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Solar energetic particles (SEPs) can pose hazardous radiation risks to both humans in space and spacecraft electronics. Numerical modeling based on first principles offers valuable insights into SEPs, providing synthetic observables for SEPs at any time and location in space. In this work, we present a high-resolution scheme based on integral relations for Poisson brackets to solve the kinetic equation for particle acceleration and transport processes. We implement this scheme within the Space Weather Modeling Framework (SWMF), developed at the University of Michigan, to conduct a comprehensive study of solar energetic protons during the 2013 April 11 SEP event. In addition, a shock capturing tool is developed to study the coronal-mass-ejection-driven shock starting from the low solar corona. Multi-point spacecraft observations, including SOHO/ERNE, SDO/AIA, GOES and ACE at Earth, and STEREO-A/B, are used for model-data comparison and validation. New synthetic observables such as white-light images, shock geometry and properties, as well as SEP intensity-time profiles and spectra provide insights for SEP studies. The influences of the mean free path on SEP intensity-time profiles and spectra are also discussed. The results demonstrate: (1) the successful implementation of the Poisson bracket scheme with a self-consistent particle tracker within the SWMF, (2) the capability of capturing the time-evolving shock surface in the SWMF, and (3) the complexity of the mean free path impacts on SEPs. Overall, this study contributes to both scientific research and operational objectives by advancing our understanding of particle behaviors and showing the readiness for more accurate SEP predictions., Comment: 51 pages, 15 figures, 2 tables

Simulations have played a critical role in the advancement of our knowledge of magnetic reconnection. However, due to the inherently multiscale nature of reconnection, it is impossible to simulate all physics at all scales. For this reason, a wide range of simulation methods have been crafted to study particular aspects and consequences of magnetic reconnection. This chapter reviews many of these methods, laying out critical assumptions, numerical techniques, and giving examples of scientific results. Plasma models described include magnetohydrodynamics (MHD), Hall MHD, Hybrid, kinetic particle-in-cell (PIC), kinetic Vlasov, Fluid models with embedded PIC, Fluid models with direct feedback from energetic populations, and the Rice Convection Model (RCM)., Comment: Chapter 5.2 of ISSI Book on Magnetic Reconnection, submitted to Space Science Reviews

The late-time behaviour of the solutions of the Fackerell-Ipser equation (which is a wave equation for the spin-zero component of the electromagnetic field strength tensor) on the closure of the domain of outer communication of sub-extremal Kerr spacetime is studied numerically. Within the Kerr family, the case of Schwarzschild background is also considered. Horizon-penetrating compactified hyperboloidal coordinates are used, which allow the behaviour of the solutions to be observed at the event horizon and at future null infinity as well. For the initial data, pure multipole configurations that have compact support and are either stationary or non-stationary are taken. It is found that with such initial data the solutions of the Fackerell-Ipser equation converge at late times either to a known static solution (up to a constant factor) or to zero. As the limit is approached, the solutions exhibit a quasinormal ringdown and finally a power-law decay. The exponents characterizing the power-law decay of the spherical harmonic components of the field variable are extracted from the numerical data for various values of the parameters of the initial data, and based on the results a proposal for a Price's law relevant to the Fackerell-Ipser equation is made. Certain conserved energy and angular momentum currents are used to verify the numerical implementation of the underlying mathematical model. In the construction of these currents a discrete symmetry of the Fackerell-Ipser equation, which is the product of an equatorial reflection and a complex conjugation, is also taken into account., Comment: 29 pages, LaTeX, minor changes

The charge exchange between the interstellar medium (ISM) and the solar wind plasma is crucial for determining the structures of the heliosphere. Since both the neutral-ion and neutral-neutral collision mean free paths are either comparable to or larger than the size of the heliosphere, the neutral phase space distribution can deviate far away from the Maxwellian distribution. A kinetic description for the neutrals is crucial for accurately modeling the heliosphere. It is computationally challenging to run three-dimensional (3D) time-dependent kinetic simulations due to the large number of macro-particles. In this paper, we present the new highly efficient SHIELD-2 model with a kinetic model of neutrals and a magnetohydrodynamic (MHD) model for the ions and electrons. To improve the simulation efficiency, we implement adaptive mesh refinement (AMR) and particle splitting and merging algorithms for the neutral particles to reduce the particle number that is required for an accurate simulation. We present several tests to verify and demonstrate the capabilities of the model.

The interaction between a Coronal Mass Ejection (CME) and a comet has been observed several times by in-situ observations from the Rosetta Plasma Consortium (RPC), which is designed to investigate the cometary magnetosphere of comet 67P/Churyumov-Gerasimenko (CG). Goetz et al. (2019) reported a magnetic field of up to 300 nT measured in the inner coma, which is among the largest interplanetary magnetic fields observed in the solar system. They suggested the large magnetic field observations in the inner coma come from magnetic field pile-up regions, which are generated by the interaction between a CME and/or corotating interaction region and the cometary magnetosphere. However, the detailed interaction between a CME and the cometary magnetosphere of comet CG in the inner coma has not been investigated by numerical simulations yet. In this manuscript, we will use a numerical model to simulate the interaction between comet CG and a Halloween class CME and investigate its magnetospheric response to the CME. We find that the plasma structures change significantly during the CME event, and the maximum value of the magnetic field strength is more than 500nT close to the nucleus. Virtual satellites at similar distances as Rosetta show that the magnetic field strength can be as large as 250nT, which is slightly less than what Goetz et al. (2019) reported., Comment: 19 pages, 5 figures, submitted to ApJ

A potential field solution is widely used to extrapolate the coronal magnetic field above the Sun's surface to a certain height. This model applies the current-free approximation and assumes that the magnetic field is entirely radial beyond the source surface height, which is defined as the radial distance from the center of the Sun. Even though the source surface is commonly specified at 2.5 Rs (solar radii), previous studies have suggested that this value is not optimal in all cases. In this study, we propose a novel approach to specify the source surface height, by comparing the areas of the open magnetic field regions from the potential field solution with predictions made by a magnetohydrodynamics model, in our case the Alfven Wave Solar atmosphere Model. We find that the adjusted source surface height is significantly less than 2.5 Rs near solar minimum, and slightly larger than 2.5 Rs near solar maximum. We also report that the adjusted source surface height can provide a better open flux agreement with the observations near the solar minimum, while the comparison near the solar maximum is slightly worse., Comment: 15 pages, 5 figures, 1 table, submitted ApjL

In a previous study, Huang et al. (2023) used the Alfven Wave Solar atmosphere Model (AWSoM), one of the widely used solar wind models in the community, driven by ADAPT-GONG magnetograms to simulate the solar wind in the last solar cycle and found that the optimal Poynting flux parameter can be estimated from either the open field area or the average unsigned radial component of the magnetic field in the open field regions. It was also found that the average energy deposition rate (Poynting flux) in the open field regions is approximately constant. In the current study, we expand the previous work by using GONG magnetograms to simulate the solar wind for the same Carrington rotations and determine if the results are similar to the ones obtained with ADAPT-GONG magnetograms. Our results indicate that similar correlations can be obtained from the GONG maps. Moreover, we report that ADAPT-GONG magnetograms can consistently provide better comparisons with 1 AU solar wind observations than GONG magnetograms, based on the best simulations selected by the minimum of the average curve distance for the solar wind speed and density., Comment: 17 pages, 5 figures, 2 tables, submitted to ApJ

Gaussian Processes (GP) have become popular machine-learning methods for kernel-based learning on datasets with complicated covariance structures. In this paper, we present a novel extension to the GP framework using a contaminated normal likelihood function to better account for heteroscedastic variance and outlier noise. We propose a scalable inference algorithm based on the Sparse Variational Gaussian Process (SVGP) method for fitting sparse Gaussian process regression models with contaminated normal noise on large datasets. We examine an application to geomagnetic ground perturbations, where the state-of-the-art prediction model is based on neural networks. We show that our approach yields shorter prediction intervals for similar coverage and accuracy when compared to an artificial dense neural network baseline.

Parker Solar Probe observations reveal that the near-Sun space is almost filled with magnetic switchbacks (``switchbacks'' hereinafter), which may be a major contributor to the heating and acceleration of solar wind. Here, for the first time, we develop an analytic model of an axisymmetric switchback with uniform magnetic field strength. In this model, three parameters control the geometry of the switchback: height (length along the background magnetic field), width (thickness along radial direction perpendicular to the background field), and the radial distance from the center of switchback to the central axis, which is a proxy of the size of the switchback along the third dimension. We carry out three-dimensional magnetohydrodynamic simulations to investigate the dynamic evolution of the switchback. Comparing simulations conducted with compressible and incompressible codes, we verify that compressibility, i.e. parametric decay instability, is necessary for destabilizing the switchback. Our simulations also reveal that the geometry of the switchback significantly affects how fast the switchback destabilizes. The most stable switchbacks are 2D-like (planar) structures with large aspect ratios (length to width), consistent with the observations. We show that when plasma beta ($\beta$) is smaller than one, the switchback is more stable as $\beta$ increases. However, when $\beta$ is greater than one, the switchback becomes very unstable as the pattern of the growing compressive fluctuations changes. Our results may explain some of the observational features of switchbacks, including the large aspect ratios and nearly constant occurrence rates in the inner heliosphere.

In this paper, we demonstrate the applicability of the data-driven and self-consistent solar energetic particle model, Solar-wind with FIeld-lines and Energetic-particles (SOFIE), to simulate acceleration and transport processes of solar energetic particles. SOFIE model is built upon the Space Weather Modeling Framework (SWMF) developed at the University of Michigan. In SOFIE, the background solar wind plasma in the solar corona and interplanetary space is calculated by the Aflv\'en Wave Solar-atmosphere Model(-Realtime) (AWSoM-R) driven by the near-real-time hourly updated Global Oscillation Network Group (GONG) solar magnetograms. In the background solar wind, coronal mass ejections (CMEs) are launched by placing an imbalanced magnetic flux rope on top of the parent active region, using the Eruptive Event Generator using Gibson-Low model (EEGGL). The acceleration and transport processes are modeled by the Multiple-Field-Line Advection Model for Particle Acceleration (M-FLAMPA). In this work, nine solar energetic particle events (Solar Heliospheric and INterplanetary Environment (SHINE) challenge/campaign events) are modeled. The three modules in SOFIE are validated and evaluated by comparing with observations, including the steady-state background solar wind properties, the white-light image of the CME, and the flux of solar energetic protons, at energies of > 10 MeV.

Magnetic switchbacks are rapid high amplitude reversals of the radial magnetic field in the solar wind that do not involve a heliospheric current sheet crossing. First seen sporadically in the seventies in Mariner and Helios data, switchbacks were later observed by the Ulysses spacecraft beyond 1 au and have been recently identified as a typical component of solar wind fluctuations in the inner heliosphere by the Parker Solar Probe spacecraft. Here we provide a simple yet predictive theory for the formation of these magnetic reversals: the switchbacks are produced by the shear of circularly polarized Alfv\'en waves by a transversely varying radial wave propagation velocity. We provide an analytic expression for the magnetic field variation, establish the necessary and sufficient conditions and show that the mechanism works in a realistic solar wind scenario., Comment: Submitted to Nature

Collisionless magnetic reconnection typically requires kinetic treatments that are, in general, computationally expensive compared to fluid-based models. In this study, we use the magnetohydrodynamics with adaptively embedded particle-in-cell (MHD-AEPIC) model to study the interaction of two magnetic flux ropes. This innovative model embeds one or more adaptive PIC regions into a global MHD simulation domain such that the kinetic treatment is only applied in regions where kinetic physics is prominent. We compare the simulation results among three cases: 1) MHD with adaptively embedded PIC regions, 2) MHD with statically (or fixed) embedded PIC regions, and 3) a full PIC simulation. The comparison yields good agreement when analyzing their reconnection rates and magnetic island separations, as well as the ion pressure tensor elements and ion agyrotropy. In order to reach a good agreement among the three cases, large adaptive PIC regions are needed within the MHD domain, which indicates that the magnetic island coalescence problem is highly kinetic in nature where the coupling between the macro-scale MHD and micro-scale kinetic physics is important., Comment: 9 pages, 10 figures

We explore model performance for the Alfven Wave Solar atmosphere Model (AWSoM) with near-real-time (NRT) synoptic maps of the photospheric vector magnetic field. These maps, produced by assimilating data from the Helioseismic Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO), use a different method developed at the National Solar Observatory (NSO) to provide a near contemporaneous source of data to drive numerical models. Here, we apply these NSO-HMI-NRT maps to simulate three Carrington rotations (CRs): 2107-2108 (centered on 2011/03/07 20:12 CME event), 2123 (integer CR) and 2218--2219 (centered on 2019/07/2 solar eclipse), which together cover a wide range of activity level for solar cycle 24. We show simulation results, which reproduce both extreme ultraviolet emission (EUV) from the low corona while simultaneously matching in situ observations at 1 au as well as quantify the total unsigned open magnetic flux from these maps.

We analyse a generalisation of the Galam model of binary opinion dynamics in which iterative discussions take place in local groups of individuals and study the effects of random deviations from the group majority. The probability of a deviation or flip depends on the magnitude of the majority. Depending on the values of the flip parameters which give the probability of a deviation, the model shows a wide variety of behaviour. We are interested in the characteristics of the model when the flip parameters are themselves randomly selected, following some probability distribution. Examples of these characteristics are whether large majorities and ties are attractors or repulsors, or the number of fixed points in the dynamics of the model. Which of the features of the model are likely to appear? Which ones are unlikely because they only present as events of low probability with respect to the distribution of the flip parameters? Answers to such questions allow us to distinguish mathematical properties which are stable under a variety of assumptions on the distribution of the flip parameters from features which are very rare and thus more of theoretical than practical interest. In this article, we present both exact numerical results for specific distributions of the flip parameters and small discussion groups and rigorous results in the form of limit theorems for large discussion groups. Small discussion groups model friend or work groups -- people that personally know each other and frequently spend time together. Large groups represent scenarios such as social media or political entities such as cities, states, or countries.

We describe our first attempt to systematically simulate the solar wind during different phases of the last solar cycle with the Alfv\'en Wave Solar atmosphere Model (AWSoM) developed at the University of Michigan. Key to this study is the determination of the optimal values of one of the most important input parameters of the model, the Poynting flux parameter, which prescribes the energy flux passing through the chromospheric boundary of the model in the form of Alfv\'en wave turbulence. It is found that the optimal value of the Poynting flux parameter is correlated with the area of the open magnetic field regions with the Spearman's correlation coefficient of 0.96 and anti-correlated with the average unsigned radial component of the magnetic field with the Spearman's correlation coefficient of -0.91. Moreover, the Poynting flux in the open field regions is approximately constant in the last solar cycle, which needs to be validated with observations and can shed light on how Alfv\'en wave turbulence accelerates the solar wind during different phases of the solar cycle. Our results can also be used to set the Poynting flux parameter for real-time solar wind simulations with AWSoM., Comment: 15 pages, 1 table, 4 figures

We model voting behaviour in the multi-group setting of a two-tier voting system using sequences of de Finetti measures. Our model is defined by using the de Finetti representation of a probability measure (i.e. as a mixture of conditionally independent probability measures) describing voting behaviour. The de Finetti measure describes the interaction between voters and possible outside influences on them. We assume that for each population size there is a (potentially) different de Finetti measure, and as the population grows, the sequence of de Finetti measures converges weakly to the Dirac measure at the origin, representing a tendency toward weakening social cohesion as the population grows large. The resulting model covers a wide variety of behaviour, ranging from independent voting in the limit under fast convergence, a critical convergence speed with its own pattern of behaviour, to a subcritical convergence speed which yields a model in line with empirical evidence of real-world voting data, contrary to previous probabilistic models used in the study of voting. These models can be used, e.g., to study the problem of optimal voting weights in two-tier voting systems.

This paper surveys the theory of multiple packings and coverings. The study of multiple arrangements started in the 60s of the last century, and it was restricted mostly to lattice arrangements on the plane or of general arrangements of balls. We emphasize two new topics which were intensively investigated recently: decomposition of multiple coverings into simple coverings and characterization of multiple tilings.

This paper suveys different variants of the following problem: Given a convex set $K$ and a sequence $\{C_i\}$ of convex bodies in $E^n$, is it possible to pack the sequence of bodies in $K$ or cover $K$ with the bodies? Algorithmic versions of these problems are on-line packing and on-line covering: The bodies of the sequence are given one at a time and the algorithm is to decide on the placement of the arriving body before the next body is revealed; once placed, the body cannot be moved.

In this paper we discuss various special problems on packing and covering. Among others we survey the problems and results concerning finite arrangements, Minkowskian, saturated, compact, and totally separable packings. We discuss shortest path problems and questions about stability of packings.

The present work surveys problems in $n$-dimensional space with $n$ large. Early development in the study of packing and covering in high dimensions was motivated by the geometry of numbers. Subsequent results, such as the discovery of the Leech lattice and the linear programming bound, which culminated in the recent solution of the sphere packing problem in dimensions 8 and 24, were influenced by coding theory. After mentioning the known results concerning existence of economical packings and coverings we discuss the different methods yielding upper bounds for the density of packing congruent balls. We summarize the few results on upper bounds for the packing density of general convex bodies. The paper closes with some remarks on the structure of optimal arrangements.

Two members of a packing are neighbors if they have a common boundary point. A multitude of problems arises in connection with neighbors in a packing. The oldest one concerns a dispute between Newton and Gregory about the maximum number of neighbors a member can have in a packing of congruent balls. Other problems ask for the average number of neighbors or the maximum number of mutually neighboring members in a packing. The present work gives a survey of these problems.

In hyperbolic space density cannot be defined by a limit as we define it in Euclidean space. We describe the local density bounds for sphere packings and we discuss the different attempts to define optimal arrangements in hyperbolic space.

The isoperimetric problem asks for the maximum area of a region of given perimeter. It is natural to consider other measurements of a region, such as the diameter and width, and ask for the extreme value of one when another is fixed. The solution of these problems is known if the competing regions are general convex disks, however several of these problems are still open if the competing regions are polygons with at most a given number of sides. The present work surveys these problems.

In this work we survey four classic problems: Borsuk's partition problem, Tarski's plank problem, the Kneser--Poulsen problem on the monotonicity of the union of balls under a contraction of their centers, and the Hadwiger--Levi problem on covering convex bodies by their smaller positively homothetic copies.

We analyse two-tier voting systems with voters described by a multi-group mean-field model that allows for correlated voters both within groups as well as across group boundaries. The objective is to determine the optimal weights each group receives in the council to minimise the expected quadratic deviation of the council vote from a hypothetical referendum of the overall population. The mean-field model exhibits different behaviour depending on the intensity of interactions between voters. When interaction is weak, we obtain optimal weights given by the sum of a constant term equal for all groups and a term proportional to the square root of the group's population. When interaction is strong, the optimal weights are in general not uniquely determined. Indeed, when all groups are positively coupled, any assignation of weights is optimal. For two competing clusters of groups, the difference in total weights must be a specific number, but the assignation of weights within each cluster is arbitrary. We also obtain conditions for both interaction regimes under which it is impossible to reach the minimal democracy deficit due to the negativity of weights.

Space plasma simulations have seen an increase in the use of magnetohydrodynamic (MHD) with embedded Particle-in-Cell (PIC) models. This combined MHD-EPIC algorithm simulates some regions of interest using the kinetic PIC method while employing the MHD description in the rest of the domain. The MHD models are highly efficient and their fluid descriptions are valid for most part of the computational domain, thus making large-scale global simulations feasible. However, in practical applications, the regions where the kinetic effects are critical can be changing, appearing, disappearing and moving in the computational domain. If a static PIC region is used, this requires a much larger PIC domain than actually needed, which can increase the computational cost dramatically. To address the problem, we have developed a new method that is able to dynamically change the region of the computational domain where a PIC model is applied. We have implemented this new MHD with Adaptively Embedded PIC (MHD-AEPIC) algorithm using the BATS-R-US Hall MHD and the Adaptive Mesh Particle Simulator (AMPS) as the semi-implicit PIC models. We describe the algorithm and present a test case of two merging flux ropes to demonstrate its accuracy. The implementation uses dynamic allocation/deallocation of memory and load balancing for efficient parallel execution. We evaluate the performance of MHD-AEPIC compared to MHD-EPIC and the scaling properties of the model to large number of computational cores.

A formulation of linearized gravity in flat background, based on the Fierz tensor as a counterpart of the electromagnetic field strength, is discussed in detail and used to study fundamental properties of the linearized gravitational field. In particular, the linearized Einstein equations are written as first order partial differential equations in terms of the Fierz tensor, in analogy with the first order Maxwell equations. An energy-momentum tensor ($T_{\mathrm{lg}}^{ab}$) with favourable properties and exhibiting remarkable similarity to the standard energy-momentum tensor of the electromagnetic field is found for the linearized gravitational field. $T_{\mathrm{lg}}^{ab}$ is quadratic in the Fierz tensor (which is constructed from the first derivatives of the linearized metric), traceless, and satisfies the dominant energy condition in a gauge that contains the transverse traceless gauge. It is further shown that in suitable gauges, including the transverse traceless gauge, linearized gravity in the absence of matter has a duality symmetry that maps the Fierz tensor, which is antisymmetric in its first two indices, into its dual. Conserved currents associated with the gauge and duality symmetries of linearized gravity are also determined. These currents show good analogy with the corresponding currents in electrodynamics., Comment: 45 pages, revised manuscript, title change

We study the effect of probabilistic distortions to the local majority rules used in the Galam model of opinion dynamics and bottom-up hierarchical voting. A different probability for a flip against the local majority within the discussion group is associated with each ratio of majority / minority. The cases of groups of sizes 3 and 5 are investigated in detail. For hierarchical voting, the local flip corresponds to a `faithless elector', a representative who decides to vote against the choice of their electing group. Depending on the flip probabilities, the model exhibits a rich variety of patterns for the dynamics, which include novel features in the topology of the landscape. In particular, for size 5, we uncover for the first time an interplay between five fixed points, which split into either three attractors and two tipping points or two attractors and three tipping points, depending on the flip probabilities. Larger groups are also analysed. These features were absent in the former versions of the Galam model, which has at maximum three fixed points for any group size. The results shed a new light on a series of social phenomena triggered by one single individual who acts against the local majority., Comment: 24 pages, 7 figures, 9 tables

MHD-based global space weather models have mostly been developed and maintained at academic institutions. While the "free spirit" approach of academia enables the rapid emergence and testing of new ideas and methods, the lack of long-term stability and support makes this arrangement very challenging. This paper describes a successful example of a university-based group, the Center of Space Environment Modeling (CSEM) at the University of Michigan, that developed and maintained the Space Weather Modeling Framework (SWMF) and its core element, the BATS-R-US extended MHD code. It took a quarter of a century to develop this capability and reach its present level of maturity that makes it suitable for research use by the space physics community through the Community Coordinated Modeling Center (CCMC) as well as operational use by the NOAA Space Weather Prediction Center (SWPC)., Comment: 105 pages, 36 figures, in press

We analyse optimal voting weights in two-tier voting systems. In our model, the overall population (or union) is split in groups (or member states) of different sizes. The individuals comprising the overall population constitute the first tier, and the council is the second tier. Each group has a representative in the council that casts votes on their behalf. By "optimal weights", we mean voting weights in the council which minimise the democracy deficit, i.e. the expected deviation of the council vote from a (hypothetical) popular vote. We assume that the voters within each group interact via what we call a local collective bias or common belief (through tradition, common values, strong religious beliefs, etc.). We allow in addition an interaction across group borders via a global bias. Thus, the voting behaviour of each voter depends on the behaviour of all other voters. This correlation may be stronger between voters in the same group, but is in general not zero for voters in different groups. We call the respective voting measure a Collective Bias Model (CBM). The "simple CBM" introduced in [12] and in particular the Impartial Culture and the Impartial Anonymous Culture are special cases of our general model. We compute the optimal weights in the large population limit. Those optimal weights are unique as long as there is no "complete" correlation between the groups. In this case, we obtain optimal weights which are the sum of a common constant equal for all groups and a summand which is proportional to the population of each group. We also analyse the conditions under which the optimal weights are negative, thus making it impossible to reach the theoretical minimum of the democracy deficit. This is a new aspect of the model owed to the correlation between votes belonging to different groups., Comment: Overhaul of the article with additional results and more detailed explanations

We study a multi-group version of the mean-field or Curie-Weiss spin model. For this model, we show how, analogously to the classical (single-group) model, the three temperature regimes are defined. Then we use the method of moments to determine for each regime how the vector of the group magnetisations behaves asymptotically. Some possible applications to social or political sciences are discussed.

In this paper, we propose a new interpretation of local limit theorems for univariate and multivariate distributions on lattices. We show that - given a local limit theorem in the standard sense - the distributions are approximated well by the limit distribution, uniformly on intervals of possibly decaying length. We identify the maximally allowable decay speed of the interval lengths. Further, we show that for continuous distributions, the interval type local law holds without any decay speed restrictions on the interval lengths. We show that various examples fit within this framework, such as standardized sums of i.i.d. random vectors or correlated random vectors induced by multidimensional spin models from statistical mechanics.

We define a multi-group version of the mean-field spin model, also called Curie-Weiss model. It is known that, in the high temperature regime of this model, a central limit theorem holds for the vector of suitably scaled group magnetisations, that is the sum of spins belonging to each group. In this article, we prove a local central limit theorem for the group magnetisations in the high temperature regime.

This paper presents the state of the art of kinetic modeling techniques for simulating plasma kinetic dynamics in magnetospheres. We describe the critical numerical techniques for enabling large-scale kinetic simulations of magnetospheres: parameter scaling, implicit Particle-in-Cell schemes, and fluid-kinetic coupling. We show an application of these techniques to study particle acceleration and heating in asymmetric magnetic reconnection in the Ganymede magnetosphere., Comment: Preprint of accepted chapter in the AGU book "Magnetospheres in the solar system"

Neutral hydrogen has been shown to greatly impact the plasma flow in the heliopshere and the location of the heliospheric boundaries. We present the results of the Solar-wind with Hydrogen Ion Exchange and Large-scale Dynamics (SHIELD) model, a new, self-consistent, kinetic-MHD model of the outer heliosphere within the Space Weather Modeling Framework. The charge-exchange mean free path is on order of the size of the heliosphere; therefore, the neutral atoms cannot be described as a fluid. The SHIELD model couples the MHD solution for a single plasma fluid to the kinetic solution from for neutral hydrogen atoms streaming through the system. The kinetic code is based on the Adaptive Mesh Particle Simulator (AMPS), a Monte Carlo method for solving the Boltzmann equation. The SHIELD model accurately predicts the increased filtration of interstellar neutrals into the heliosphere. In order to verify the correct implementation within the model, we compare the results of the SHIELD model to other, well-established kinetic-MHD models. The SHIELD model matches the neutral hydrogen solution of these studies as well as the shift in all heliospheric boundaries closer to the Sun in comparison the the multi-fluid treatment of the neutral hydrogen atoms. Overall the SHIELD model shows excellent agreement to these models and is a significant improvement to the fluid treatment of interstellar hydrogen., Comment: 21 pages, 6 figures. ApJS submitted

We use the MHD with embedded particle-in-cell model (MHD-EPIC) to study the Geospace Environment Modeling (GEM) dayside kinetic processes challenge event at 01:50-03:00 UT on 2015-11-18, when the magnetosphere was driven by a steady southward IMF. In the MHD-EPIC simulation, the dayside magnetopause is covered by a PIC code so that the dayside reconnection is properly handled. We compare the magnetic fields and the plasma profiles of the magnetopause crossing with the MMS3 spacecraft observations. Most variables match the observations well in the magnetosphere, in the magnetosheath, and also during the current sheet crossing. The MHD-EPIC simulation produces flux ropes, and we demonstrate that some magnetic field and plasma features observed by the MMS3 spacecraft can be reproduced by a flux rope crossing event. We use an algorithm to automatically identify the reconnection sites from the simulation results. It turns out that there are usually multiple X-lines at the magnetopause. By tracing the locations of the X-lines, we find the typical moving speed of the X-line endpoints is about 70~km/s, which is higher than but still comparable with the ground-based observations.

A deep learning network, Long-Short Term Memory (LSTM) network, is used in this work to predict whether the maximum flare class an active region (AR) will produce in the next 24 hours is class $\Gamma$. We considered $\Gamma$ are $\ge M$, $\ge C$ and any flare class. The essence of using LSTM, which is a recurrent neural network, is its capability to capture temporal information of the data samples. The input features are time sequences of 20 magnetic parameters from SHARPs - Space-weather HMI Active Region Patches. We analyzed active regions from June 2010 to Dec 2018, using the Geostationary Operational Environmental Satellite (GOES) X-ray flare catalogs and label the data samples with identified ARs in the GOES X-ray flare catalogs. Our results (i) shows consistent skill scores with recently published results using LSTMs and better than the previous work using single time input (eg. DeFN) (ii) The skill scores from the model show essential differences when different years of data was chosen for training and testing.

Simulation of plasmas in electromagnetic fields requires numerical solution of a kinetic equation that describes the time evolution of the particle distribution function. In this paper we propose a finite volume scheme based on integral relation for Poisson brackets to solve the Liouville equation, the most fundamental kinetic equation. The proposed scheme conserves the number of particles, maintains the total-variation-diminishing (TVD) property, and provides high-quality numerical results. Other types of kinetic equations may be also formulated in terms of Poisson brackets and solved with the proposed method including the transport equations describing the acceleration and propagation of Solar Energetic Particles (SEPs), which is of practical importance, since the high energy SEPs produce radiation hazards. The proposed scheme is demonstrated to be accurate and efficient, which makes it applicable to global simulation systems analyzing space weather., Comment: 50 pages, 9 figures

The Rosetta Orbiter Spectrometer for Ion and Neutral Analysis (ROSINA) suite of instruments operated throughout the over two years of the Rosetta mission operations in the vicinity of comet 67P/Churyumov-Gerasimenko. It measured gas densities and composition throughout the comet's atmosphere, or coma. Here we present two-years' worth of measurements of the relative densities of the four major volatile species in the coma of the comet, H2O. CO2, CO and O2, by one of the ROSINA sub-systems called the Double Focusing Mass Spectrometer (DFMS). The absolute total gas densities were provided by the Comet Pressure Sensor (COPS), another ROSINA sub-system. DFMS is a very high mass resolution and high sensitivity mass spectrometer able to resolve at a tiny fraction of an atomic mass unit. We have analyzed the combined DFMS and COPS measurements using an inversion scheme based on spherical harmonics that solves for the distribution of potential surface activity of each species as the comet rotates, changing solar illumination, over short intervals and as the comet changes distance from the sun and orientation of its spin axis over long time intervals. We also use the surface boundary conditions derived from the inversion scheme to simulate the whole coma with our fully kinetic Direct Simulation Monte Carlo model and calculate the production rates of the four major species throughout the mission. We compare the derived production rates with revised remote sensing observations by the Visible and Infrared Thermal Imaging Spectrometer (VIRTIS) as well as with published observations from the Microwave Instrument for the Rosetta Orbiter (MIRO). Finally we use the variation of the surface production of the major species to calculate the total mass loss over the mission and, for different estimates of the dust/gas ratio, calculate the variation of surface loss over the nucleus., Comment: 144 pages, 9 figures, 8 tables, 1 supplemental table

The time evolution of linear fields of spin $s = \pm 1$ and $s = \pm 2$ on Kerr black hole spacetimes are investigated by solving the homogeneous Teukolsky equation numerically. The applied numerical setup is based on a combination of conformal compactification and the hyperbolic initial value problem. The evolved basic variables are expanded in terms of spin-weighted spherical harmonics which allows us to evaluate all the angular derivatives analytically, whereas the evolution of the expansion coefficients, in the time-radial section, is determined by applying the method of lines implemented in a fourth order accurate finite differencing stencil. Concerning the initialization, in all of our investigations single mode excitations---either static or purely dynamical type initial data---are applied. Within this setup the late time tail behavior is investigated. Due to the applied conformal compactification the asymptotic decay rates are determined at three characteristic locations---in the domain of outer communication, at the event horizon and at future null infinity---simultaneously. Recently introduced new type of `energy' and `angular momentum' balance relations are also applied in order to demonstrate the feasibility and robustness of the developed numerical schema, and also to verify the proper implementation of the underlying mathematical model., Comment: 38 pages, 5 figures, typos corrected

The relations between two construction methods (called multiplier and embedding methods) for conserved currents of general systems of ordinary or partial differential equations (DEs) are investigated. Recent studies indicate that the multiplier method, which is a generalization of Noether's theorem, has significant advantages in comparison with the embedding method, which uses adjoint-symmetry/symmetry pairs and is based on embedding the original system of DEs in a larger one that follows from a Lagrangian. In particular, the multiplier method can generally give a wider range of conserved currents than the embedding method. In this paper simple extended forms of general systems of DEs, obtained by treating parameters present in the equations or introduced into them as dependent variables, are studied. A variant of a fundamental result on the connection between the embedding method and the action of symmetries on conserved currents that correspond to a multiplier is derived for the extended systems of DEs. Using this connection and by considering particular extensions that endow the extended DEs with scaling symmetry, it is shown that the embedding method becomes significantly stronger if it is also allowed to be applied to the extended forms of the original DEs. It is also shown that up to equivalence the multipliers of an extended DE system contain the parametric multipliers of the original system together with the derivatives of the corresponding conserved currents with respect to the parameters., Comment: 21 pages, changes in the presentation, minor corrections, 3 references added

MESSENGER has observed a lot of dawn-dusk asymmetries in Mercury's magnetotail, such as the asymmetries of the cross-tail current sheet thickness and the occurrence of flux ropes, dipolarization events and energetic electron injections. In order to obtain a global pictures of Mercury's magnetotail dynamics and the relationship between these asymmetries, we perform global simulations with the magnetohydrodynamics with embedded particle-in-cell (MHD-EPIC) model, where Mercury's magnetotail region is covered by a PIC code. Our simulations show that the dawnside current sheet is thicker, the plasma density is larger, and the electron pressure is higher than the duskside. Under a strong IMF driver, the simulated reconnection sites prefer the dawnside. We also found the dipolarization events and the planetward electron jets are moving dawnward while they are moving towards the planet, so that almost all dipolarization events and high-speed plasma flows concentrate in the dawn sector. The simulation results are consistent with MESSENGER observations.

We present several methods towards construction of precursors, which show great promise towards early predictions, of solar flare events in this paper. A data pre-processing pipeline is built to extract useful data from multiple sources, Geostationary Operational Environmental Satellites (GOES) and Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI), to prepare inputs for machine learning algorithms. Two classification models are presented: classification of flares from quiet times for active regions and classification of strong versus weak flare events. We adopt deep learning algorithms to capture both the spatial and temporal information from HMI magnetogram data. Effective feature extraction and feature selection with raw magnetogram data using deep learning and statistical algorithms enable us to train classification models to achieve almost as good performance as using active region parameters provided in HMI/Space-Weather HMI-Active Region Patch (SHARP) data files. Case studies show a significant increase in the prediction score around 20 hours before strong solar flare events.

We present a six-moment multi-fluid model, which solves the governing equations for both ions and electrons, with pressure anisotropy along and perpendicular to the magnetic field direction, as well as the complete set of Maxwell equations. This set of equations includes the Hall effect, different temperatures for different species and pressure anisotropy. It is more comprehensive than the five-moment equations with isotropic pressures and significantly less expensive than the ten-moment equations with a full pressure tensors. Similarly to the five- and ten-moment equations, the wave speeds are naturally limited by the speed of light, which eliminates the issue of unlimited whistler wave speeds present in Hall magnetohydrodynamics (MHD). It is also possible to simulate multiple negatively charged fluids, which cannot be done in MHD models. The six-moment model is a reasonable description of the plasma outside magnetic reconnection regions and therefore well-suited to be coupled with an embedded particle-in-cell model that covers the reconnection region. Our numerical implementation uses a point-implicit scheme for the stiff source terms, and we use a second-order accurate Rusanov-type scheme with carefully selected wave speeds. For the plasma variables and the magnetic field the maximum wave speed is based on the fast magnetosonic speed of MHD with anisotropic pressures that we derive. For the electric field related variables the speed of light is used. The divergence of the magnetic field and Gauss's law are controlled with a hyperbolic-parabolic scheme. We present a number of numerical tests to demonstrate that this numerical model is robust without being excessively diffusive., Comment: 38 pages, 12 figurs

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