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The slowly positively drifting bursts (SPDBs) are rarely observed in radio emission of solar flares. To understand how the SPDBs are generated, we studied the radio observations at 600--5000 MHz together with the imaging observations made in ultraviolet (UV) and extreme ultraviolet (EUV) during the SPDB-rich C8.7 flare of 2014 May 10 (SOL2014-05-10T0702). Because the SPDBs propagate towards locations of higher plasma density, we studied their associations with individual flare kernels, located either within the flare core itself, or distributed at longer distances, but connected to the flaring region by large-scale hot loops. For each kernel we constructed light curves using 1600 A and 304 A observations and compared these light curves with the temporal evolution of radio flux at 1190 MHz, representing all observed groups of SPDBs. We also analysed the UV/EUV observations to understand the evolution of magnetic connectivity during the flare. The flare starts with a growing hot sigmoid observed in 131 A. As the sigmoid evolves, it extends to and interacts with a half dome present within the active region. The evolving sigmoid reconnects at the respective hyperbolic flux tube, producing large-scale magnetic connections and an EUV swirl. Three groups of SPDBs are observed during this large-scale magnetic reconnection, along with a group of narrow-band type III bursts. The light curves of a kernel corresponding to the footpoint of spine line analogue show good agreement with the radio flux at 1190 MHz, indicating that the SPDBs are produced by the large-scale magnetic reconnection at the half dome. In addition, one of the kernels appeared in the neighbouring active region and also showed a similar evolution to the radio flux, implying that beams of accelerated particles can synchronize radio and UV/EUV light curves across relatively large distances., Comment: Astronomy & Astrophysics, accepted

The KAPPA package is designed for calculations of optically thin spectra for the non-Maxwellian \k{appa}-distributions. This paper presents extension of the database to allow calculations of the spectra for extreme values of \k{appa} < 2, which are important for accurate diagnostics of the \k{appa}-distributions in the outer solar atmosphere. In addition, two improvements were made to the ionization equilibrium calculations within the database. First, the ionization equilibrium calculations now include the effect of electron impact multi-ionization (EIMI). Although relatively unimportant for Maxwellian distribution, the EIMI becomes important for some elements such as Fe and low values of \k{appa}, where it modifies the ionization equilibrium significantly. Second, the KAPPA database now includes the suppression of dielectronic recombination at high electron densities, evaluated via the suppression factors. We find that at the same temperature, the suppression of dielectronic recombination is almost independent of \k{appa}. The ionization equilibrium calculations for the \k{appa}-distributions are now provided for a range of electron densities., Comment: Astrophys. J. Suppl. Ser., accepted

Laminated glass achieves improved post-critical response through the composite effect of stiff glass layers and more compliant polymer films, manifested in progressive layer failure by multiple localized cracks. As a result, laminated glass exhibits greater ductility than non-laminated glass, making structures made with it suitable for safety-critical applications while maintaining their aesthetic qualities. However, such post-critical response is challenging to reproduce using deterministic failure models, which mostly predict failure through a single through-thickness crack localized simultaneously in all layers. This numerical-experimental study explores the extent to which progressive failure can be predicted by a simple randomized model, where layer-wise tensile strength is modeled by independent, identically distributed Weibull variables. On the numerical side, we employ a computationally efficient, dimensionally-reduced phase field formulation -- with each layer considered to be a Timoshenko beam -- to study progressive failure through combinatorial analysis and detailed Monte Carlo simulations. The reference experimental data were obtained from displacement-controlled four-point bending tests performed on multi-layer laminated glass beams. For certain combinations of the glass layer strengths, results show that the randomized model can reproduce progressive structural failure and the formation of multiple localized cracks in the glass layers. However, the predicted response was less ductile than that observed in experiments, and the model could not reproduce the most frequent glass layer failure sequence. These findings highlight the need to consider strength variability along the length of a beam and to include it in phase-field formulations., Comment: 30 pages, 18 figures, and 2 tables

We report on interaction of the legs of the erupting filament of 2012 August 31 and associated prominent supra-arcade downflows (P-SADs) as observed by the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory. We employ a number of image processing techniques to enhance weak interacting features. As the filament erupts, both legs stretch outwards. The positive-polarity leg also untwists and splits into two parts. The first part runs into the conjugate (negative-polarity) leg, tearing it apart. The second part then converges into the remnant of the conjugate leg, after which both weaken and finally disappear. All these episodes of interaction of oppositely-oriented filament legs are followed by appearance of P-SADs, seen in the on-disk projection to be shaped as loop-tops, along with many weaker SADs. All SADs are preceded by hot supra-arcade downflowing loops. This observed evolution is consistent with the three-dimensional rr-rf (leg-leg) reconnection, where the erupting flux rope reconnects with itself. In our observations, as well as in some models, the reconnection in this geometry is found to be long-lasting. It plays a substantial role in the evolution of the flux rope of the erupting filament and leads to prominent supra-arcade downflows., Comment: 9 pages, 5 figures Accepted for publication in the ApJL

Through pendulum impact testing on suspended samples, we demonstrate the effect of the multi-layer layout on the low-velocity impact response of laminated glass plates consisting of three or four glass layers and PVB interlayers. Non-destructive tests proved the repeatability and the consistency of performed experiments. Destructive tests revealed significant differences in impact energies and breakage forces leading to glass fracture for individual specimens under impacts of increasing height. Nevertheless, the fracture consistently initiated in outer glass layers around the impact point and vibrations of partially fractured samples exhibited similar first natural frequencies. Partially fractured samples also withstood in many cases higher contact forces than those leading to the fracture of the previous glass layer, and PVB interlayers provided a stiff shear connection between glass layers for all impact heights. Altogether, our experimental results provide comprehensive information on the pre-fracture, fracture, and post-fracture response of laminated glass, suitable particularly for validating computational models for multi-layer glass samples under low-velocity impact., Comment: 40 pages, 29 figures, 3 tables

We present multispectral analysis (radio, H$\alpha$, UV/EUV, and hard X-ray) of a confined flare from 2015 March 12. This flare started within the active region NOAA 12 297 and then it expanded into a large preexisting magnetic rope embedded with a cold filament. The expansion started with several brightenings located along the rope. This process was accompanied by a group of slowly positively drifting bursts in the 0.8--2 GHz range. The frequency drift of these bursts was 45 -- 100 MHz s$^{-1}$. One of the bursts had an S-like form. During the brightening of the rope we observed an unique bright EUV structure transverse to the rope axis. The structure was observed in a broad range of temperatures and it moved along the rope with the velocity of about 240 km s$^{-1}$. When the structure dissipated, we saw a plasma further following twisted threads in the rope. The observed slowly positively drifting bursts were interpreted considering particle beams and we show that one with the S-like form could be explained by the beam propagating through the helical structure of the magnetic rope. The bright structure transverse to the rope axis was interpreted considering line-of-sight effects and the dissipation-spreading process, which we found to be more likely., Comment: 24 pages, 11 figures

A phase-field description of brittle fracture is employed in the reported four-point bending analyses of monolithic and laminated glass plates. Our aims are: (i) to compare different phase-field fracture formulations applied to thin glass plates, (ii) to assess the consequences of the dimensional reduction of the problem and mesh density and refinement, and (iii) to validate for quasi-static loading the time/temperature-dependent material properties we derived recently for two commonly used polymer foils made of Polyvinyl Butyral or Ethylene-Vinyl Acetate. As the nonlinear response prior to fracture, typical of the widely used Bourdin-Francfort-Marigo model, can lead to a significant overestimation of the response of thin plates under bending, the numerical study investigates two additional phase-field fracture models providing the linear elastic phase of the stress-strain diagram. The typical values of the critical fracture energy and tensile strength of glass lead to a phase-field length-scale parameter that is challenging to resolve in the numerical simulations. So, we show how to determine the fracture energy concerning the applied dimensional reduction and the value of the length-scale parameter relative to the thickness of the plate. The comparison shows that the phase-field models provide very good agreement with the measured stresses and resistance of laminated glass, despite the fact that only one/two cracks localised using the quasi-static analysis, whereas multiple cracks evolved during the experiment. It has also been observed that the stiffness and resistance of the partially fractured laminated glass can be well approximated using a 2D plane-stress model with initially predefined cracks, which provides a better estimation than the one-glass-layer limit.}, Comment: 29 pages, 20 figures, and 6 tables

This paper investigates a time-stepping procedure of the Newmark type for dynamic analyses of viscoelastic structures characterized by a generalized Maxwell model. We depart from a scheme developed for a three-parameter model by Hatada et al. in 2000, which we extend to a generic Maxwell chain and demonstrate that the resulting algorithm can be derived from a suitably discretized Hamilton variational principle. This variational structure manifests itself in an excellent stability and a low artificial damping of the integrator, as we confirm with a mass-spring-dashpot example. After a straightforward generalization to distributed systems, the integrator may find use in, e.g., fracture simulations of laminated glass units, once combined with variationally-based fracture models., Comment: 9 pages, 4 figures, 1 table

We report on observations of the two newly-identified reconnection geometries involving erupting flux ropes. In 3D, a flux rope can reconnect either with a surrounding coronal arcade (recently named "ar-rf" reconnection) or with itself ("rr-rf" reconnection), and both kinds of reconnection create a new flux rope field line and a flare loop. For the first time, we identify all four constituents of both reconnections in a solar eruptive event, the filament eruption of 2011 June 07 observed by SDO/AIA. The ar-rf reconnection manifests itself as shift of one leg of the filament by more than 25" northward. At its previous location, a flare arcade is formed, while the new location of the filament leg previously corresponded to a footpoint of a coronal loop in 171 A. In addition, the evolution of the flare ribbon hooks is also consistent with the occurrence of ar--rf reconnection as predicted by MHD simulations. Specifically, the growing hook sweeps footpoints of preeruptive coronal arcades, and these locations become inside the hook. Furthermore, the rr-rf reconnection occurs during the peak phase above the flare arcade, in an apparently X-type geometry involving a pair of converging bright filament strands in the erupting filament. A new flare loop forms near the leg of one of the strands, while a bright blob, representing a remnant of the same strand, is seen ascending into the erupting filament. All together, these observations vindicate recent predictions of the 3D standard solar flare model., Comment: The Astrophysical Journal, accepted

We analyze the imaging observations of an M-class eruptive flare of 2015 November, 4. The pre-eruptive H alpha filament was modelled by the non-linear force free field model, which showed that it consisted of two helical systems. Tether-cutting reconnection involving these two systems led to the formation of a hot sigmoidal loop structure rooted in a small hook that formed at the end of the flare ribbon. Subsequently, the hot loops started to slip away form the small hook until it disappeared. The loops continued slipping and the ribbon elongated itself by several tens of arc seconds. A new and larger hook then appeared at the end of elongated ribbon with hot and twisted loops rooted there. After the eruption of these hot loops, the ribbon hook expanded and later contracted. We interpret these observations in the framework of the recent three dimensional (3D) extensions to the standard solar flare model, which predict the drift of the flux rope footpoints. The hot sigmoidal loop is interpreted as the flux rope, whose footpoints drift during the eruption. While the deformation and drift of the new hook can be described by the model, the displacement of the flux rope footpoint from the filament to that of the erupting flux rope indicate that the hook evolution can be more complex than those captured by the model., Comment: ApJ, accepted

We report on observations of flare ribbon kernels during the 2012 August 31 filament eruption. In the 1600\,\AA{} and 304\,\AA{} channels of the Atmospheric Imaging Assembly, flare kernels were observed to move along flare ribbons at velocities $v_\parallel$ of up to $450$ km\,s$^{-1}$. Kernel velocities were found to be roughly anti-correlated with strength of the magnetic field. Apparent slipping motion of flare loops was observed in the 131\,\AA{} only for the slowest kernels moving through strong-$B$ region. In order to interpret the observed relation between $B_{\text{LOS}}$ and $v_\parallel$, we examined distribution of the norm $N$, a quantity closely related to the slippage velocity. We then calculated the norm $N$ of the quasi-separatrix layers (QSLs) in MHD model of a solar eruption adapted to the magnetic environment which qualitatively agrees to that of the observed event. We found that both the modelled $N$ and velocities of kernels reach their highest values in the same weak-field regions, one located in the curved part of the ribbon hook and the other in the straight part of the conjugate ribbon located close to a parasitic polarity. Oppositely, lower values of the kernel velocities are seen at the tip of the ribbon hook, where the modelled $N$ is low. Since the modelled distribution of $N$ matches the observed dynamics of kernels, this supports that the kernel motions can be interpreted as a signature of QSL reconnection during the eruption.

At the beginning of the 4 November 2015 flare, in the 1300 -- 2000 MHz frequency range, we observed a very rare slowly positively drifting burst. We searched for associated phenomena in simultaneous EUV observations made by IRIS, SDO/AIA, Hinode/XRT and in H alpha observations. We found that this radio burst was accompanied with the bright blob, visible at transition region, coronal, and flare temperatures, falling down to the chromosphere along the dark loop with the velocity of about 280 km/s. The dark loop was visible in H alpha but disappeared afterwards. Furthermore, we found that the falling blob interacted with the chromosphere as expressed by a sudden change of the H alpha spectra at the location of this interaction. Considering different possibilities we propose that the observed slowly positively drifting burst is generated by the thermal conduction front formed in front of the falling hot EUV blob.

Spectroscopic observations made by the Extreme Ultraviolet Variability Experiment (EVE) on board the Solar Dynamics Observatory (SDO) during the 2012 March 7 X5.4-class flare (SOL2012-03-07T00:07) are analyzed for signatures of the non-Maxwellian kappa-distributions. Observed spectra were averaged over 1 minute to increase photon statistics in weaker lines and the pre-flare spectrum was subtracted. Synthetic line intensities for the kappa-distributions are calculated using the KAPPA database. We find strong departures (kappa < 2) during the early and impulsive phases of the flare, with subsequent thermalization of the flare plasma during the gradual phase. If the temperatures are diagnosed from a single line ratio, the results are strongly dependent on the value of kappa. For kappa=2, we find temperatures about a factor of two higher than the commonly used Maxwellian ones. The non-Maxwellian effects could also cause the temperatures diagnosed from line ratios and from the ratio of GOES X-ray channels to be different. Multithermal analysis reveals the plasma to be strongly multithermal at all times with flat DEMs. For lower kappa, the DEM_kappa are shifted towards higher temperatures. The only parameter that is nearly independent of kappa is electron density, where we find log(N_e) $\approx$ 11.5 almost independently of time. We conclude that the non-Maxwellian effects are important and should be taken into account when analyzing solar flare observations, including spectroscopic and imaging ones., Comment: The Astrophysical Journal, accepted

This paper focuses on the modal analysis of laminated glass beams. In these multilayer elements, the stiff glass plates are connected by compliant interlayers with frequency/temperature-dependent behavior. The aim of our study is (i) to assess whether approximate techniques can accurately predict the behavior of laminated glass structures and (ii) to propose an easy tool for modal analysis based on the enhanced effective thickness concept by Galuppi and Royer-Carfagni. To this purpose, we consider four approaches to the solution of the related nonlinear eigenvalue problem: a complex-eigenvalue solver based on the Newton method, the modal strain energy method, and two effective thickness concepts. A comparative study of free vibrating laminated glass beams is performed considering different geometries of cross-sections, boundary conditions, and material parameters for interlayers under two ambient temperatures. The viscoelastic response of polymer foils is represented by the generalized Maxwell model. We show that the simplified approaches predict natural frequencies with an acceptable accuracy for most of the examples. However, there is a considerable scatter in predicted loss factors. The enhanced effective thickness approach adjusted for modal analysis leads to lower errors in both quantities compared to the other two simplified procedures, reducing the extreme error in loss factors to one half compared to the modal strain energy method or to one quarter compared to the original dynamic effective thickness method., Comment: 31 pages, 12 figures, 10 tables

Laminated glass elements, which consist of stiff elastic glass layers connected with a compliant viscoelastic polymer foil, exhibit geometrically non-linear and time/temperature-sensitive behavior. In computational modeling, the viscoelastic effects are often neglected or a detailed continuum formulation typically based on the volumetric-deviatoric elastic-viscoelastic split is used for the interlayer. Four layerwise beam theories are introduced in this paper, which differ in the non-linear beam formulation at the layer level (von K\'{a}rm\'{a}n/Reissner) and in constitutive assumptions for the interlayer (a viscoelastic solid with the time-independent bulk modulus/Poisson ratio). We perform detailed verification and validation studies at different temperatures and compare the accuracy of the selected formulation with simplified elastic solutions used in practice. We show that all the four formulations predict very similar responses. Therefore, our suggestion is to use the most straightforward formulation that combines the von K\'{a}rm\'{a}n model with the assumption of time-independent Poisson ratio. The simplified elastic model mostly provides a response in satisfactory agreement with full viscoelastic solutions. However, it can lead to unsafe or inaccurate predictions for rapid changes of loading. These findings provide a suitable basis for extensions towards laminated plates and glass layer fracture, owing to the modular format of layerwise theories., Comment: 30 pages, 11 figures, 8 tables, 1 algorithm

We report on the SDO/AIA and Hinode/EIS observations of a transient coronal loop. The loop brightens up in the same location after the disappearance of an arcade formed during a B8.9-class microflare three hours earlier. EIS captures this loop during its brightening phase as observed in most of the AIA filters. We use the AIA data to study the evolution of the loop, as well as to perform the DEM diagnostics as a function of $\kappa$. Fe XI--XIII lines observed by EIS are used to perform the diagnostics of electron density and subsequently the diagnostics of $\kappa$. Using ratios involving the Fe XI 257.772\AA selfblend, we diagnose $\kappa$ $\lesssim$ 2, i.e., an extremely non-Maxwellian distribution. Using the predicted Fe line intensities derived from the DEMs as a function of $\kappa$, we show that, with decreasing $\kappa$, all combinations of ratios of line intensities converge to the observed values, confirming the diagnosed $\kappa$ $\lesssim$ 2. These results represent the first positive diagnostics of $\kappa$-distributions in the solar corona despite the limitations imposed by calibration uncertainties., Comment: The Astrophysical Journal, accepted

The non-Maxwellian $\kappa$-distributions have been detected in the solar transition region and flares. These distributions are characterized by a high-energy tail and a near-Maxwellian core and are known to have significant impact on the resulting optically thin spectra arising from collisionally dominated astrophysical plasmas. We developed the KAPPA package (http://kappa.asu.cas.cz) for synthesis of such line and continuum spectra. The package is based on the freely available CHIANTI database and software, and can be used in a similar manner. Ionization and recombination rates together with the ionization equilibria are provided for a range of $\kappa$ values. Distribution-averaged collision strengths for excitation are obtained by an approximate method for all transitions in all ions available within CHIANTI. The validity of this approximate method is tested by comparison with direct calculations. Typical precisions of better than 5% are found, with all cases being within 10%. Tools for calculation of synthetic line and continuum intensities are provided and described. Examples of the synthetic spectra and SDO/AIA responses to emission for the $\kappa$-distributions are given., Comment: The Astrophysical Journal Supplement Series, accepted

Laminated glass units exhibit complex response as a result of different mechanical behavior and properties of glass and polymer foil. We aim to develop a finite element model for elastic laminated glass plates based on the refined plate theory by Mau. For a geometrically nonlinear description of the behavior of units, each layer behaves according to the Reissner-Mindlin kinematics, complemented with membrane effects and the von K\'{a}rm\'{a}n assumptions. Nodal Lagrange multipliers enforce the compatibility of independent layers in this approach. We have derived the discretized model by the energy-minimization arguments, assuming that the unknown fields are approximated by bi-linear functions at the element level, and solved the resulting system by the Newton method with consistent linearization. We have demonstrated through verification and validation examples that the proposed formulation is reliable and accurately reproduces the behavior of laminated glass units. This study represents a first step to the development of a comprehensive, mechanics-based model for laminated glass systems that is suitable for implementation in common engineering finite element solvers., Comment: 22 pages, 10 figures, 3 tables

Laminated glass structures are formed by stiff layers of glass connected with a compliant plastic interlayer. Due to their slenderness and heterogeneity, they exhibit a complex mechanical response that is difficult to capture by single-layer models even in the elastic range. The purpose of this paper is to introduce an efficient and reliable finite element approach to the simulation of the immediate response of laminated glass beams. It proceeds from a refined plate theory due to Mau (1973), as we treat each layer independently and enforce the compatibility by the Lagrange multipliers. At the layer level, we adopt the finite-strain shear deformable formulation of Reissner (1972) and the numerical framework by Ibrahimbegovi\'{c} and Frey (1993). The resulting system is solved by the Newton method with consistent linearization. By comparing the model predictions against available experimental data, analytical methods and two-dimensional finite element simulations, we demonstrate that the proposed formulation is reliable and provides accuracy comparable to the detailed two-dimensional finite element analyzes. As such, it offers a convenient basis to incorporate more refined constitutive description of the interlayer., Comment: Moderate revisions; 17 pages, 6 figures, 8 tables

This contribution presents a simple Finite Element model aimed at efficient simulation of layered glass units. The adopted approach is based on considering independent kinematics of each layer, tied together via Lagrange multipliers. Validation and verification of the resulting model against independent data demonstrate its accuracy, showing its potential for generalization towards more complex problems., Comment: 10 pages, 3 figures