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The properties of the solar wind measured in-situ in the heliosphere are largely controlled by energy deposition in the solar. Previous studies have shown that long duration and large scale magnetic structures show an inverse relation between the solar wind velocity measured in situ near 1 au and the expansion factor of the magnetic flux tubes in the solar atmosphere. We exploit Solar Orbiter data in conjunction with the Potential Field Source Surface (PFSS) coronal model, and the solar wind trajectory to evaluate the flux expansion factor - speed relation at the solar "source surface" at rss. We find a statistically weak anti-correlation between the in-situ bulk velocity and the coronal expansion factor, for about 1.5 years of solar data. Classification of the data by source latitude reveals different levels of anticorrelation. We show the existence of fast solar wind that originates in strong magnetic field regions at low latitudes and undergoes large expansion factor. We provide evidence that such winds become supersonic during the super radial expansion (below rss), and are theoretically governed by a positive correlation v-f. We find that faster winds on average have a flux tube expansion at a larger radius than slower winds. An anticorrelation between solar wind speed and expansion factor is present for solar winds originating in high latitude structures in solar minimum activity, typically associated with coronal hole-like structures, but this cannot be generalized to lower latitude sources. Therefore, the value of the expansion factor alone cannot be used to predict the solar wind speed. Other parameters, such as the height at which the expansion gradient is the strongest must also be taken into account., Comment: 18 pages, 10 figures, 1 table

The present study provides statistical information on the coronal magnetic field and intensity properties of small-scale bright and faint loops in the quiet Sun. We aim to quantitatively investigate the morphological and topological properties of the coronal magnetic field in bright and faint small-scale loops, with the former known as coronal bright points (CBPs). We analyse 126 small-scale loops using quasi-temporal imaging and line-of-sight magnetic field observations. We employ a recently developed automatic tool that uses a linear magneto-hydro-static model to compute the magnetic field in the solar atmosphere and automatically match individual magnetic field lines with small-scale loops. For most of the loops, we automatically obtain an excellent agreement of the magnetic field lines from the LMHS model and the loops seen in AIA 193 A. One stand-out result is that the magnetic field is non-potential. We obtain the typical ranges of loop heights, lengths, intensities, mean magnetic field strength along the loops and at loop tops, and magnetic field strength at loop footpoints. We find that loops below the classic chromospheric height of 1.5 Mm are flatter suggesting that non-magnetic forces (one of which is the plasma pressure) play an important role below this height. We find a strong correlation (Pearson coefficient of 0.9) between loop heights and lengths. The average intensity along the loops correlates stronger with the average magnetic field along the loops than with the field strength at loop tops. The latter correlation indicates that the energy release in the loops is more likely linked to the average magnetic field along the loops than the field strength on the loop tops. In other words, the energy is probably released all along the loops, but not just at the loop top. This result is consistent with the recent benchmarking radiative 3D MHD model of N\'obrega-Siberio etal., Comment: Accepted for publication in A&A

This work introduces the Supervised Expectation-Maximization Framework (SEMF), a versatile and model-agnostic approach for generating prediction intervals in datasets with complete or missing data. SEMF extends the Expectation-Maximization algorithm, traditionally used in unsupervised learning, to a supervised context, leveraging latent variable modeling for uncertainty estimation. Extensive empirical evaluations across 11 tabular datasets show that SEMF often achieves narrower normalized prediction intervals and higher coverage rates than traditional quantile regression methods. Furthermore, SEMF can be integrated with machine learning models like gradient-boosted trees and neural networks, highlighting its practical applicability. The results indicate that SEMF enhances uncertainty quantification, particularly in scenarios with complete data.

Coronal Mass Ejections (CMEs) are the main drivers of the disturbances in interplanetary space. Understanding the CME interior magnetic structure is crucial for advancing space weather studies. Assessing the capabilities of a numerical heliospheric model is crucial, as understanding the nature and extent of its limitations can be used for improving the model and the space weather predictions based on it. The present paper aims to test the capabilities of the recently developed heliospheric model Icarus and the linear force-free spheromak model that has been implemented in it. To validate the Icarus space weather modeling tool, two CME events were selected that were observed by two spacecraft located near Mercury and Earth, respectively. This enables testing the heliospheric model computed with Icarus at two distant locations. The source regions for the CMEs were identified, and the CME parameters were determined and later optimized. Different adaptive mesh refinement levels were applied in the simulations to assess its performance by comparing the simulation results to in-situ measurements. The first CME event erupted on SOL2013-07-09T15:24. The modeled time series were in good agreement with the observations both at MESSENGER and ACE. The second CME event started on SOL2014-02-16T10:24 and was more complicated, as three CME interactions occurred in this event. It was impossible to recover the observed profiles without modeling the other two CMEs that were observed, one before the main CME and one afterward. For both CME studies, AMR level 3 was sufficient to reconstruct small-scale features near Mercury, while at Earth, AMR level 4 was necessary due to the radially stretched grid that was used., Comment: 16 pages, 17 figures

Active regions (ARs) appear in the solar atmosphere as a consequence of the emergence of magnetic flux-ropes (FR). In this study, we use Bayesian methods to analyze line-of-sight magnetograms of emerging ARs. We employ a FR model consisting of a half-torus field structure based on eight parameters. The goal is to derive constrained physical parameters of the originating FR which are consistent with the observations. Specifically, we aim to obtain a precise estimation of the AR tilt angle and magnetic twist at different stages of the emergence process. To achieve this, we propose four temporal methods that correlate the field parameter evolutions with a single coherent FR. These methods differ from each other in the size of the explored parameter space. We test the methods on four bipolar ARs observed with the Michelson Doppler Imager on board the Solar and Heliospheric Observatory. We find that tilt angles are typically consistent between the temporal methods, improving previous estimations at all stages of the emergence. The twist sign derived from the temporal methods is consistent with previous estimations. The standard errors of all the methods used are similar, indicating that they model the observations equally well. These results indicate that the proposed methods can be used to obtain global magnetic parameters of ARs during their early evolution. The derived parameters contribute to a better understanding of the formation of FRs, and the role of ARs in the magnetic recycling process along the solar cycle.

Causal asymmetry is based on the principle that an event is a cause only if its absence would not have been a cause. From there, uncovering causal effects becomes a matter of comparing a well-defined score in both directions. Motivated by studying causal effects at extreme levels of a multivariate random vector, we propose to construct a model-agnostic causal score relying solely on the assumption of the existence of a max-domain of attraction. Based on a representation of a Generalized Pareto random vector, we construct the causal score as the Wasserstein distance between the margins and a well-specified random variable. The proposed methodology is illustrated on a hydrologically simulated dataset of different characteristics of catchments in Switzerland: discharge, precipitation, and snowmelt.

Within the coronae of stars, abundances of those elements with low first ionization potential (FIP) often differ from their photospheric values. The coronae of the Sun and solar-type stars mostly show enhancements of low-FIP elements (the FIP effect) while more active stars such as M dwarfs have coronae generally characterized by the inverse-FIP (I-FIP) effect. Highly localized regions of I-FIP effect solar plasma have been observed by Hinode/EIS in a number of highly complex active regions, usually around strong light bridges of the umbrae of coalescing/merging sunspots. These observations can be interpreted in the context of the ponderomotive force fractionation model which predicts that plasma with I-FIP effect composition is created by the refraction of waves coming from below the plasma fractionation region in the chromosphere. A plausible source of these waves is thought to be reconnection in the (high-plasma \b{eta}) subchromospheric magnetic field. In this study, we use the 3D visualization technique of Chintzoglou & Zhang (2013) combined with observations of localized I-FIP effect in the corona of AR 11504 to identify potential sites of such reconnection and its possible consequences in the solar atmosphere. We found subtle signatures of episodic heating and reconnection outflows in the expected places, in between magnetic flux tubes forming a light bridge, within the photosphere of the active region. Furthermore, on either side of the light bridge, we observed small antiparallel horizontal magnetic field components supporting the possibility of reconnection occuring where we observe I-FIP plasma. When taken together with the I-FIP effect observations, these subtle signatures provide a compelling case for indirect observational evidence of reconnection below the fractionation layer of the chromosphere, however, direct evidence remains elusive., Comment: Accepted ApJ

In this work, we summarize the state-of-the-art methods in causal inference for extremes. In a non-exhaustive way, we start by describing an extremal approach to quantile treatment effect where the treatment has an impact on the tail of the outcome. Then, we delve into two primary causal structures for extremes, offering in-depth insights into their identifiability. Additionally, we discuss causal structure learning in relation to these two models as well as in a model-agnostic framework. To illustrate the practicality of the approaches, we apply and compare these different methods using a Seine network dataset. This work concludes with a summary and outlines potential directions for future research.

Configurations where two spacecraft, such as Parker Solar Probe (PSP) and Solar Orbiter (SolO), are radially aligned provide opportunities to study the evolution of a single solar wind parcel during so called plasma line-ups. The most critical part of such studies is arguably the identification of what can be considered a same plasma crossing both spacecraft. We present here a method that allowed us to find what we believe to be the same plasma parcel passing through PSP ($\sim 0.075$ au) and SolO ($\sim 0.9$ au) after their radial alignment the 29/04/2021. We started by modeling the plasma propagation in order to get a first estimation of the plasma line-up intervals. The identification of the same density structure (with a crossing duration $\sim 1.5$ h) passing through the two spacecraft allows to precise and confirm this estimation. Our main finding is how stable the density structure is, remaining well recognizable from PSP to SolO despite its $\sim 137$ hours journey in the inner heliosphere. We moreover found that the studied slow solar wind plasma parcel undergone a significant acceleration (from $\sim 200$ to $\sim 300$ km/s) during its propagation., Comment: 12 pages, 9 figures, submitted to Astronomy and Astrophysics (A&A) - Revised version after referee report

Active regions (ARs) appear in the solar atmosphere as a consequence of the emergence of magnetic flux ropes (FRs). Due to the presence of twist, the photospheric line-of-sight (LOS) magnetograms of emerging ARs show an elongation of the polarities known as magnetic tongues. These tongues can affect the estimation of tilt angles during their emergence phase. In this work, we propose a Bayesian method to model LOS magnetograms of emerging ARs using a half-torus twisted FR model. We apply this model to 21 emerging ARs observed during Solar Cycle 23. We find that the Bayesian method corrects the tilt when compared to other methods, removing the spurious rotation of the polarities produced by the retraction of the tongues during the emergence. We find a variation in Joy's law with the stage of the AR emergence and the method used for its estimation.

Controlling ultrafast material transformations with atomic precision is essential for future nanotechnology. Pulsed laser annealing (LA), inducing extremely rapid and localized phase transitions, is a powerful way to achieve this, but it requires careful optimization together with the appropriate system design. We present a multiscale LA computational framework able to simulate atom-by-atom the highly out-of-equilibrium kinetics of a material as it interacts with the laser, including effects of structural disorder. By seamlessly coupling a macroscale continuum solver to a nanoscale super-lattice Kinetic Monte Carlo code, this method overcomes the limits of state-of-the-art continuum-based tools. We exploit it to investigate nontrivial changes in composition, morphology and quality of laser-annealed SiGe alloys. Validations against experiments and phase-field simulations, as well as advanced applications to strained, defected, nanostructured and confined SiGe are presented, highlighting the importance of a multiscale atomistic-continuum approach. Current applicability and potential generalization routes are finally discussed.

We consider the problem of learning a set of direct causes of a target variable from an observational joint distribution. Learning directed acyclic graphs (DAGs) that represent the causal structure is a fundamental problem in science. Several results are known when the full DAG is identifiable from the distribution, such as assuming a nonlinear Gaussian data-generating process. Here, we are only interested in identifying the direct causes of one target variable (local causal structure), not the full DAG. This allows us to relax the identifiability assumptions and develop possibly faster and more robust algorithms. In contrast to the Invariance Causal Prediction framework, we only assume that we observe one environment without any interventions. We discuss different assumptions for the data-generating process of the target variable under which the set of direct causes is identifiable from the distribution. While doing so, we put essentially no assumptions on the variables other than the target variable. In addition to the novel identifiability results, we provide two practical algorithms for estimating the direct causes from a finite random sample and demonstrate their effectiveness on several benchmark and real datasets.

This paper explores Neural Operators to predict turbulent flows, focusing on the Fourier Neural Operator (FNO) model. It aims to develop reduced-order/surrogate models for turbulent flow simulations using Machine Learning. Different model configurations are analyzed, with U-NET structures (UNO and U-FNET) performing better than the standard FNO in accuracy and stability. U-FNET excels in predicting turbulence at higher Reynolds numbers. Regularization terms, like gradient and stability losses, are essential for stable and accurate predictions. The study emphasizes the need for improved metrics for deep learning models in fluid flow prediction. Further research should focus on models handling complex flows and practical benchmarking metrics., Comment: ETMM14 proceedings

We study intermittent coherent structures in solar wind magnetic turbulence from MHD to kinetic plasma scales using Parker Solar Probe data during its first perihelion (at 0.17 au), when the satellite was in the Alfv\'enic slow wind of 340 km/s. The coherent structures are energetic events localized in time and covering wide range of scales. We detect them using Morlet wavelets. For the first time, we apply a multi-scale analyses in physical space to study these structures. At MHD scales within the inertial range, times scales $\tau \in (1, 10^{2} )$ s, we find (i) current sheets including switchback boundaries and (ii) Alfv\'en vortices. Within these events, there are embedded structures at smaller scales: typically Alfv\'en vortices at ion scales, $\tau \in (0.08, 1)$ s, and a compressible vortices at sub-ion scales, $\tau \in (8,80)$ ms. The number of coherent structures grows toward smaller scales: we observe about $\sim 200$ events during 5 h time interval at MHD scales, $\sim 10^{3}$ events ai ion scales and $\sim 10^{4}$ events at sub-ion scales. In general, there are multiple structures of ion and sub-ion scales embedded within one MHD structure. There are also examples of ion and sub-ion scales structures outside of MHD structures. To quantify the relative importance of different type of structures, we do a statistical comparison of the observed structures with the expectations of models of the current sheets and vortices. This comparison is based on amplitude anisotropy of magnetic fluctuations within the structures. The results show the dominance of Alfv\'en vortices at all scales in contrast to the widespread view of dominance of current sheets. This means that Alfv\'en vortices are important building blocs of solar wind turbulence., Comment: Revised version of the article, accepted for publication in Astrophysical Journal, 30 pages, 15 figures

The Solar Orbiter mission completed its first remote-sensing observation windows in the spring of 2022. On 2/4/2022, an M-class flare followed by a filament eruption was seen both by the instruments on board the mission and from several observatories in Earth's orbit. The complexity of the observed features is compared with the predictions given by the standard flare model in 3D. We use the observations from a multi-view dataset, which includes EUV imaging to spectroscopy and magnetic field measurements. These data come from IRIS, SDO, Hinode, as well as several instruments on Solar Orbiter. Information given by SDO/HMI and Solar Orbiter PHI/HRT shows that a parasitic polarity emerging underneath the filament is responsible for bringing the flux rope to an unstable state. As the flux rope erupts, Hinode/EIS captures blue-shifted emission in the transition region and coronal lines in the northern leg of the flux rope prior to the flare peak. Solar Orbiter SPICE captures the whole region, complementing the Doppler diagnostics of the filament eruption. Analyses of the formation and evolution of a complex set of flare ribbons and loops show that the parasitic emerging bipole plays an important role in the evolution of the flaring region. While the analysed data are overall consistent with the standard flare model, the present particular magnetic configuration shows that surrounding magnetic activity such as nearby emergence needs to be taken into account to fully understand the processes at work. This filament eruption is the first to be covered from different angles by spectroscopic instruments, and provides an unprecedented diagnostic of the multi-thermal structures present before and during the flare. This dataset of an eruptive event showcases the capabilities of coordinated observations with the Solar Orbiter mission., Comment: Accepted for publication in the Astronomy & Astrophysics special edition "Solar Orbiter First Results (Nominal Mission Phase)" (23/05/2023)

The propagation of Interplanetary Coronal Mass Ejections (ICMEs) in the heliosphere is influenced by many physical phenomena, related to the internal structure of the ICME and its interaction with the ambient solar wind and magnetic field. As the solar magnetic field is modulated by the 11-year dynamo cycle, our goal is to perform a theoretical exploratory study to assess the difference of propagation of an ICME in typical minimum and maximum activity backgrounds. We define a median representative CME at 0.1~au, using both observations and numerical simulations, and describe it using a spheromak model. We use the heliospheric propagator European Heliospheric FORecasting Information Asset (EUHFORIA) to inject the same ICME in two different background wind environments. We then study how the environment and the internal CME structure impact the propagation of the ICME towards Earth, by comparison with an unmagnetized CME. At minimum of activity, the structure of the heliosphere around the ecliptic causes the ICME to slow down, creating a delay with the polar parts of the ejecta. This delay is more important if the ICME is faster. At maximum of activity, a southern coronal hole causes a northward deflection. For these cases, we always find that the ICME at maximum of activity arrives first, while the ICME at minimum of activity is actually more geo-effective. The helicity sign of the ICME is also a crucial parameter but at minimum of activity only, since it affects the magnetic profile and the arrival time of up to 8 hours., Comment: 25 pages, 16 figures, accepted in ApJ

We study the tail asymptotics of two functionals (the maximum and the sum of the marks) of a generic cluster in two sub-models of the marked Poisson cluster process, namely the renewal Poisson cluster process and the Hawkes process. Under the hypothesis that the governing components of the processes are regularly varying, we extend results due to [18] and [5] notably, relying on Karamata's Tauberian Theorem to do so. We use these asymptotics to derive precise large deviation results in the fashion of [30] for the above-mentioned processes.

The Slow Solar Wind Connection Solar Orbiter Observing Plan (Slow Wind SOOP) was developed to utilise the extensive suite of remote sensing and in situ instruments on board the ESA/NASA Solar Orbiter mission to answer significant outstanding questions regarding the origin and formation of the slow solar wind. The Slow Wind SOOP was designed to link remote sensing and in situ measurements of slow wind originating at open-closed field boundaries. The SOOP ran just prior to Solar Orbiter's first close perihelion passage during two remote sensing windows (RSW1 and RSW2) between 2022 March 3-6 and 2022 March 17-22, while Solar Orbiter was at a heliocentric distance of 0.55-0.51 and 0.38-0.34 au from the Sun, respectively. Coordinated observation campaigns were also conducted by Hinode and IRIS. The magnetic connectivity tool was used, along with low latency in situ data, and full-disk remote sensing observations, to guide the target pointing of Solar Orbiter. Solar Orbiter targeted an active region complex during RSW1, the boundary of a coronal hole, and the periphery of a decayed active region during RSW2. Post-observation analysis using the magnetic connectivity tool along with in situ measurements from MAG and SWA/PAS, show that slow solar wind, with velocities between 210 and 600 km/s, arrived at the spacecraft originating from two out of the three of the target regions. The Slow Wind SOOP, despite presenting many challenges, was very successful, providing a blueprint for planning future observation campaigns that rely on the magnetic connectivity of Solar Orbiter., Comment: 24 pages, 10 figures

In situ observations of interplanetary (IP) coronal mass ejections (ICMEs) and IP shocks are important to study as they are the main components of the solar activity. Hundreds of IP shocks have been detected by various space missions at different times and heliocentric distances. Some of these are followed by clearly identified drivers, while some others are not. In this study, we carry out a statistical analysis of the distributions of plasma and magnetic parameters of the IP shocks recorded at various distances to the Sun. We classify the shocks according to the heliocentric distance, namely from 0.29 to 0.99 AU (Helios-1/2); near 1 AU (Wind, ACE and STEREO-A/B); and from 1.35 to 5.4 AU (Ulysses). We also differentiate the IP shocks into two populations, those with a detected ICME and those without one. We find, as expected, that there are no significant differences in the results from spacecraft positioned at 1 AU. Moreover, the distributions of shock parameters, as well as the shock normal have no significant variations with the heliocentric distance. Additionally, we investigate how the number of shocks associated to stream-interaction regions (SIRs) increases with distance in proportion of ICME/shocks. From 1 to 5 AU, SIRs/ shock occurrence increases slightly from 21% to 34%, in contrast ICME/shocks occurrence decreases from 47% to 17%. We find also indication of an asymmetry induced by the Parker spiral for SIRs and none for ICMEs., Comment: 29 Pages, 11 Figures. Accepted for Publication in Solar Physics

Field-Programmable Gate Arrays (FPGAs) are more energy efficient and cost effective than CPUs for a wide variety of datacenter applications. Yet, for latency-sensitive and bursty workloads, this advantage can be difficult to harness due to high FPGA spin-up costs. We propose that a hybrid FPGA and CPU computing framework can harness the energy efficiency benefits of FPGAs for such workloads at reasonable cost. Our key insight is to use FPGAs for stable-state workload and CPUs for short-term workload bursts. Using this insight, we design Spork, a lightweight hybrid scheduler that can realize these energy efficiency and cost benefits in practice. Depending on the desired objective, Spork can trade off energy efficiency for cost reduction and vice versa. It is parameterized with key differences between FPGAs and CPUs in terms of power draw, performance, cost, and spin-up latency. We vary this parameter space and analyze various application and worker configurations on production and synthetic traces. Our evaluation of cloud workloads shows that energy-optimized Spork is not only more energy efficient but it is also cheaper than homogeneous platforms--for short application requests with tight deadlines, it is 1.53x more energy efficient and 2.14x cheaper than using only FPGAs. Relative to an idealized version of an existing cost-optimized hybrid scheduler, energy-optimized Spork provides 1.2-2.4x higher energy efficiency at comparable cost, while cost-optimized Spork provides 1.1-2x higher energy efficiency at 1.06-1.2x lower cost., Comment: 13 pages

Ultraviolet nanosecond laser annealing (LA) is a powerful tool where strongly confined heating and melting are desirable. In semiconductor technologies the importance of LA increases with the increasing complexity of the proposed integration schemes. Optimizing the LA process along with the experimental design is challenging, especially when complex 3D nanostructured systems with various shapes and phases are involved. Within this context, reliable simulations of laser melting are required for optimizing the process parameters while reducing the number of experimental tests. This gives rise to a virtual Design of Experiments (DoE). $Si_{1-x}Ge_{x}$ alloys are nowadays used for their compatibility with silicon devices enabling to engineer properties such as strain, carrier mobilities and bandgap. In this work, the laser melting process of relaxed and strained $Si_{1-x}Ge_{x}$ is simulated with a finite element method / phase field approach. Particularly, we calibrated the dielectric functions of the alloy for its crystalline and liquid phase using experimental data. We highlighted the importance of reproducing the exact reflectivity of the interface between air and the material in its different aggregation states, to correctly mimic the process. We indirectly discovered intriguing features on the optical behavior of melt silicon-germanium.

Causal discovery from observational data typically requires strong assumptions about the data-generating process. Previous research has established the identifiability of causal graphs under various models, including linear non-Gaussian, post-nonlinear, and location-scale models. However, these models may have limited applicability in real-world situations that involve a mixture of discrete and continuous variables or where the cause affects the variance or tail behavior of the effect. In this study, we introduce a new class of models, called Conditionally Parametric Causal Models (CPCM), which assume that the distribution of the effect, given the cause, belongs to well-known families such as Gaussian, Poisson, Gamma, or heavy-tailed Pareto distributions. These models are adaptable to a wide range of practical situations where the cause can influence the variance or tail behavior of the effect. We demonstrate the identifiability of CPCM by leveraging the concept of sufficient statistics. Furthermore, we propose an algorithm for estimating the causal structure from random samples drawn from CPCM. We evaluate the empirical properties of our methodology on various datasets, demonstrating state-of-the-art performance across multiple benchmarks.

From 2022 March 18-21, active region (AR) 12967 was tracked simultaneously by Solar Orbiter (SO) at 0.35 au and Hinode/EIS at Earth. During this period, strong blue-shifted plasma upflows were observed along a thin, dark corridor of open field originating at the AR's leading polarity and continuing towards the southern extension of the northern polar coronal hole. A potential field source surface (PFSS) model shows large lateral expansion of the open magnetic field along the corridor. Squashing factor Q-maps of the large scale topology further confirm super-radial expansion in support of the S-Web theory for the slow wind. The thin corridor of upflows is identified as the source region of a slow solar wind stream characterised by approx. 300 km s-1 velocities, low proton temperatures of approx. 5 eV, extremely high density over 100 cm-3, and a short interval of moderate Alfvenicity accompanied by switchback events. When connectivity changes from the corridor to the eastern side of the AR, the in situ plasma parameters of the slow wind indicate a distinctly different source region. These observations provide strong evidence that the narrow open field corridors, forming part of the S-Web, produce extreme properties in their associated solar wind streams., Comment: Accepted ApJ

Determining the causes of extreme events is a fundamental question in many scientific fields. An important aspect when modelling multivariate extremes is the tail dependence. In application, the extreme dependence structure may significantly depend on covariates. As for the general case of modelling including covariates, only some of the covariates are causal. In this paper, we propose a methodology to discover the causal covariates explaining the tail dependence structure between two variables. The proposed methodology for discovering causal variables is based on comparing observations from different environments or perturbations. It is a desired methodology for predicting extremal behaviour in a new, unobserved environment. The methodology is applied to a dataset of $\text{NO}_2$ concentration in the UK. Extreme $\text{NO}_2$ levels can cause severe health problems, and understanding the behaviour of concurrent severe levels is an important question. We focus on revealing causal predictors for the dependence between extreme $\text{NO}_2$ observations at different sites.

Magnetic clouds (MCs) are observed insitu by spacecraft. The rotation of their magnetic field is typically interpreted as the crossing of a twisted magnetic flux tube, or flux rope, which was launched from the solar corona. The detailed magnetic measurements across MCs permit us to infer the flux rope characteristics. Still, the precise spatial distribution of the magnetic twist is challenging, and thus is debated. In order to improve the robustness of the results, we performed a superposed epoch analysis (SEA) of a set of well observed MCs at 1 au. While previous work was done using the MC central time, we here used the result of a fitted flux rope model to select the time of the closest approach to the flux rope axis. This implies a precise separation of the in- and outbound regions to coherently phase the observed signals. We also searched for and minimised the possible biases such as magnetic asymmetry and a finite impact parameter. We applied the SEA to derive the median profiles both for the flux rope remaining when crossed by the spacecraft and to recover the one present before erosion. In particular, the median azimuthal B component is nearly a linear function of the radius. More generally, the results confirm our previous results realised without such a deep analysis. The twist profile is nearly uniform in the flux rope core, with a steep increase at the border of the flux rope and with similar profiles in the in- and outbound regions. The main difference with our previous study is a larger twist by $\sim 20\%$., Comment: 11 pages, 6 figures

Germanium (Ge) is increasingly used as a substrate for high-performance optoelectronic, photovoltaic, and electronic devices. These devices are usually grown on thick and rigid Ge substrates manufactured by classical wafering techniques. Nanomembranes (NMs) provide an alternative to this approach while offering wafer-scale lateral dimensions, weight reduction, limitation of waste, and cost effectiveness. Herein, we introduce the Porous germanium Efficient Epitaxial LayEr Release (PEELER) process, which consists of the fabrication of wafer-scale detachable monocrystalline Ge NMs on porous Ge (PGe) and substrate reuse. We demonstrate monocrystalline Ge NMs with surface roughness below 1 nm on top of nanoengineered void layer enabling layer detachment. Furthermore, these Ge NMs exhibit compatibility with the growth of III-V materials. High-resolution transmission electron microscopy (HRTEM) characterization shows Ge NMs crystallinity and high-resolution X-ray diffraction (HRXRD) reciprocal space mapping endorses high-quality GaAs layers. Finally, we demonstrate the chemical reconditioning process of the Ge substrate, allowing its reuse, to produce multiple free-standing NMs from a single parent wafer. The PEELER process significantly reduces the consumption of Ge during the fabrication process which paves the way for a new generation of low-cost flexible optoelectronics devices., Comment: 17 pages and 6 figures along with 3 figures in supporting information

Context. Active regions (ARs) appear in the solar atmosphere as a consequence of the emergence of magnetic flux tubes. The presence of elongated magnetic polarities in line-of-sight (LOS) magnetograms indicates the existence of twist in the flux tubes forming them. These polarity elongations, called magnetic tongues, bias the measurement of AR characteristics obtained during their emergence phase (e.g. their tilt angle and magnetic flux, among others). In particular, obtaining a good estimation of the tilt angle evolution plays a key role in constraining flux-transport dynamo models. Aims. In this work we aim to estimate the intrinsic properties of the twisted flux tubes, or flux ropes, that form ARs by quantitatively comparing observed LOS magnetograms with synthetic ones derived from a toroidal magnetic flux tube model. Methods. For this reason, we develop a Bayesian inference method to obtain the statistical distributions of the inferred model parameters. As an example, we apply the method to NOAA AR 10268. Next, we test the results using a synthetic-AR generator to quantify the effect of small scale perturbations over the inferred parameter distributions. Results. We conclude that this method can significantly remove the effects of magnetic tongues on the derived AR global characteristics, providing a better knowledge of the intrinsic properties of the emerging flux rope. Conclusions. These results provide a framework for future analysis of the physical properties of emerging ARs using Bayesian statistics.

Statistical classification of the Helios solar wind observations into several populations sorted by bulk speed has revealed an outward acceleration of the wind. The faster the wind is, the smaller is this acceleration in the 0.3 - 1 au radial range (Maksimovic et al. 2020). In this article we show that recent measurements from the Parker Solar Probe (PSP) are compatible with an extension closer to the Sun of the latter Helios classification. For instance the well established bulk speed/proton temperature (u,Tp) correlation and bulk speed/electron temperature (u,Te) anti-correlation, together with the acceleration of the slowest winds, are verified in PSP data. We also model the combined PSP and Helios data, using empirical Parker-like models for which the solar wind undergoes an "iso-poly" expansion: isothermal in the corona, then polytropic at distances larger than the sonic point radius. The polytropic indices are derived from the observed temperature and density gradients. Our modelling reveals that the electron thermal pressure has a major contribution in the acceleration process of slow and intermediate winds (in the range of 300-500 km/s at 1 au), over a broad range of distances and that the global (electron and protons) thermal energy, alone, is able to explain the acceleration profiles. Moreover, we show that the very slow solar wind requires in addition to the observed pressure gradients, another source of acceleration., Comment: 14 pages, 7 figures

Coronal mass ejections (CMEs) are large scale eruptions observed close to the Sun. They are travelling through the heliosphere and possibly interacting with the Earth environment creating interruptions or even damaging new technology instruments. Most of the time their physical conditions (velocity, density, pressure) are only measured in situ at one point in space, with no possibility to have information on the variation of these parameters during their journey from Sun to Earth. Our aim is to understand the evolution of internal physical parameters of a set of three particular fast halo CMEs. These CMEs were launched between 15 and 18 July 2002. Surprisingly, the related interplanetary CMEs (ICMEs), observed near Earth, have a low, and in one case even very low, plasma density. We use the EUropean Heliosphere FORecasting Information Asset (EUHFORIA) model to simulate the propagation of the CMEs in the background solar wind by placing virtual spacecraft along the Sun--Earth line. We set up the initial conditions at 0.1 au, first with a cone model and then with a linear force free spheromak model. A relatively good agreement between simulation results and observations concerning the speed, density and arrival times of the ICMEs is obtained by adapting the initial CME parameters. In particular, this is achieved by increasing the initial magnetic pressure so that a fast expansion is induced in the inner heliosphere. This implied the develop First, we show that a magnetic configuration with an out of force balance close to the Sun mitigates the EUHFORIA assumptions related to an initial uniform velocity. Second, the over-expansion of the ejected magnetic configuration in the inner heliosphere is one plausible origin for the low density observed in some ICMEs at 1 au. The in situ observed very low density has a possible coronal origin of fast expansion for two of the three ICMEs., Comment: 20 pages

How filaments form and erupt are topics about which solar researchers have wondered since more than a century and that are still open to debate. We present observations of a filament formation, its failed eruption, and the associated flare (SOL2019-05-09T05:51) that occurred in active region (AR) 12740 using data from SDO, STEREO-A, IRIS, and NSO/GONG. AR 12740 was a decaying region formed by a very disperse following polarity and a strong leading spot, surrounded by a highly dynamic zone where moving magnetic features (MMFs) were seen constantly diverging from the spot. Our analysis indicates that the filament was formed by the convergence of fibrils at a location where magnetic flux cancellation was observed. Furthermore, we conclude that its destabilization was also related to flux cancellation associated to the constant shuffling of the MMFs. A two-ribbon flare occurred associated to the filament eruption; however, because the large-scale magnetic configuration of the AR was quadrupolar, two additional flare ribbons developed far from the two main ones. We model the magnetic configuration of the AR using a force-free field approach at the AR scale size. This local model is complemented by a global potential-field source-surface one. Based on the local model, we propose a scenario in which the filament failed eruption and flare are due to two reconnection processes, one occurring below the erupting filament, leading to the two-ribbon flare, and another one above it between the filament flux-rope configuration and the large-scale closed loops. Our computation of the reconnected magnetic flux added to the erupting flux rope, compared to that of the large-scale field overlying it, lets us conclude that the latter was large enough to prevent the filament eruption. A similar conjecture can be drawn from the computation of the magnetic tension derived from the global field model., Comment: 32 pages, 17 figures, Accepted for publication in Solar Physics

In this paper, we are interested in linear prediction of a particular kind of stochastic process, namely a marked temporal point process. The observations are event times recorded on the real line, with marks attached to each event. We show that in this case, linear prediction extends straightforwardly from the theory of prediction for stationary stochastic processes. Following classical lines, we derive a Wiener-Hopf-type integral equation to characterise the linear predictor, extending the "model independent origin" of the Hawkes process (Jaisson, 2015) as a corollary. We propose two recursive methods to solve the linear prediction problem and show that these are computationally efficient in known cases. The first solves the Wiener-Hopf equation via a set of differential equations. It is particularly well-adapted to autoregressive processes. In the second method, we develop an innovations algorithm tailored for moving-average processes. A small simulation study on two typical examples shows the application of numerical schemes for estimation of a Hawkes process intensity.

Using Localized Surface Plasmon Resonance (LSPR) as an optical probe we demonstrate the presence of free carriers in phosphorus doped silicon nanocrystals (SiNCs) embedded in a silica matrix. In small SiNCs, with radius ranging from 2.6 to 5.5 nm, the infrared spectroscopy study coupled to numerical simulations allows us to determine the number of electrically active phosphorus atoms with a precision of a few atoms. We demonstrate that LSP resonances can be supported with only about 10 free electrons per nanocrystal, confirming theoretical predictions and probing the limit of the collective nature of plasmons. We reveal a phenomenon, unique to embedded nanocrystals, with the appearance of an avoided crossing behavior linked to the hybridization between the localized surface plasmon in the doped nanocrystals and the silica matrix phonon modes. Finally, a careful analysis of the scattering time dependence versus carrier density in the small size regime allows us to detect the appearance of a new scattering process at high dopant concentration.

The need of surface-localized thermal processing is strongly increasing especially w.r.t three-dimensionally (3D) integrated electrical devices. UV laser annealing (UV-LA) technology well addresses this challenge. Particularly UV-LA can reduce resistivity by enlarging metallic grains in lines or thin films, irradiating only the interconnects for short timescales. However, the risk of failure in electrical performance must be correctly managed, and that of UV-LA has not been deeply studied yet. In this work microsecond-scale UV-LA is applied on a stack comparable to an interconnect structure (dielectric/Cu/Ta/SiO2/Si) in either melt or sub-melt regime for grain growth. The failure modes such as (i) Cu diffusion into SiO2, (ii) O incorporation into Cu, and (iii) intermixing between Cu and Ta are investigated., Comment: Accepted Paper for the IEEE International Interconnect Technology Conference (IITC) 2022

Using the observations from Solar Dynamics Observatory, we study an eruption of a hot-channel flux rope (FR) near the solar-limb on February 9, 2015. The pre-eruptive structure is visible mainly in EUV 131 $\mathring{\mathrm{A}}$ images with two highly-sheared loop structures. They undergo slow rise motion and then reconnect to form an eruptive hot-channel as in the tether-cutting reconnection model. The J-shaped flare-ribbons trace the footpoint of the FR which is identified as the hot-channel. Initially, the hot channel is observed to rise slowly at 40 km s$^{-1}$, followed by an exponential rise from 22:55 UT at a coronal height of 87$\pm$2 Mm. Following the onset of the eruption at 23:00 UT, the flare-reconnection adds to the acceleration process of the CME within 3 R$_\odot$. Later on, the CME continues to accelerate at 8 m s$^{-2}$ during its propagation period. Further, the eruption launched type-II followed by III, IVm radio bursts. The start and end times of type-IVm correspond to the CME core height of 1.5 and 6.1 R$_\odot$, respectively. Also the spectral index is negative suggesting the non-thermal electrons trapped in the closed loop structure. Accompanied with type-IVm, this event is unique in the sense that the flare ribbons are very clearly observed along with the erupting hot channel, which strongly supports that the hooked-part of J-shaped flare ribbons outlines the boundary of the erupting FR., Comment: 12 pages, 6 figures, Accepted to publish in The Astrophysical Journal

The mid-infrared (mid-IR) range has been mostly unexplored for the investigation of solar flares. It is only recently that new mid-IR flare observations have begun opening a new window into the response and evolution of the solar chromosphere. These new observations have been mostly performed by the AR30T and BR30T telescopes that are operating in Argentina and Brazil, respectively. We present the analysis of SOL2019-05-15T19:24, a GOES class C2.0 solar flare observed at 30~THz (10$\ \mu$m) by the ground-based telescope AR30T. Our aim is to characterize the evolution of the flaring atmosphere and the energy transport mechanism in the context of mid-IR emission. We performed a multi-wavelength analysis of the event by complementing the mid-IR data with diverse ground- and space-based data from the Solar Dynamics Observatory (SDO), the H--$\alpha$ Solar Telescope for Argentina (HASTA), and the Expanded Owens Valley Solar Array (EOVSA). Our study includes the analysis of the magnetic field evolution of the flaring region and of the development of the flare. The mid-IR images from AR30T show two bright and compact flare sources that are spatially associated with the flare kernels observed in ultraviolet (UV) by SDO. We confirm that the temporal association between mid-IR and UV fluxes previously reported for strong flares is also observed for this small flare. The EOVSA microwave data revealed flare spectra consistent with thermal free-free emission, which lead us to dismiss the existence of a significant number of non-thermal electrons. We thus consider thermal conduction as the primary mechanism responsible for energy transport. Our estimates for the thermal conduction energy and total radiated energy fall within the same order of magnitude, reinforcing our conclusions., Comment: 10 pages, 8 figures. Accepted for publication in Astronomy and Astrophysics

Magnetic flux ropes are bundles of twisted magnetic field enveloping a central axis. They harbor free magnetic energy and can be progenitors of coronal mass ejections (CMEs), but identifying flux ropes on the Sun can be challenging. One of the key coronal observables that has been shown to indicate the presence of a flux rope is a peculiar bright coronal structure called a sigmoid. In this work, we show Hinode EUV Imaging Spectrometer (EIS) observations of sigmoidal active region 10977. We analyze the coronal plasma composition in the active region and its evolution as the sigmoid (flux rope) forms and erupts as a CME. Plasma with photospheric composition was observed in coronal loops close to the main polarity inversion line during episodes of significant flux cancellation, suggestive of the injection of photospheric plasma into these loops driven by photospheric flux cancellation. Concurrently, the increasingly sheared core field contained plasma with coronal composition. As flux cancellation decreased and the sigmoid/flux rope formed, the plasma evolved to an intermediate composition in between photospheric and typical active region coronal compositions. Finally, the flux rope contained predominantly photospheric plasma during and after a failed eruption preceding the CME. The Hence, plasma composition observations of active region 10977 strongly support models of flux rope formation by photospheric flux cancellation forcing magnetic reconnection first at the photospheric level then at the coronal level.

Confounding variables are a recurrent challenge for causal discovery and inference. In many situations, complex causal mechanisms only manifest themselves in extreme events, or take simpler forms in the extremes. Stimulated by data on extreme river flows and precipitation, we introduce a new causal discovery methodology for heavy-tailed variables that allows the effect of a known potential confounder to be almost entirely removed when the variables have comparable tails, and also decreases it sufficiently to enable correct causal inference when the confounder has a heavier tail. We also introduce a new parametric estimator for the existing causal tail coefficient and a permutation test. Simulations show that the methods work well and the ideas are applied to the motivating dataset., Comment: Extremes (2022)

Interplanetary Coronal Mass Ejections (ICMEs) are known to modify the structure of the solar wind as well as interact with the space environment of planetary systems. Their large magnetic structures have been shown to interact with galactic cosmic rays, leading to the Forbush decrease (FD) phenomenon. We revisit in the present article the 17 years of Advanced Composition Explorer spacecraft ICME detection along with two neutron monitors (McMurdo and Oulu) with a superposed epoch analysis to further analyze the role of the magnetic ejecta in driving FDs. We investigate in the following the role of the sheath and the magnetic ejecta in driving FDs, and we further show that for ICMEs without a sheath, a magnetic ejecta only is able to drive significant FDs of comparable intensities. Furthermore, a comparison of samples with and without a sheath with similar speed profiles enable us to show that the magnetic field intensity, rather than its fluctuations, is the main driver for the FD. Finally, the recovery phase of the FD for isolated magnetic ejecta shows an anisotropy in the level of the GCRs. We relate this finding at 1 au to the gradient of the GCR flux found at different heliospheric distances from several interplanetary missions., Comment: 19 pages, 8 figures, accepted for publication in The Astrophysical Journal

We analyze the observations of EUV loop evolution associated with the filament eruption located at the border of an active region. The event SOL2013-03-16T14:00 was observed with a large difference of view point by the Solar Dynamics Observatory and Solar Terrestrial Relations Observatory --A spacecraft. The filament height is fitted with the sum of a linear and exponential function. These two phases point to different physical mechanisms such as: tether-cutting reconnection and a magnetic instability. While no X-ray emission is reported, this event presents the classical eruption features like: separation of double ribbons and the growth of flare loops. We report the migration of the southern foot of the erupting filament flux rope due to the interchange reconnection with encountered magnetic loops of a neighbouring AR. Parallel to the erupting filament, a stable filament remains in the core of active region. The specificity of this eruption is that coronal loops, located above the nearly joining ends of the two filaments, first contract in phase, then expand and reach a new stable configuration close to the one present at the eruption onset. Both contraction and expansion phases last around 20 min. The main difference with previous cases is that the PIL bent about 180 deg around the end of the erupting filament because the magnetic configuration is at least tri-polar. These observations are challenging for models which interpreted previous cases of loop contraction within a bipolar configuration. New simulations are required to broaden the complexity of the configurations studied., Comment: 32 pages, 9 figures, Accepted for publication in The Astrophysical Journal

With climate change accelerating, the frequency of climate disasters is expected to increase in the decades to come. There is ongoing debate as to how different climatic regions will be affected by such an acceleration. In this paper, we describe a model for predicting the frequency of climate disasters and the severity of the resulting number of deaths. The frequency of disasters is described as a Poisson process driven by aggregate CO2 emissions. The severity of disasters is described using a generalized Pareto distribution driven by the trend in regional real gross domestic product (GDP) per capita. We predict the death toll for different types of climate disasters based on the projections made by the Intergovernmental Panel on Climate Change for the population, the regional real GDP per capita, and aggregate CO2 emissions in the "sustainable" and "business-as-usual" baseline scenarios.

One of the major discoveries of Hinode's Extreme-ultraviolet Imaging Spectrometer (EIS) is the presence of upflows at the edges of active regions. As active regions are magnetically connected to the large-scale field of the corona, these upflows are a likely contributor to the global mass cycle in the corona. Here we examine the driving mechanism(s) of the very strong upflows with velocities in excess of 70 km/s, known as blue-wing asymmetries, observed during the eruption of a flux rope in AR 10977 (eruptive flare SOL2007-12-07T04:50). We use Hinode/EIS spectroscopic observations combined with magnetic-field modeling to investigate the possible link between the magnetic topology of the active region and the strong upflows. A Potential Field Source Surface (PFSS) extrapolation of the large-scale field shows a quadrupolar configuration with a separator lying above the flux rope. Field lines formed by induced reconnection along the separator before and during the flux-rope eruption are spatially linked to the strongest blue-wing asymmetries in the upflow regions. The flows are driven by the pressure gradient created when the dense and hot arcade loops of the active region reconnect with the extended and tenuous loops overlying it. In view of the fact that separator reconnection is a specific form of the more general quasi-separatrix (QSL) reconnection, we conclude that the mechanism driving the strongest upflows is, in fact, the same as the one driving the persistent upflows of approx. 10 - 20 km/s observed in all active regions.

Context. Prominence eruptions provide key observations to understand the launch of coronal mass ejections as their cold plasma traces a part of the unstable magnetic configuration. Aims. We select a well observed case to derive observational constraints for eruption models. Methods. We analyze the prominence eruption and loop expansion and contraction observed on 02 March 2015 associated with a GOES M3.7 class flare (SOL2015-03-02T15:27) using the data from Atmospheric Imaging Assembly (AIA) and the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). We study the prominence eruption and the evolution of loops using the time-distance techniques. Results. The source region is a decaying bipolar active region where magnetic flux cancellation is present for several days before the eruption. AIA observations locate the erupting prominence within a flux rope viewed along its local axis direction. We identify and quantify the motion of loops in contraction and expansion located on the side of the erupting flux rope. Finally, RHESSI hard X-ray observations identify the loop top and two foot-point sources. Conclusions. Both AIA and RHESSI observations support the standard model of eruptive flares. The contraction occurs 19 minutes after the start of the prominence eruption indicating that this contraction is not associated with the eruption driver. Rather, this prominence eruption is compatible with an unstable flux rope where the contraction and expansion of the lateral loop is the consequence of a side vortex developing after the flux rope is launched., Comment: 16 pages, 9 figures, 1 table, and appendix

In this study, we investigate the spatial distribution of highly varying plasma composition around one of the largest sunspots of solar cycle 24. Observations of the photosphere, chromosphere, and corona are brought together with magnetic field modelling of the sunspot in order to probe the conditions which regulate the degree of plasma fractionation within loop populations of differing connectivities. We find that in the coronal magnetic field above the sunspot umbra, the plasma has photospheric composition. Coronal loops rooted in the penumbra contain fractionated plasma, with the highest levels observed in the loops that connect within the active region. Tracing field lines from regions of fractionated plasma in the corona to locations of Alfvenic fluctuations detected in the chromosphere shows that they are magnetically linked. These results indicate a connection between sunspot chromospheric activity and observable changes in coronal plasma composition., Comment: 14 pages, 6 figure, accepted by ApJ on 15 November 2020

Interest in stealth coronal mass ejections (CMEs) is increasing due to their relatively high occurrence rate and space weather impact. However, typical CME signatures such as extreme-ultraviolet dimmings and post-eruptive arcades are hard to identify and require extensive image processing techniques. These weak observational signatures mean that little is currently understood about the physics of these events. We present an extensive study of the magnetic field configuration in which the stealth CME of 3 March 2011 occurred. Three distinct episodes of flare ribbon formation are observed in the stealth CME source active region (AR). Two occurred prior to the eruption and suggest the occurrence of magnetic reconnection that builds the structure which will become eruptive. The third occurs in a time close to the eruption of a cavity that is observed in STEREO-B 171A data; this subsequently becomes part of the propagating CME observed in coronagraph data. We use both local (Cartesian) and global (spherical) models of the coronal magnetic field, which are complemented and verified by the observational analysis. We find evidence of a coronal null point, with field lines computed from its neighbourhood connecting the stealth CME source region to two ARs in the northern hemisphere. We conclude that reconnection at the null point aids the eruption of the stealth CME by removing field that acted to stabilise the pre-eruptive structure. This stealth CME, despite its weak signatures, has the main characteristics of other CMEs, and its eruption is driven by similar mechanisms., Comment: 15 pages, 12 figures, accepted for publication in The Astrophysical Journal

We give a construction of the Hawkes process as a piecewise competing risks model. We argue that the most natural interpretation of the self-excitation kernel is the hazard function of a defective random variable. This establishes a link between desired qualitative features of the process and a parametric form for the kernel, which we illustrate using examples from the literature. Two families of cure rate models taken from the survival analysis literature are proposed as new models for the self-excitation kernel. Finally, we show that the competing risks viewpoint leads to a general simulation algorithm which avoids inverting the compensator of the point process or performing an accept-reject step, and is therefore fast and quite general., Comment: 14 pages, 2 figures; submitted version

Interplanetary coronal mass ejections (ICMEs) are magnetic structures propagating from the Sun's corona to the interplanetary medium. With over 20 years of observations at the L1 libration point, ACE offers hundreds of ICMEs detected at different times during several solar cycles and with different features such as the propagation speed. We investigate a revisited catalog of more than 400 ICMEs using the superposed epoch method on the mean, median, and the most probable values of the distribution of magnetic and plasma parameters. We also investigate the effects of the speed of ICMEs relative to the solar wind, the solar cycle, and the existence of a magnetic cloud on the generic ICME profile. We find that fast-propagating ICMEs (relatively to the solar wind in front) still show signs of compression at 1 au, as seen by the compressed sheath and the asymmetric profile of the magnetic field. While the solar cycle evolution does not impact the generic features of ICMEs, there are more extreme events during the active part of the cycle, widening the distributions of all parameters. Finally, we find that ICMEs with or without a detected magnetic cloud show similar profiles, which confirms the hypothesis that ICMEs with no detected magnetic clouds are crossed further away from the flux rope core. Such a study provides a generic understanding of processes that shape the overall features of ICMEs in the solar wind and can be extended with future missions at different locations in the solar system., Comment: 30 pages, 7 figures. The two first links in the acknowledgments might not work because of the _ which can be taken as a blank. Here you have the two links: MAG data http://www.srl.caltech.edu/ACE/ASC/level2/lvl2DATA_MAG.html and SWEPAM data http://www.srl.caltech.edu/ACE/ASC/level2/lvl2DATA_SWEPAM.html

Relative magnetic helicity is conserved by magneto-hydrodynamic evolution even in the presence of moderate resistivity. For that reason, it is often invoked as the most relevant constraint to the dynamical evolution of plasmas in complex systems, such as solar and stellar dynamos, photospheric flux emergence, solar eruptions, and relaxation processes in laboratory plasmas. However, such studies often indirectly imply that relative magnetic helicity in a given spatial domain can be algebraically split into the helicity contributions of the composing subvolumes, i.e., that it is an additive quantity. A limited number of very specific applications have shown that this is not the case. Progress in understanding the non-additivity of relative magnetic helicity requires removal of restrictive assumptions in favour of a general formalism that can be used both in theoretical investigations as well as in numerical applications. We derive the analytical gauge-invariant expression for the partition of relative magnetic helicity between contiguous finite-volumes, without any assumptions on either the shape of the volumes and interface, or the employed gauge. The non-additivity of relative magnetic helicity in finite volumes is proven in the most general, gauge-invariant formalism, and verified numerically. More restrictive assumptions are adopted to derive known specific approximations, yielding a unified view of the additivity issue. As an example, the case of a flux rope embedded in a potential field shows that the non-additivity term in the partition equation is, in general, non-negligible. The relative helicity partition formula can be applied to numerical simulations to precisely quantify the effect of non-additivity on global helicity budgets of complex physical processes., Comment: 14 pages, 3 figures, accepted for publication in Astronomy & Astrophysics