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A numerical algorithm (implemented in Matlab) for computing the zeros of the parabolic cylinder function $U(a,z)$ in domains of the complex plane is presented. The algorithm uses accurate approximations to the first zero plus a highly efficient method based on a fourth-order fixed point method with the parabolic cylinder functions computed by Taylor series and carefully selected steps, to compute the rest of the zeros. For $|a|$ small, the asymptotic approximations are complemented with a few fixed point iterations requiring the evaluation of $U(a,z)$ and $U'(a,z)$ in the region where the complex zeros are located. Liouville-Green expansions are derived to enhance the performance of a computational scheme to evaluate $U(a,z)$ and $U'(a,z)$ in that region. Several tests show the accuracy and efficiency of the numerical algorithm.

BabyIAXO is the intermediate stage of the International Axion Observatory (IAXO) to be hosted at DESY. Its primary goal is the detection of solar axions following the axion helioscope technique. Axions are converted into photons in a large magnet that is pointing to the sun. The resulting X-rays are focused by appropriate X-ray optics and detected by sensitive low-background detectors placed at the focal spot. The aim of this article is to provide an accurate quantitative description of the different components (such as the magnet, optics, and X-ray detectors) involved in the detection of axions. Our efforts have focused on developing robust and integrated software tools to model these helioscope components, enabling future assessments of modifications or upgrades to any part of the IAXO axion helioscope and evaluating the potential impact on the experiment's sensitivity. In this manuscript, we demonstrate the application of these tools by presenting a precise signal calculation and response analysis of BabyIAXO's sensitivity to the axion-photon coupling. Though focusing on the Primakoff solar flux component, our virtual helioscope model can be used to test different production mechanisms, allowing for direct comparisons within a unified framework., Comment: 36 pages, 18 figures, 4 tables, Submitted to JHEP

Cryptographic protocols play a fundamental role in securing modern digital infrastructure, but they are often deployed without prior formal verification. This could lead to the adoption of distributed systems vulnerable to attack vectors. Formal verification methods, on the other hand, require complex and time-consuming techniques that lack automatization. In this paper, we introduce a benchmark to assess the ability of Large Language Models (LLMs) to autonomously identify vulnerabilities in new cryptographic protocols through interaction with Tamarin: a theorem prover for protocol verification. We created a manually validated dataset of novel, flawed, communication protocols and designed a method to automatically verify the vulnerabilities found by the AI agents. Our results about the performances of the current frontier models on the benchmark provides insights about the possibility of cybersecurity applications by integrating LLMs with symbolic reasoning systems.

We characterize, in terms of the defining graph, when a twisted right-angled Artin group (a group whose only relations among pairs of generators are either commuting or Klein-bottle type relations) is left-orderable.

We investigate the stability of weak symmetry-protected topological phases (SPTs) in the presence of short-range interactions, focusing on the tenfold way classification. Using Atiyah's Real $\mathit{KR}$-theory and Anderson-dualized bordism, we classify free and interacting weak phases across all Altland-Zirnbauer symmetry classes in low dimensions. Extending the free-to-interacting map of Freed-Hopkins, we mathematically compute how the behavior of free weak SPTs changes when interactions are introduced as well as predict intrinsically-interacting weak phases in certain classes. Our mathematical techniques involve T-duality and the James splitting of the torus. Our results provide a mathematical framework for understanding the persistence of weak SPTs under interactions, with potential implications for experimental and theoretical studies of these phases., Comment: 48 pages. Comments welcome!

The synthesis of porous, lattice, or microstructure geometries has captured the attention of many researchers in recent years. Implicit forms, such as triply periodic minimal surfaces (TPMS) has captured a significant attention, recently, as tiles in lattices, partially because implicit forms have the potential for synthesizing with ease more complex topologies of tiles, compared to parametric forms. In this work, we show how variable offsets of implicit forms could be used in lattice design as well as lattice analysis, while graded wall and edge thicknesses could be fully controlled in the lattice and even vary within a single tile. As a result, (geometrically) heterogeneous lattices could be created and adapted to follow analysis results while maintaining continuity between adjacent tiles. We demonstrate this ability on several 3D models, including TPMS., Comment: 15 pages, 17 figures

Traditional models of coronal oscillations rely on modelling the coronal structures that support them as compact cylindrical waveguides. Recently, an alternative model of the structure of the corona has been proposed, where the thin strand-like coronal loops observable in the EUV emission are a result of line-of-sight integration of warps in more complex coronal structures, referred to as the coronal veil model. We extend the implications of the coronal veil model of the solar corona to models of coronal oscillations. Using the convection-zone-to-corona simulations with the radiation-magnetohydrodynamics code Bifrost, we analysed the structure of the self-consistently formed simulated corona. We focus on the spatial variability of the volumetric emissivity of the Fe IX 171.073 {\AA} EUV line, and on the variability of the Alfv\'en speed, which captures the density and magnetic structuring of the simulated corona. We traced features associated with large magnitudes of the Alfv\'en speed gradient, which are the most likely to trap MHD waves and act as coronal waveguides, and looked for the correspondence with emitting regions which appear as strand-like loops in line-of-sight-integrated EUV emission. The waveguide filling factors corresponding to the fraction of the waveguides filled with plasma emitting in the given EUV wavelength range from 0.09 to 0.44. This suggests that we can observe only a small fraction of the waveguide. Similarly, the projected waveguide widths in the plane of the sky are several times larger than the widths of the apparent loops observable in EUV. We conclude that the 'coronal veil' structure is model-independent. As a result, we find a lack of straightforward correspondence between a peak in the integrated emission profile which constitutes an apparent coronal loop and regions of plasma bound by a large Alfv\'en speed gradient acting as waveguides., Comment: 8 pages, 7 figures, accepted for publication in A&A

Interacting crystalline SPT phases were first classified by Thorngren and Else through the crystalline equivalence principle, suggesting that a spatial group symmetry can be treated as if it were an internal symmetry group. Using techniques from topology we elucidate how this principle holds for one of the proposals for the interacting bosonic case and yet fails for weak free fermion phases. Last we show how a variant of the principle does hold for strong crystalline free fermion phases., Comment: 3 pages, comments welcome!

This work utilizes the Immersed Boundary Conformal Method (IBCM) to analyze Kirchhoff-Love and Reissner-Mindlin shell structures within an immersed domain framework. Immersed boundary methods involve embedding complex geometries within a background grid, which allows for great flexibility in modeling intricate shapes and features despite the simplicity of the approach. The IBCM method introduces additional layers conformal to the boundaries, allowing for the strong imposition of Dirichlet boundary conditions and facilitating local refinement. In this study, the construction of boundary layers is combined with high-degree spline-based approximation spaces to further increase efficiency. The Nitsche method, employing non-symmetric average operators, is used to couple the boundary layers with the inner patch, while stabilizing the formulation with minimal penalty parameters. High-order quadrature rules are applied for integration over cut elements and patch interfaces. Numerical experiments demonstrate the efficiency and accuracy of the proposed formulation, highlighting its potential for complex shell structures modeled through Kirchhoff-Love and Reissner-Mindlin theories. These tests include the generation of conformal interfaces, the coupling of Kirchhoff-Love and Reissner-Mindlin theories, and the simulation of a damaged shell.

The real and complex zeros of the parabolic cylinder function $U(a,z)$ are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and these are valid for $a$ positive or negative and large in absolute value, uniformly for unbounded $z$ (real or complex). The accuracy of the approximations of the complex zeros is then demonstrated with some comparative tests using a highly precise numerical algorithm for finding the complex zeros of the function.

Chromospheric evaporation (CE) and coronal rain (CR) represent two crucial phenomena encompassing the circulation of mass and energy during solar flares. While CE marks the start of the hot inflow into the flaring loop, CR marks the end, indicating the outflow in the form of cool and dense condensations. With \textit{IRIS} and \textit{AIA/SDO}, we examine and compare the evolution, dynamics, morphology, and energetics of the CR and CE during a C2.1 flare. The CE is directly observed in imaging and spectra in the \ion{Fe}{XXI} line with \textit{IRIS} and in the \ion{Fe}{XVIII} line of AIA, with upward average total speeds of $138\pm[35]~$km~s$^{-1}$ and a temperature of $[9.03\pm3.28]\times10^{6}$~K. An explosive to gentle CE transition is observed, with an apparent reduction in turbulence. From quiescent to gradual flare phase, the amount and density of CR increases by a factor of $\approx4.4$ and 6, respectively. The rain's velocity increases by a 1.4, in agreement with gas pressure drag. In contrast, the clump widths variation is negligible. The location and morphology of CE match closely those of the rain showers, with similar CE sub-structure to the rain strands, reflecting fundamental scales of mass and energy transport. We obtain a CR outflow mass three times larger than the CE inflow mass, suggesting the presence of unresolved CE, perhaps at higher temperatures. The CR energy corresponds to half that of the CE. These results suggest an essential role of coronal rain in the mass-energy cycle of a flare.

We study the homotopy type of spaces of commuting elements in connected nilpotent Lie groups, via almost commuting elements in their Lie algebras. We give a necessary and sufficient condition on the fundamental group of such a Lie group $G$ to ensure $\mathrm{Hom}(\mathbb{Z}^k,G)$ is path-connected. In particular for the reduced upper unitriangular groups and the reduced generalized Heisenberg groups, $\mathrm{Hom}(\mathbb{Z}^k,G)$ is not path-connected, and we compute the homotopy type of its path-connected components in terms of Stiefel manifolds and the maximal torus of $G$., Comment: 27 pages. Comments welcome!

Decayless kink oscillations are ubiquitously observed in active region coronal loops with an almost constant amplitude for several cycles. Decayless kink oscillations of coronal loops triggered by coronal rain have been analysed, but the impact of coronal rain formation in an already oscillating loop is unclear. As kink oscillations can help diagnose the local plasma conditions, it is important to understand how these are affected by coronal rain phenomena. In this study, we present the analysis of an event of coronal rain that occurred on 25 April 2014 and was simultaneously observed by \textit{Slit-Jaw Imager} (SJI) onboard \textit{Interface Region Imaging Spectrograph} (IRIS) and \textit{Atmospheric Imaging Assembly} (AIA) onboard \textit{Solar Dynamic Observatory} (SDO). The oscillation properties of the coronal loop in AIA are investigated before and after the appearance of coronal rain in SJI. We find signatures of decayless oscillations before and after coronal rain at similar positions to those during coronal rain. The individual cases show a greater amplitude and period during coronal rain. The mean period is increased by 1.3 times during coronal rain, while the average amplitude is increased by 2 times during rain, in agreement with the expected density increase from coronal rain. The existence of the oscillations in the same loop at the time of no coronal rain indicates the presence of a footpoint driver. The properties of the observed oscillations during coronal rain can result from the combined contribution of coronal rain and a footpoint driver. The oscillation amplitude associated with coronal rain is approximated to be 0.14 Mm. The properties of decayless oscillations are considerably affected by coronal rain, and without prior knowledge of coronal rain in the loop, a significant discrepancy can arise from coronal seismology with respect to the true values., Comment: 12 pages. Accepted for publication in Astronomy & Astrophysics

Gas time projection chambers (TPCs) with Micromegas pixelated readouts are being used in dark matter searches and other rare event searches, due to their potential in terms of low background levels, energy and spatial resolution, gain, and operational stability. Moreover, these detectors can provide precious features,such as topological information, allowing for event directionality and powerful signal-background discrimination. The Micromegas technology of the microbulk type is particularly suited to low-background applications and is being exploited by detectors for CAST and IAXO (solar axions) and TREX-DM (low-mass WIMPs) experiments. Challenges for the future include reducing intrinsic background levels, reaching lower energy detection levels, and technical issues such as robustness of detector, new design choices, novel gas mixtures and operation points, scaling up to larger detector sizes, handling large readout granularity, etc. We report on the status and prospects of the development ongoing in the context of IAXO and TREX-DM experiments, pointing to promising perspectives for the use of Micromegas detectors in directdark matter searches

This work focuses on the coupling of trimmed shell patches using Isogeometric Analysis, based on higher continuity splines that seamlessly meet the $C^1$ requirement of Kirchhoff-Love-based discretizations. Weak enforcement of coupling conditions is achieved through the symmetric interior penalty method, where the fluxes are computed using their correct variationally consistent expression that was only recently proposed and is unprecedentedly adopted herein in the context of coupling conditions. The constitutive relationships account for generically laminated materials, although the proposed tests are conducted under the assumption of uniform thickness and lamination sequence. Numerical experiments assess the method for an isotropic and a laminated plate, as well as an isotropic hyperbolic paraboloid shell from the new shell obstacle course. The boundary conditions and domain force are chosen to reproduce manufactured analytical solutions, which are taken as reference to compute rigorous convergence curves in the $L^2$, $H^1$, and $H^2$ norms, that closely approach optimal ones predicted by theory. Additionally, we conduct a final test on a complex structure comprising five intersecting laminated cylindrical shells, whose geometry is directly imported from a STEP file. The results exhibit excellent agreement with those obtained through commercial software, showcasing the method's potential for real-world industrial applications., Comment: Engineering with Computers. 2024

The hour-long, gradual phase of solar flares is well-observed across the electromagnetic spectrum, demonstrating many multi-phase aspects, where cold condensations form within the heated post-flare system, but a complete three-dimensional (3D) model is lacking. Using a state-of-the-art 3D magnetohydrodynamic simulation, we identify the key role played by the Lorentz force through the entire flare lifespan, and show that slow variations in the post-flare magnetic field achieve the bulk of the energy release. Synthetic images in multiple passbands closely match flare observations, and we quantify the role of conductive, radiative and Lorentz force work contributions from flare onset to decay. This highlights how the non-force-free nature of the magnetic topology is crucial to trigger Rayleigh-Taylor dynamics, observed as waving coronal rays in extreme ultraviolet observations. Our C-class solar flare reproduces multi-phase aspects such as post-flare coronal rain. In agreement with observations, we find strands of cooler plasma forming spontaneously by catastrophic cooling, leading to cool plasma draining down the post-flare loops. As there is force balance between magnetic pressure and tension and the plasma pressure in gradual-phase flare loops, this has potential for coronal seismology to decipher the magnetic field strength variation from observations., Comment: 22 pages, 10 figures

Speech intelligibility can be affected by multiple factors, such as noisy environments, channel distortions or physiological issues. In this work, we deal with the problem of automatic prediction of the speech intelligibility level in this latter case. Starting from our previous work, a non-intrusive system based on LSTM networks with attention mechanism designed for this task, we present two main contributions. In the first one, it is proposed the use of per-frame modulation spectrograms as input features, instead of compact representations derived from them that discard important temporal information. In the second one, two different strategies for the combination of per-frame acoustic log-mel and modulation spectrograms into the LSTM framework are explored: at decision level or late fusion and at utterance level or Weighted-Pooling (WP) fusion. The proposed models are evaluated with the UA-Speech database that contains dysarthric speech with different degrees of severity. On the one hand, results show that attentional LSTM networks are able to adequately modeling the modulation spectrograms sequences producing similar classification rates as in the case of log-mel spectrograms. On the other hand, both combination strategies, late and WP fusion, outperform the single-feature systems, suggesting that per-frame log-mel and modulation spectrograms carry complementary information for the task of speech intelligibility prediction, than can be effectively exploited by the LSTM-based architectures, being the system with the WP fusion strategy and Attention-Pooling the one that achieves best results.

Speech intelligibility can be degraded due to multiple factors, such as noisy environments, technical difficulties or biological conditions. This work is focused on the development of an automatic non-intrusive system for predicting the speech intelligibility level in this latter case. The main contribution of our research on this topic is the use of Long Short-Term Memory (LSTM) networks with log-mel spectrograms as input features for this purpose. In addition, this LSTM-based system is further enhanced by the incorporation of a simple attention mechanism that is able to determine the more relevant frames to this task. The proposed models are evaluated with the UA-Speech database that contains dysarthric speech with different degrees of severity. Results show that the attention LSTM architecture outperforms both, a reference Support Vector Machine (SVM)-based system with hand-crafted features and a LSTM-based system with Mean-Pooling.

This paper proposes a speech-based method for automatic depression classification. The system is based on ensemble learning for Convolutional Neural Networks (CNNs) and is evaluated using the data and the experimental protocol provided in the Depression Classification Sub-Challenge (DCC) at the 2016 Audio-Visual Emotion Challenge (AVEC-2016). In the pre-processing phase, speech files are represented as a sequence of log-spectrograms and randomly sampled to balance positive and negative samples. For the classification task itself, first, a more suitable architecture for this task, based on One-Dimensional Convolutional Neural Networks, is built. Secondly, several of these CNN-based models are trained with different initializations and then the corresponding individual predictions are fused by using an Ensemble Averaging algorithm and combined per speaker to get an appropriate final decision. The proposed ensemble system achieves satisfactory results on the DCC at the AVEC-2016 in comparison with a reference system based on Support Vector Machines and hand-crafted features, with a CNN+LSTM-based system called DepAudionet, and with the case of a single CNN-based classifier.

In this paper, based on the ideas of Blagojevi\'c, Karasev & Magazinov, we consider an extension of the center transversal theorem to mass assignments with an improved Rado depth. In particular we substitute the marginal of a measure by a more general concept called a mass assignment over a flag manifold. Our results also allow us to solve the main problem proposed by Blagojevi\'c, Karasev & Magazinov in a linear subspace of lower dimension, as long as it is contained in a high-dimensional enough ambient space., Comment: 7 pages

This paper addresses the overwhelming computational resources needed with standard numerical approaches to simulate architected materials. Those multiscale heterogeneous lattice structures gain intensive interest in conjunction with the improvement of additive manufacturing as they offer, among many others, excellent stiffness-to-weight ratios. We develop here a dedicated HPC solver that benefits from the specific nature of the underlying problem in order to drastically reduce the computational costs (memory and time) for the full fine-scale analysis of lattice structures. Our purpose is to take advantage of the natural domain decomposition into cells and, even more importantly, of the geometrical and mechanical similarities among cells. Our solver consists in a so-called inexact FETI-DP method where the local, cell-wise operators and solutions are approximated with reduced order modeling techniques. Instead of considering independently every cell, we end up with only few principal local problems to solve and make use of the corresponding principal cell-wise operators to approximate all the others. It results in a scalable algorithm that saves numerous local factorizations. Our solver is applied for the isogeometric analysis of lattices built by spline composition, which offers the opportunity to compute the reduced basis with macro-scale data, thereby making our method also multiscale and matrix-free. The solver is tested against various 2D and 3D analyses. It shows major gains with respect to black-box solvers; in particular, problems of several millions of degrees of freedom can be solved with a simple computer within few minutes., Comment: 30 pages, 12 figures, 2 tables

Decayless kink oscillations of plasma loops in the solar corona may contain an answer to the enigmatic problem of solar and stellar coronal heating. The polarisation of the oscillations gives us a unique information about their excitation mechanisms and energy supply. However, unambiguous determination of the polarisation has remained elusive. Here, we show simultaneous detection of a 4-min decayless kink oscillation from two non-parallel lines-of-sights, separated by about 104\textdegree, provided by unique combination of the High Resolution Imager on Solar Orbiter and the Atmospheric Imaging Assembly on Solar Dynamics Observatory. The observations reveal a horizontal or weakly oblique linear polarisation of the oscillation. This conclusion is based on the comparison of observational results with forward modelling of the observational manifestation of various kinds of polarisation of kink oscillations. The revealed polarisation favours the sustainability of these oscillations by quasi-steady flows which may hence supply the energy for coronal heating., Comment: 19 pages, 7 figures, accepted to Nature Communications

In the current industry, the development of optimized mechanical components able to satisfy the customer requirements evolves quickly. Therefore, companies are asked for efficient solutions to improve their products in terms of stiffness and strength. In this sense, Topology Optimization has been extensively used to determine the best topology of structural components from the mechanical point of view. Its main objective is to distribute a given amount of material into a predefined domain to reach the maximum overall stiffness of the component. Besides, high-resolution solutions are essential to define the final distribution of material. Standard Topological Optimization tools are able to propose an optimal topology for the whole component, but when small topological details are required (i.e. trabecular-type structures) the computational cost is prohibitive. In order to mitigate this issue, the present work proposes a two-level topology optimization method to solve high-resolution problems by using density-based methods. The proposed methodology includes three steps: The first one subdivides the whole component in cells and generates a coarse optimized low-definition material distribution assigning one different density to each cell. The second one uses an equilibrating technique that provides tractions continuity between adjacent cells, thus ensuring the material inter-cell continuity after the cells optimization process. Finally, each cell is optimized at fine scale taking as input data the densities and the equilibrated tractions obtained from the macro problem. The main goal of this work is to efficiently solve high-resolution topology optimization problems using density-based methods, which would be unaffordable with standard computing facilities and the current methodologies., Comment: 23 pages

It was conjectured by Goyal, Shukla and Singh that the independence complex of the categorical product $K_2\times K_3\times K_n$ has the homotopy type of a wedge of $(n-1)(3n-2)$ spheres of dimension $3$. Here we prove this conjecture by calculating the homotopy type of the independence complex of the graphs $C_{3r}\times K_n$ and $K_2\times K_m\times K_n$. For $C_m \times K_n$ when $m$ is not a multiple of $3$, we calculate the homotopy type for $m = 4, 5$ and show that for other values it has to have the homotopy type of a wedge of spheres of at most $2$ consecutive dimensions and maybe some Moore spaces.

This contribution presents a model order reduction framework for real-time efficient solution of trimmed, multi-patch isogeometric Kirchhoff-Love shells. In several scenarios, such as design and shape optimization, multiple simulations need to be performed for a given set of physical or geometrical parameters. This step can be computationally expensive in particular for real world, practical applications. We are interested in geometrical parameters and take advantage of the flexibility of splines in representing complex geometries. In this case, the operators are geometry-dependent and generally depend on the parameters in a non-affine way. Moreover, the solutions obtained from trimmed domains may vary highly with respect to different values of the parameters. Therefore, we employ a local reduced basis method based on clustering techniques and the Discrete Empirical Interpolation Method to construct affine approximations and efficient reduced order models. In addition, we discuss the application of the reduction strategy to parametric shape optimization. Finally, we demonstrate the performance of the proposed framework to parameterized Kirchhoff-Love shells through benchmark tests on trimmed, multi-patch meshes including a complex geometry. The proposed approach is accurate and achieves a significant reduction of the online computational cost in comparison to the standard reduced basis method., Comment: 44 pages, 23 figures, 3 tables

For a topological group $G$ let $E_{\textsf{com}}(G)$ be the total space of the universal transitionally commutative principal $G$-bundle as defined by Adem--Cohen--Torres-Giese. So far this space has been most studied in the case of compact Lie groups; but in this paper we focus on the case of infinite discrete groups. For a discrete group $G$, the space $E_{\textsf{com}}(G)$ is homotopy equivalent to the geometric realization of the order complex of the poset of cosets of abelian subgroups of $G$. We show that for fundamental groups of closed orientable geometric $3$-manifolds, this space is always homotopy equivalent to a wedge of circles. On our way to prove this result we also establish some structural results on the homotopy type of $E_{\textsf{com}}(G)$., Comment: 36 pages, 4 figures, comments very welcome!

Oscillations are abundant in the solar corona. Coronal loop oscillations are typically studied using highly idealised models of magnetic flux tubes. In order to improve our understanding of coronal oscillations, it is necessary to consider the effect of realistic magnetic field topology and density structuring. We analyse the damping of coronal oscillations using a self-consistent 3D radiation-MHD simulation of the solar atmosphere spanning from the convection zone into the corona, the associated oscillation dissipation and heating, and finally the physical processes responsible for the damping and dissipation. The simulated corona formed in such a model does not depend on any prior assumptions about the shape of the coronal loops. We find that the bundle of magnetic loops shows damped transverse oscillations in response to perturbations in two separate instances with oscillation periods of 177 s and 191 s, velocity amplitudes of 10 km/s and 16 km/s and damping times of 176 s and 198 s, respectively. The coronal oscillations lead to the development of velocity shear in the simulated corona resulting in the formation of vortices seen in the velocity field caused by the Kelvin-Helmholtz instability, contributing to the damping and dissipation of the transverse oscillations. The oscillation parameters and evolution observed are in line with the values typically seen in observations of coronal loop oscillations. The dynamic evolution of the coronal loop bundle suggests the models of monolithic and static coronal loops with constant lengths might need to be re-evaluated by relaxing the assumption of highly idealised waveguides., Comment: 9 pages, 7 figures, accepted for publication in A&A

We present a novel stabilized isogeometric formulation for the Stokes problem, where the geometry of interest is obtained via overlapping NURBS (non-uniform rational B-spline) patches, i.e., one patch on top of another in an arbitrary but predefined hierarchical order. All the visible regions constitute the computational domain, whereas independent patches are coupled through visible interfaces using Nitsche's formulation. Such a geometric representation inevitably involves trimming, which may yield trimmed elements of extremely small measures (referred to as bad elements) and thus lead to the instability issue. Motivated by the minimal stabilization method that rigorously guarantees stability for trimmed geometries [1], in this work we generalize it to the Stokes problem on overlapping patches. Central to our method is the distinct treatments for the pressure and velocity spaces: Stabilization for velocity is carried out for the flux terms on interfaces, whereas pressure is stabilized in all the bad elements. We provide a priori error estimates with a comprehensive theoretical study. Through a suite of numerical tests, we first show that optimal convergence rates are achieved, which consistently agrees with our theoretical findings. Second, we show that the accuracy of pressure is significantly improved by several orders using the proposed stabilization method, compared to the results without stabilization. Finally, we also demonstrate the flexibility and efficiency of the proposed method in capturing local features in the solution field., Comment: 38 pages, 29 figures. Reviewed version

We prove a Tits alternative theorem for subgroups of finitely generated even Artin groups of FC type (EAFC groups), stating that there exists a finite index subgroup such that every subgroup of it is either finitely generated abelian, or maps onto a non-abelian free group. Parabolic subgroups play a key role, and we show that parabolic subgroups of EAFC groups are closed under taking roots.

Coronal rain is the most dramatic cooling phenomenon of the solar corona and an essential diagnostic tool for the coronal heating properties. A puzzling feature of the solar corona, besides the heating, is its EUV filamentary structure and variability. We aim to identify observable features of the TNE-TI scenario underlying coronal rain at small and large spatial scales, to understand the role it plays in the solar corona. We use EUV datasets at unprecedented spatial resolution of ~240 km from EUI/HRIEUV and SPICE of Solar Orbiter from the spring 2022 perihelion. EUV absorption features produced by coronal rain are detected at scales as small as 260 km. As the rain falls, heating and compression is produced immediately downstream, leading to a small EUV brightening accompanying the fall and producing a "fireball" phenomenon. Just prior to impact, a flash-like EUV brightening downstream of the rain, lasting a few minutes is observed for the fastest events. For the first time, we detect the atmospheric response to the rain's impact on the chromosphere and consists of upward propagating rebound shocks and flows partly reheating the loop. The observed widths of the rain clumps are 500 +- 200 km. They exhibit a broad velocity distribution of 10 - 150 km s^-1, peaking below 50 km s^-1. Coronal strands of similar widths are observed along the same loops co-spatial with cool filamentary structure, which we interpret as the CCTR. Matching with the expected cooling, prior to the rain appearance sequential loop brightenings are detected in gradually cooler lines from corona to chromospheric temperatures. Despite the large rain showers, most cannot be detected in AIA 171 in quadrature, indicating that LOS effects play a major role in coronal rain visibility. Still, AIA 304 and SPICE observations reveal that only a small fraction of the rain can be captured by HRIEUV., Comment: Astronomy & Astrophysics; 32 Pages, 24 Main Figures, Appendix

The solar corona produces coronal rain, hundreds of times colder and denser material than the surroundings. Coronal rain is known to be deeply linked to coronal heating, but its origin, dynamics, and morphology are still not well understood. The leading theory for its origin is thermal instability (TI) occurring in coronal loops in a state of thermal non-equilibrium (TNE), the TNE-TI scenario. Under steady heating conditions, TNE-TI repeats in cycles, leading to long-period EUV intensity pulsations and periodic coronal rain. In this study, we investigate coronal rain on the large spatial scales of an active region (AR) and over the long temporal scales of EUV intensity pulsations to elucidate its distribution at such scales. We conduct a statistical study of coronal rain observed over an AR off-limb with IRIS and SDO imaging data, spanning chromospheric to transition region (TR) temperatures. The rain is widespread across the AR, irrespective of the loop inclination, and with minimal variation over the 5.45-hour duration of the observation. Most rain has a downward ($87.5\%$) trajectory; however, upward motions ($12.5\%$) are also ubiquitous. The rain dynamics are similar over the observed temperature range, suggesting that the TR and chromospheric emission are co-located on average. The average clump widths and lengths are similar in the SJI channels and wider in the AIA 304 channel. We find ubiquitous long-period EUV intensity pulsations in the AR. Short-term periodicity is found (16 min) linked to the rain appearance, which constitutes a challenge to explain under the TNE-TI scenario.

Context. The Extreme Ultraviolet Imager (EUI), onboard Solar Orbiter consists of three telescopes: the two High Resolution Imagers in EUV (HRIEUV) and in Lyman-{\alpha} (HRILya), and the Full Sun Imager (FSI). Solar Orbiter/EUI started its Nominal Mission Phase on 2021 November 27. Aims. EUI images from the largest scales in the extended corona off limb, down to the smallest features at the base of the corona and chromosphere. EUI is therefore a key instrument for the connection science that is at the heart of the Solar Orbiter mission science goals. Methods. The highest resolution on the Sun is achieved when Solar Orbiter passes through the perihelion part of its orbit. On 2022 March 26, Solar Orbiter reached for the first time a distance to the Sun close to 0.3 au. No other coronal EUV imager has been this close to the Sun. Results. We review the EUI data sets obtained during the period 2022 March-April, when Solar Orbiter quickly moved from alignment with the Earth (2022 March 6), to perihelion (2022 March 26), to quadrature with the Earth (2022 March 29). We highlight the first observational results in these unique data sets and we report on the in-flight instrument performance. Conclusions. EUI has obtained the highest resolution images ever of the solar corona in the quiet Sun and polar coronal holes. Several active regions were imaged at unprecedented cadences and sequence durations. We identify in this paper a broad range of features that require deeper studies. Both FSI and HRIEUV operate at design specifications but HRILya suffered from performance issues near perihelion. We conclude emphasising the EUI open data policy and encouraging further detailed analysis of the events highlighted in this paper.

Context: On 2020 May 30, small and short-lived EUV brightenings were observed in the Quiet Sun (QS) during a four minutes sequence by EUI/HRIEUV on board Solar Orbiter. Their physical origin and possible impact on coronal or Transition Region (TR) heating are still to be determined. Aims: Our aim is to derive the statistical thermal evolution of these events in order to establish their coronal or TR origin. Methods. Our thermal analysis takes advantage of the multithermal sensitivity of the Atmospheric Imaging Assembly (AIA) imager on board the Solar Dynamics Observatory (SDO). We first identified these HRIEUV events in the six coronal bands of AIA. We then performed a statistical time lag analysis, which quantifies the delays between the light curves from different bands. These time lags can give significant insights into the temperature evolution of these events. The analysis is performed taking into account the possible contribution to the results from the background and foreground emissions. Results: The events are characterized by time lags inferior to the AIA cadence of 12 s, for all nine couples of AIA bands analyzed. Our interpretation is the possible co-presence of events which reach or do not reach coronal temperatures ($\approx$ 1MK). We believe that the cool population dominates the events analyzed in this work., Comment: 14 pages, 8 figures, language and typo editing, accepted in A&A

This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient projection-based ROMs, which rely on techniques such as the reduced basis method and discrete empirical interpolation. The presence of geometrical parameters in unfitted domain discretizations entails challenges for the application of standard ROMs. Therefore, in this work we propose a methodology based on i) extension of snapshots on the background mesh and ii) localization strategies to decrease the number of reduced basis functions. The method we obtain is computationally efficient and accurate, while it is agnostic with respect to the underlying discretization choice. We test the applicability of the proposed framework with numerical experiments on two model problems, namely the Poisson and linear elasticity problems. In particular, we study several benchmarks formulated on two-dimensional, trimmed domains discretized with splines and we observe a significant reduction of the online computational cost compared to standard ROMs for the same level of accuracy. Moreover, we show the applicability of our methodology to a three-dimensional geometry of a linear elastic problem., Comment: 35 pages, 19 figures, 5 tables. Preprint accepted in Computer Methods in Applied Mechanics and Engineering

The hot carrier solar cell (HCSC) has the potential for converting solar energy into electrochemical energy with an efficiency of 85.4%. For this, in addition to an idealized light absorber, the HCSC has to be connected to the external load by means of the so-called \emph{mono-energetic energy selective contacts} (ESCs). However, the thermodynamic properties that these types of contact have to exhibit, such as their electric, thermal conductivity and Seebeck coefficient, have not been explored. This paper aims to fill this gap. In this respect, we model electron transport in non-ideal ESCs using the transport theory proposed by Datta and Landauer which has allowed us to calculate the value of these parameters as a function of the temperature and electrochemical potential of operation. Our findings also reveal that, to preserve the HCSC efficiency above 82%, the ESCs could require in the order of $3 \times 10^{19}$ cm$^{-3}$ electron states. As the ESCs depart from ideality, the temperature of the hot carriers at which optimum efficiency is obtained increases to above 2540 K. The mono-enenergetic selective contact characterized by the highest energy demands an electric, thermal conductivity and Seebeck coefficient that, when combined, are characterized by a high thermoelectric figure of merit $(ZT\approx 8)$. We are not aware of any material exhibiting this figure of merit which illustrates the difficulty in putting the HCSC concept into practice. Conversely, our work supports the idea that pursuing materials capable of transporting electrons ballistically through mono-energetic electron channels can provide the key for achieving materials characterized by high $ZT$, Comment: 14 pages, 5 figures

We show that if a complex has free finitely generated reduced homology groups for two consecutive dimensions and trivial homology for all other dimensions, then it must have the homotopy type of a wedge of spheres of two consecutive dimensions. We also show other pairs of dimensions for which the last result can be generalized.

Local modifications of a computational domain are often performed in order to simplify the meshing process and to reduce computational costs and memory requirements. However, removing geometrical features of a domain often introduces a non-negligible error in the solution of a differential problem in which it is defined. In this work, we extend the results from [1] by studying the case of domains containing an arbitrary number of distinct Neumann features, and by performing an analysis on Poisson's, linear elasticity, and Stokes' equations. We introduce a simple, computationally cheap, reliable, and efficient a posteriori estimator of the geometrical defeaturing error. Moreover, we also introduce a geometric refinement strategy that accounts for the defeaturing error: Starting from a fully defeatured geometry, the algorithm determines at each iteration step which features need to be added to the geometrical model to reduce the defeaturing error. These important features are then added to the (partially) defeatured geometrical model at the next iteration, until the solution attains a prescribed accuracy. A wide range of two- and three-dimensional numerical experiments are finally reported to illustrate this work., Comment: 40 pages