adsabs/FOCAL huggingface dataset:
The RADYN code (Carlsson & Stein 1992, 1995, 1997; Allred et al. 2015) is a one-dimensional radiative hydrodynamic code that can be used to study the interaction of particle beams with the solar atmosphere. It uses the Fokker–Planck formalism (McTiernan & Petrosian 1990), which takes into account the beam energy losses due to Coulomb collisions and pitch-angle diffusion when incorporating relativistic effects. RADYN includes a six-level hydrogen atom, a nine-level helium atom, and a six-level calcium atom. A return current has also been included in the simulations. We generated a set of models that simulates the conditions in the solar atmosphere during weak to intense WLFs. The beam fluxes used had values of 3 × 109, 1 × 1010, and 3 × 1010 erg cm−2 s−1, while the low-energy cutoff EC covered the parameter space where flare values are usually found (20–120 keV; Warmuth & Mann 2016). The spectral index δ was equal to 3 for all models. The beams were applied continuously and the outputs were analyzed at t = 20 s. This value is consistent with the X-ray analysis of the best observed type II WLF to date (Procházka et al. 2018). The initial atmosphere used in this work has the transition region placed at a height of 1200 km above the photospheric floor and has a coronal temperature of 3 MK at 10 Mm (QS.SL.HT loop described in Allred et al. 2015). The beams were injected at the top of a half-loop with a Gaussian distribution with an HWHM of 235. Line synthesis was carried out using the RH code (Uitenbroek 2001) incorporating partial redistribution that is particularly important for resonance line profiles. We used the 20-level hydrogen atom and the 6-level calcium atom to produce synthetic spectra for the Lyman and Balmer line and continuum diagnostics. A VOIGT profile was used for Ca ii K line, Lyman γ the higher-order Lyman lines. The Ca ii H and Lyα and β profiles were modeled in PRD. The Balmer lines had profiles of type VOIGT_VCS_STARK, which incorporates the unified Stark effect theory (Kowalski et al. 2017). The spectra were synthesized by setting a minimal spectral resolution of 0.05 nm.
Citation: Warmuth & Mann 2016
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In the present survey of GCSs in BCGs, we use the color index 





 (from here on we drop the accents on the SDSS indices). In the following discussion it will be useful to have a calibration of this index versus cluster metallicity [Fe/H]. To do this, we would ideally need to have GC photometry of the same clusters in both the Kron-Cousins and SDSS systems, in addition to spectroscopically based metallicity measurements. At present, there are no ideal solutions to that problem. Galaxies satisfying all three of these criteria are rare; in principle the Milky Way GC databases could be used, but cluster-to-cluster foreground reddenings differ strongly, the published SDSS indices (Vanderbeke et al. 2014) show considerable scatter versus metallicity, and the variety of studies from which the UBVRI indices were derived are completely different from the SDSS survey, so that aperture-size mismatches are significant. Similar problems affect the M31 GC sample. The best option at the present time for developing a 





 transformation is likely to be from the nearby early-type giant galaxy NGC 5128: here, UBVRI photometry is available from Peng et al. (2004), griz photometry from Sinnott et al. (2010), and [Fe/H] values derived through 





 from Woodley et al. (2010); these [Fe/H] values are in turn well correlated with the Sloan-system spectroscopic index [MgFe]’ (see Woodley et al.). We have extracted the GCs in common from these three catalogs, with the results shown in Figure 1. The great majority of these GCs lie well outside the central few kiloparsecs of NGC 5128 and thus are unaffected by the well-known dust lane. We have therefore applied only the foreground reddening of the Galaxy, for which we adopt 





 (Cardelli et al. 1989) to obtain the intrinsic colors. We note, however, that the UBVRI measurements were done on 





 aperture diameters corrected to 





 through median curves of growth (Peng et al. 2004), while the griz measures were done through 





 apertures (Sinnott et al. 2010), which means that a small aperture mismatch may exist here as well that affects the zero-point of 





.
Citation: Vanderbeke et al. 2014
Citation function: Compare/Contrast; Compare/Contrast
Since the perturbation in equation (22) is not conservative, we shall focus on the extension of Noether's theorem to non-conservative systems by Djukic & Vujanovic (1975). It must be $F_i-q^\prime _if\ne 0$ for the conservation law to hold (Vujanovic, Strauss & Jones 1986). For the case of non-conservative systems the generators Fi, f, and the gauge Ψ need to satisfy the following relation:

(29)

\begin{eqnarray}
&amp;&amp;{\sum _i\left\lbrace \left( \frac{\mathrm{\partial} {\scr {L}}}{\mathrm{\partial} {q_i}} \right) F_i + \left(\frac{\mathrm{\partial} {\scr {L}}}{\mathrm{\partial} {q^\prime _i}} \right)( {F}^\prime _i - q^\prime _i{f}^\prime ) + Q_i(F_i-q^\prime _if)\right\rbrace} \nonumber\\
&amp;&amp;{\quad+ f^\prime \scr {L} + f\frac{\mathrm{\partial} {\scr {L}}}{\mathrm{\partial} {\tau }} = {\Psi }^\prime .}
\end{eqnarray}

This equation and the condition $F_i-q^\prime _if\ne 0$ furnish the generalized NBH equations (Trautman 1967; Djukic & Vujanovic 1975; Vujanovic et al. 1986). The NBH equations involve the full derivative of the gauge function and the generators with respect to τ, meaning that equation (29) depends on the partial derivatives of Ψ, Fi, and f with respect to time, the coordinates, and the velocities. By expanding the convective terms the NBH equations decompose in the system of Killing equations:

(30)

\begin{eqnarray}
&amp;&amp;{ \scr {L} \frac{\mathrm{\partial} {f}}{\mathrm{\partial} {q_j^\prime }} +\sum _i \frac{\mathrm{\partial} {\scr {L}}}{\mathrm{\partial} {q^\prime _i}}\left( \frac{\mathrm{\partial} {F_i}}{\mathrm{\partial} {q_j^\prime }} - q^\prime _i\frac{\mathrm{\partial} {f}}{\mathrm{\partial} {q_j^\prime }} \right) = \frac{\mathrm{\partial} {\Psi }}{\mathrm{\partial} {q_j^\prime }},} \nonumber \\
&amp;&amp;{ \frac{\mathrm{\partial} {}}{\mathrm{\partial} {\tau }}(f\scr {L} - \Psi ) + \sum _i \Bigg\lbrace \frac{\mathrm{\partial} {\scr {L}}}{\mathrm{\partial} {q_i}}F_i + \scr {L}\frac{\mathrm{\partial} {f}}{\mathrm{\partial} {q_i}}q_i^\prime + Q_i(F_i-q_i^\prime f)+ \frac{\mathrm{\partial} {\scr {L}}}{\mathrm{\partial} {q_i^\prime }}} \nonumber \\
&amp;&amp;{\times\, \left[ \frac{\mathrm{\partial} {F_i}}{\mathrm{\partial} {\tau }} - q_i^\prime \frac{\mathrm{\partial} {f}}{\mathrm{\partial} {\tau }} + \sum _j\left( \frac{\mathrm{\partial} {F_i}}{\mathrm{\partial} {q_j}}q_j^\prime - q_i^\prime q_j^\prime \frac{\mathrm{\partial} {f}}{\mathrm{\partial} {q_j}} \right) \right] - \frac{\mathrm{\partial} {\Psi }}{\mathrm{\partial} {q_i}}q_i^\prime \Bigg \rbrace = 0.}\nonumber\\
\end{eqnarray}
The system (30) decomposes in three equations that can be solved for the generators Fρ, Fθ, and f given a certain gauge. If the transformation defined in equation (26) satisfies the NBH equations, then the system admits the integral of motion (28).
Citation: Trautman 1967
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A well-studied way to look at antenna spectral requirements is from the perspective of foreground avoidance in power spectrum space. In the avoidance scheme, smooth-spectrum foregrounds should, in the ideal case, occupy a wedge–shaped region of the two–dimensional power spectrum space (where the wavenumber k can be decomposed into k⊥ and $k_\Vert$ that are the transverse and line-of-sight wave numbers, respectively) whereas the remaining area – the so-called EoR window – is dominated by the 21 cm emission (Datta, Bowman & Carilli 2010; Morales et al. 2012; Trott, Wayth & Tingay 2012; Vedantham, Udaya Shankar & Subrahmanyan 2012; Thyagarajan et al. 2013; Liu, Parsons & Trott 2014a,b). Sources have most of their emission at low k∥ values although, due to the inherent chromatic interferometric response, this area increases with baseline length to resemble a characteristic wedge-like shape (Parsons et al. 2012; Trott et al. 2012; Vedantham et al. 2012; Liu et al. 2014a,b; Thyagarajan et al. 2015). In the most optimistic scenario, the EoR power spectrum can be directly measured in the EoR window, whose boundaries are set by the so-called horizon limit, i.e. the maximum delay that an astrophysical signal can experience, given by the separation of the two receiving elements. In practice, the boundaries of the EoR window can be narrowed by a number of mechanisms that spread power from the foreground dominated region into the EoR window, in particular calibration errors (Barry et al. 2016; Patil et al. 2016), leakage of foreground polarization (Bernardi et al. 2010; Jelić et al. 2010; Moore et al. 2013; Asad et al. 2015, 2016) and intrinsic chromaticity of the instrumental response. Recent attention has indeed been given to simulate and characterize the element response, particularly for the HERA (DeBoer et al. 2017), realizing that it may be one of the critical items responsible for spilling power from the wedge into the EoR window.
Citation: Morales et al. 2012
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The H α studies of Umeda et al. (2004) and Stroe et al. (2014a, 2015) are tracing instantaneous (averaged over 10 Myr) SF and little is known about SF on longer time-scales and the reservoir of gas that would enable future SF. An excellent test case for studying the gas content of galaxies within merging clusters with shocks is CIZA J2242.8+5301 (Kocevski et al. 2007). For this particular cluster unfortunately, its location in the Galactic plane, prohibits studies of the rest-frame UV or FIR tracing SF on longer time-scales, as the emission is dominated by Milky Way dust. However, the rich multiwavelength data available for the cluster give us an unprecedented detailed view on the interaction of their shock systems with the member galaxies. CIZA J2242.8+5301 is an extremely massive (M200 ∼ 2 × 1015 M⊙; Dawson et al. 2015; Jee et al. 2015) and X-ray disturbed cluster (Akamatsu & Kawahara 2013; Ogrean et al. 2013, 2014) which most likely resulted from a head-on collision of two, equal-mass systems (van Weeren et al. 2011; Dawson et al. 2015). The cluster merger induced relatively strong shocks, which travelled through the ICM, accelerated particles to produce relics towards the north and south of the cluster (van Weeren et al. 2010; Stroe et al. 2013). There is evidence for a few additional smaller shock fronts throughout the cluster volume (Stroe et al. 2013; Ogrean et al. 2014). Of particular interest is the northern relic, which earned the cluster the nickname ‘Sausage’. The relic, tracing a shock of Mach number M ∼ 3 (Stroe et al. 2014c), is detected over a spatial extent of ∼1.5 Mpc in length and up to ∼150 kpc in width and over a wide radio frequency range (150 MHz–16 GHz; Stroe et al. 2013, 2014b). There is evidence that the merger and the shocks shape the evolution of cluster galaxies. The radio jets are bent into a head–tail morphology aligned with the merger axis of the cluster. This is probably ram pressure caused by the relative motion of galaxies with respect to the ICM (Stroe et al. 2013). The cluster was also found to host a high fraction of H α emitting galaxies (Stroe et al. 2014a, 2015). The cluster galaxies not only exhibit increased SF and AGN activity compared to their field counterparts, but are also more massive, more metal rich and show evidence for outflows likely driven by SNe (Sobral et al. 2015). Stroe et al. (2015) and Sobral et al. (2015) suggest that these relative massive galaxies (stellar masses of up to ∼1010.0–10.7 M⊙) retained the metal-rich gas, which was triggered to collapse into dense star-forming clouds by the passage of the shocks, travelling at speeds up to ∼2500 km s−1 (Stroe et al. 2014c), in line with simulations by Roediger et al. (2014).
Citation: Stroe et al. 2013
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Citation: Stroe et al. 2013
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Citation: Stroe et al. 2013
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There are some existing studies applying machine learning to transient studies. For example, the spectral types of the SNe can be classified based on their light-curve data (Möller et al. 2016; Muthukrishna et al. 2019a; Takahashi et al. 2020; Villar et al. 2020), and transients can be identified from the astronomical survey images (Goldstein et al. 2015; Mahabal et al. 2019; Gómez et al. 2020). The light curves of SNe Ia can be well modeled by functional principal component analysis (FPCA; He et al. 2018), where it was shown remarkably that a set of FPCA eigenvectors that are independent of the photometric filters can be derived from the observed light curves of SNe Ia. There are a few studies of the application of deep learning neural networks to the spectral data of SNe. For example, Muthukrishna et al. (2019b) used a convolutional neural network (CNN) for automated SN type classification based on SN spectra. Several other works (Chen et al. 2020; Vogl et al. 2020; Kerzendorf et al. 2021) applied a Gaussian process, principal component analysis (PCA), and deep learning neural networks to radiative transfer models of SNe. Sasdelli et al. (2016) used unsupervised learning algorithms to investigate the subtypes of SNe Ia. Stahl et al. (2020) developed neural networks to predict the photometric properties of SNe Ia (phase and Δm
15) based on spectroscopic data. Saunders et al. (2018) used PCA to find low dimensional representations of the spectral sequences of 140 well-observed SNe Ia. Chen et al. (2020), in particular, built an artificial intelligence assisted inversion (AIAI) of radiative transfer models and used that to link the observed SN spectra with theoretical models. The AIAI is able to retrieve the elemental abundances and density and temperature profiles from observed SN spectra. The AIAI approach has the potential for quantitatively coupling complex theoretical models with the ever-increasing amount of high-quality observational data.
Citation: Vogl et al. 2020
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In the past, as well as in the more recent literature, there have been many attempts to explain the different chemical evolutionary paths of different MW components, particular those of the thin and thick discs. The outcome of these studies is that the observed different chemical evolutionary paths are related to differences in the main physical processes that drive galaxy evolution, the most significant of which are the gas accretion time-scale and the star formation efficiency and, possibly, radial migration (Larson 1972; Lynden-Bell 1975; Pagel & Edmunds 1981; Matteucci & Greggio 1986; Matteucci & Brocato 1990; Ferrini et al. 1994; Prantzos & Aubert 1995; Chiappini et al. 1997, 2001; Portinari & Chiosi 1999; Bekki & Tsujimoto 2011; Micali et al. 2013; Sahijpal 2014; Snaith et al. 2014; Grisoni et al. 2017; Grand et al. 2018; Spitoni et al. 2021). A good agreement between observations and theoretical predictions for the Galaxy is obtained by models that are based on the assumption that the disc formed via the infalling of gas (Chiosi 1980; Matteucci & Francois 1989; Chiappini et al. 1997). The formation of the different components is associated with distinct sequential main episodes of gas accretion (infall phases) that, at first, rapidly accumulates in the central regions and then, more slowly, in the more external ones, according to the so-called ‘inside-out scenario’ (Chiappini et al. 2001). In particular, the three-infall model, devised by Micali et al. (2013), is capable of reproducing the abundance patterns of the MW halo, thick and thin disc at once. In this model, the halo forms in a first gas infall episode of short timescale (0.2 Gyr) and mild star formation efficiency, ν = 2 Gyr−1, lasting for about 0.4 Gyr. It is immediately followed by the thick disc formation, characterised by a somewhat longer infall timescale (1.2 Gyr), a longer duration (about 2 Gyr) and a higher star formation efficiency (ν = 10 Gyr−1). Finally, star formation continues in the thin disc with a longer infall timescale (6 Gyr in the solar vicinity) and is still continuing to this day, with a star-formation efficiency of ν = 1 Gyr−1. The [O/Fe] vs. [Fe/H] path is thus continuous across the regions populated by halo, thick, and thin disc stars. While Micali et al. (2013) described the chemical enrichment as continuous across the three different infall stages, Grisoni et al. (2017) used also an alternative scheme where the thin and thick disc components evolve separately, in a parallel approach (see also Chiappini 2009). In such a parallel approach, the disc populations are assumed to form in parallel but to proceed at different rates. The gas infall exponentially decreases with a timescale that is 0.1 Gyr and 7 Gyr, for the thick and thin disc, respectively. This alternative approach better reproduces the presence of the metal-rich α-enhanced stars in the [Mg/Fe] vs. [Fe/H] diagram obtained with the recent AMBRE data (Mikolaitis et al. 2017).
Citation: Chiosi 1980
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Exploration of the stationary points of the [H, P, S, O] molecular system was initially carried out using Møller–Plesset second order Perturbation Theory (MP2) (Møller & Plesset 1934; Frisch et al. 1990a,b; Head-Gordon & Head-Gordon 1994; Head-Gordon et al. 1988; Sæbø & Almlöf 1989) with the 6-311++G(d, p) basis set (McLean & Chandler 1980; Krishnan et al. 1980). Following the initial survey, transition state structures connecting various isomers of [H, P, S, O] were located using MP2/6-311++G(d, p) and confirmed via an intrinsic reaction coordinate (IRC) calculation. To achieve a quantitative picture of the ground state potential energy surface, coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)] (Knowles et al. 1993, 2000) single point calculations employing the aug-cc-pV(Q+d)Z basis set were performed at the MP2 equilibrium geometries. Entrance channel pathways were explored via relaxed scans and individual searches for transition states. Following this, higher level calculations on the electronic structure, rotational constants, and harmonic vibrational frequencies of each isomer were performed using CCSD(T) together with the Dunning basis sets aug-cc-pV(X+d)Z (X = T, Q, 5) (Dunning 1989; Woon & Dunning 1993; Kendall et al. 1992), including additional tight d functions on the sulfur and phosphorous atoms (Dunning et al. 2001). CCSD(T) including all electrons was then performed using the second order Douglas-Kroll–Hess Hamiltonian in conjunction with the contracted relativistic Douglas–Kroll aug-cc-pwCVTZ-DK basis set to correct for scalar relativistic and core-correlation effects (Jorge et al. 2009). The aforementioned combinationof level of theory and basis set will be referred to as CCSD(T)-AE/TZ-DK. Finally, explicit correlation of the electrons was included using the CCSD(T)-F12b method (Werner et al. 2011) with the Dunning basis sets aug-cc-pVXZ (X = T, Q, 5). Single-reference character of the wavefunction was confirmed via single-state complete active spaceself-consistent field theory in addition to the coupled cluster T1 diagnostic. Energies and geometry parameters were then extrapolated to the complete basis set limit using the two-point (Q, 5) extrapolation scheme E(x)= ECBS + AX−3, where E(x) is the value calculated using the basis set of cardinal number X, ECBS is the extrapolated energy, and A is a parameter fit in the least-squares fitting procedure. Mulliken population analysis was performed on cis-HOPS using MOLPRO. Corrections to the rotational constants, spectroscopic data, and anharmonic vibrational data were calculated for the four lowest energy isomers at the CCSD(T)/aug-cc-pV(T+d)Z level of theory using CFOUR (Matthews et al. 2020; Stanton et al. 2019). Permanent dipole moments for each isomer were calculated using the finite field method (field strengths of 0, 0.005, and −0.005 au) as implemented in MOLPRO.
Citation: Kendall et al. 1992
Citation function: Uses
There are three possible explanations for the origin of these systems: (1) they formed from the fragmentation of the same molecular cloud (Elmegreen & Elmegreen 1983), (2) they were generated in distinct molecular clouds and then became bound systems after a close encounter leading to a tidal capture (Vallenari, Bettoni & Chiosi 1998; Leon, Bergond & Vallenari 1999), or (3) they are the result of division of a single star-forming region (Goodwin & Whitworth 2004; Arnold et al. 2017). Their subsequent evolution may also have different outcomes. Dynamical models and N-body simulations (see, e.g., Barnes & Hut 1986; de Oliveira, Dottori & Bica 1998, and references therein) have shown that, depending on the initial conditions, a bound pair of clusters may either become unbound, because of significant mass-loss in the early phases of stellar evolution, or merge into a single and more massive cluster on a short time-scale (≈60 Myr) due to loss of angular momentum from escaping stars (see Portegies Zwart & Rusli 2007). The final product of a merger may be characterized by a variable degree of kinematic and morphologic complexity, mostly depending on the values of the impact parameter of the pre-merger binary system (de Oliveira, Bica & Dottori 2000; Priyatikanto et al. 2016). In some cases, the stellar system resulting from the merger event may show significant internal rotation (in fact, for many years this has been the preferred dynamical route to form rotating star clusters; see Sugimoto & Makino 1989; Makino, Akiyama & Sugimoto 1991; Okumura, Ebisuzaki & Makino 1991; de Oliveira, Dottori & Bica 1998). Merger of cluster pairs has been sometimes invoked to interpret the properties of particularly massive and dynamically complex clusters (e.g. see the study of ω Centauri by Lee et al. 1999, G1 by Baumgardt et al. 2003 and NGC  2419 by Brüns & Kroupa 2011), and, more in general, as an avenue to form clusters with multiple populations with different chemical abundances both in terms of iron and light elements (e.g. van den Bergh 1996; Catelan 1997; Amaro-Seoane et al. 2013; Gavagnin, Mapelli & Lake 2016; Hong et al. 2017).
Citation: de Oliveira, Dottori & Bica 1998
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Citation: de Oliveira, Dottori & Bica 1998
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