics

Conserved currents associated with the time translation and axial symmetries of the Kerr spacetime and with scaling symmetry are constructed for the Teukolsky Master Equation (TME). Three partly different approaches are taken, of which the third one applies only to the spacetime symmetries. The results yielded by the three approaches, which correspond to three variants of Noether's theorem, are essentially the same, nevertheless. The construction includes the embedding of the TME into a larger system of equations, which admits a Lagrangian and turns out to consist of two TMEs with opposite spin weight. The currents thus involve two independent solutions of the TME with opposite spin weights. The first approach provides an example of the application of an extension of Noether's theorem to nonvariational differential equations. This extension is also reviewed in general form. The variant of Noether's theorem applied in the third approach is a generalization of the standard construction of conserved currents associated with spacetime symmetries in general relativity, in which the currents are obtained by the contraction of the symmetric energy-momentum tensor with the relevant Killing vector fields. Symmetries and conserved currents related to boundary conditions are introduced as well, and Noether's theorem and its variant for nonvariational differential equations are extended to them. The extension of the latter variant is used to construct conserved currents related to the Sommerfeld boundary condition., Comment: 19 pages, revised manuscript, new subsections on boundary conditions

We attempt to evaluate energy budget over a restricted but extremely well studied oceanic region along the shorelines of Oregon and California. The analysis is based on a recently updated geostrophic flow field data set covering 22 years with daily resolution on a grid of 0.25$^\circ\times$0.25$^\circ$, and turbulent wind stress data from the ERA-Interim reanalysis over the same geographic region with the same temporal and spatial resolutions. Integrated 2D kinetic energy, enstrophy, wind stress work and { kinetic energy tendency} are determined separately for the shore- and open water regions. The empirical analysis is supported by 2D lattice Boltzmann simulations of freely decaying vortices along a rough solid wall, which permits to separate the pure shoreline effects and dissipation properties of surface flow fields. Comparisons clearly demonstrate that kinetic energy and vorticity { of the geostrophic flow field} are mostly generated along the shorelines and advected to the open water regions, where the net wind stress work is almost negligible. Our results support that the geostrophic flow field is quasistationary on the timescale of a couple of days, thus total forcing is practically equal to total dissipation. Estimates of unknown terms in the equation of oceanic kinetic energy budget are based on other studies, nevertheless our results suggest that { an effective} eddy kinematic viscosity is in the order of magnitude $10^{-2}$ m$^2$/s along the shorelines, and it is lower { by a factor of two} in the open water region.

We show for two disjoint groups of spins in a Curie-Weiss model and a homogeneous coupling matrix that the law of large numbers holds for the normed sums of both groups' spin variables. We also show that the central limit theorem holds only for low inverse temperatures., Comment: 18 pages. Second version acknowledges similar results by other authors we had been unaware of and corrects some typos

We present a three-species multi-fluid MHD model (H$^+$, H$_2$O$^+$ and e$^-$), endowed with the requisite atmospheric chemistry, that is capable of accurately quantifying the magnitude of water ion losses from exoplanets. We apply this model to a water world with Earth-like parameters orbiting a Sun-like star for three cases: (i) current normal solar wind conditions, (ii) ancient normal solar wind conditions, and (iii) one extreme "Carrington-type" space weather event. We demonstrate that the ion escape rate for (ii), with a value of 6.0$\times$10$^{26}$ s$^{-1}$, is about an order of magnitude higher than the corresponding value of 6.7$\times$10$^{25}$ s$^{-1}$ for (i). Studies of ion losses induced by space weather events, where the ion escape rates can reach $\sim$ 10$^{28}$ s$^{-1}$, are crucial for understanding how an active, early solar-type star (e.g., with frequent coronal mass ejections) could have accelerated the depletion of the exoplanet's atmosphere. We briefly explore the ramifications arising from the loss of water ions, especially for planets orbiting M-dwarfs where such effects are likely to be significant., Comment: ApJ Letters, in press, 8 pages, 2 figures, 3 tables

We perform a three-dimensional (3D) global simulation of Earth's magnetosphere with kinetic reconnection physics to study the flux transfer events (FTEs) and dayside magnetic reconnection with the recently developed magnetohydrodynamics with embedded particle-in-cell model (MHD-EPIC). During the one-hour long simulation, the FTEs are generated quasi-periodically near the subsolar point and move toward the poles. We find the magnetic field signature of FTEs at their early formation stage is similar to a `crater FTE', which is characterized by a magnetic field strength dip at the FTE center. After the FTE core field grows to a significant value, it becomes an FTE with typical flux rope structure. When an FTE moves across the cusp, reconnection between the FTE field lines and the cusp field lines can dissipate the FTE. The kinetic features are also captured by our model. A crescent electron phase space distribution is found near the reconnection site. A similar distribution is found for ions at the location where the Larmor electric field appears. The lower hybrid drift instability (LHDI) along the current sheet direction also arises at the interface of magnetosheath and magnetosphere plasma. The LHDI electric field is about 8 mV/m and its dominant wavelength relative to the electron gyroradius agrees reasonably with MMS observations.