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The propagation of electromagnetic waves in a linearly-varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact solution is obtained for a given incoming wavefield specified on the boundary transverse to the direction of inhomogeneity by performing a spectral, rather than asymptotic, matching. Two case studies are then presented: a Gaussian beam at oblique incidence and a speckled wavefield at normal incidence. For the Gaussian beam, it is shown that when the waist $W$ is sufficiently large, oblique incidence manifests simply as rigid translation and focal shift of the corresponding diffraction pattern at normal incidence. The destruction of the hyperbolic umbilic caustic (corresponding to a critically focused beam) as $W$ is reduced is then demonstrated. The caustic disappears once $W \lesssim \delta_a \sqrt{L}$ ($L$ being the medium lengthscale normalized by the Airy skin depth $\delta_a$), at which point the wave behavior is increasingly described by Airy functions, but experiences less focusing as a result. To maximize the intensity of a launched Gaussian beam at a turning point, one should therefore minimize the imaginary part of the launched complex beam parameter while having the real part satisfy critical focusing. For the speckled wavefield, it is shown that the transverse speckle pattern only couples to the Airy longitudinal pattern when the coupling parameter $\eta = \sqrt{L}/f_\#$ is large, with $f_\#$ being the f-number of the launching aperture. When $\eta \ll 1$, a reduced description of the total wavefield can be obtained by simply multiplying the incoming speckle pattern with the Airy swelling., Comment: 16 pages, 8 figures, 2 appendices. Submission to special issue on contributions to EFTC 2023

High-beta magnetized plasmas often exhibit anomalously structured temperature profiles, as seen from galaxy cluster observations and recent experiments. It is well known that when such plasmas are collisionless, temperature gradients along the magnetic field can excite whistler waves that efficiently scatter electrons to limit their heat transport. Only recently has it been shown that parallel temperature gradients can excite whistler waves also in collisional plasmas. Here we develop a Wigner--Moyal theory for the collisional whistler instability starting from Braginskii-like fluid equations in a slab geometry. This formalism is necessary because, for a large region in parameter space, the fastest-growing whistler waves have wavelengths comparable to the background temperature gradients. We find additional damping terms in the expression for the instability growth rate involving inhomogeneous Nernst advection and resistivity. They (i) enable whistler waves to re-arrange the electron temperature profile via growth, propagation, and subsequent dissipation, and (ii) allow non-constant temperature profiles to exist stably. For high-beta plasmas, the marginally stable solutions take the form of a temperature staircase along the magnetic field lines. The electron heat flux can also be suppressed by the Ettingshausen effect when the whistler intensity profile is sufficiently peaked and oriented opposite the background temperature gradient. This mechanism allows cold fronts without magnetic draping, might reduce parallel heat losses in inertial fusion experiments, and generally demonstrates that whistler waves can regulate transport even in the collisional limit., Comment: 40 pages (31 pages main article), 15 figures, 7 appendices

Metaplectic geometrical optics (MGO) is a recently developed ray-tracing framework to accurately compute the wavefield behavior near a caustic (turning point or focal point), where traditional ray-tracing breaks down. However, MGO has thus far been restricted to having real-valued wavevectors. This is disadvantageous because often upon crossing a caustic from the `illuminated' region to the `shadow' region, two real-valued rays coalesce into one complex-valued ray corresponding to the transition from propagating to evanescent behavior. One can distinguish caustics as having either `illuminated shadows' or `proper shadows' -- the former corresponds to when the shadow still contains real-valued rays (albeit in a fewer quantity than in the illuminated region), while the latter corresponds to when the shadow contains no real-valued rays. Here, by means of examples, we show how MGO can be used to model both types of shadows. First, for illuminated shadows we show that MGO can actually be used `as is', provided a corrected quadrature-angle bias is used compared to that proposed in the original references. This is then implemented and demonstrated in a recently developed MGO ray-tracing code. Second, we show that for proper shadows, the MGO formalism can still be used if the symplectic rotation matrix that removes caustics along rays is allowed to be complex-valued. In both cases, strong agreement is seen between the MGO and the exact solution, demonstrating the potential of MGO for improving the predictive capability of ray-tracing codes and laying the foundations for modeling more complicated evanescent phenomena such as tunnelling with MGO., Comment: 10 pages, 5 figures, 2 appendices. Minor changes to figures and text. Added journal reference

The scrape-off layer parallel heat flux decay lengths measured at ST40, a high field, low aspect ratio spherical tokamak, have been observed to bifurcate into two groups. The wide group matches closely with the scale of ion poloidal Larmour radius and follows existing H-mode scalings, while the narrow group falls up to 10 times below scalings, on the scale of ion total Larmour radius. The onset of the narrow scrape-off layer width is observed to be associated with suppressed magnetic fluctuations, suggesting reduced electromagnetic turbulence levels in the SOL., Comment: 6 pages, 4 figures

Context. Dust polarization observations of the massive protocluster G31.41+0.31 carried out at ~1'' (~3750 au) resolution with the SMA at 870 microm have revealed one of the clearest examples to date of an hourglass-shaped magnetic field morphology in the high-massregime. Additionally, ~0.24'' (~900 au) resolution observations with ALMA at 1.3 mm have confirmed these results. The next step is to investigate whether the magnetic field maintains its hourglass-shaped morphology down to circumstellar scales. Aims. To study the magnetic field morphology toward the four (proto)stars A, B, C, and D contained in G31.41+0.31 and examine whether the self-similarity observed at core scales (1'' and 0.24'' resolution) still holds at circumstellar scales, we carried out ALMA observations of the polarized dust continuum emission at 1.3 mm and 3.1 mm at an angular resolution of ~0.068'' (~250 au), sufficient to resolve the envelope emission of the embedded protostars. Methods. We used ALMA to perform full polarization observations at 233 GHz (Band 6) and 97.5 GHz (Band 3) with a synthesized beam of 0.072'' x 0.064''. We carried out polarization observations at two different wavelengths to confirm that the polarization traces magnetically aligned dust grains and is not due to dust self-scattering. Results. The polarized emission and the direction of the magnetic field obtained at the two wavelengths are basically the same, except for an area between the embedded sources C and B. In such an area, the emission at 1.3 mm could be optically thick and affected by dichroic extinction. ..., Comment: 15 pages, 15 figures, Accepted for publication in A&A

A bipartite graph $G=(V,E)$ with $V=V_1\cup V_2$ is biregular if all the vertices of each stable set, $V_1$ and $V_2$, have the same degree, $r$ and $s$, respectively. This paper studies difference sets derived from both Abelian and non-Abelian groups. From them, we propose some constructions of bipartite biregular graphs with diameter $d=3$ and asymptotically optimal order for given degrees $r$ and $s$. Moreover, we find some biMoore graphs, that is, bipartite biregular graphs that attain the Moore bound.

Only indirect evidence of the role of magnetic braking in regulating gravitational collapse and the formation of circumstellar disks was found from observational work, such as compact disk sizes and the launching of high-velocity collimated protostellar jets. More direct tests of the magnetic braking shaping the angular momentum (AM) of the gas in Class 0 protostars are crucially needed. In the present work we have used non-ideal MHD models of protostellar collapse and synthetic observations of molecular gas spectral emission that we analyze to test whether possible kinematic signatures of the magnetic braking in the gas velocity field can be captured from maps of the molecular gas emission in protostellar envelopes. By comparing the 3D Specific AM of models with varying turbulent energy and magnetization, we show that, in the numerical models of protostellar evolution explored, the increase in magnetization and its consequences on the spatial redistribution of SAM modifies the shapes of the radial profiles of SAM. We show that widely used observational methods fail to quantitatively capture the magnitude of SAM of the gas in protostellar envelopes, and that no method allows to measure the differences in radial evolution of SAM due to different magnetization at all envelope radii. This is especially true in the more magnetized cases. However, our analysis suggests that the detection of symmetric patterns and organized velocity fields, in the moment-1 maps of the molecular line emission as well as monotonous radial profiles of the SAM showing a power-law decline, should be suggestive of a less magnetized scenario. Protostellar cores where efficient magnetic braking is at work are more likely to present a highly asymmetric velocity field, and more prone to show complex radial profiles of their specific angular momentum measured in the equatorial plane., Comment: Accepted A&A, 19 pages, 10 figures

Background and objective Risk prediction models aim at identifying people at higher risk of developing a target disease. Feature selection is particularly important to improve the prediction model performance avoiding overfitting and to identify the leading cancer risk (and protective) factors. Assessing the stability of feature selection/ranking algorithms becomes an important issue when the aim is to analyze the features with more prediction power. Methods This work is focused on colorectal cancer, assessing several feature ranking algorithms in terms of performance for a set of risk prediction models (Neural Networks, Support Vector Machines (SVM), Logistic Regression, k-Nearest Neighbors and Boosted Trees). Additionally, their robustness is evaluated following a conventional approach with scalar stability metrics and a visual approach proposed in this work to study both similarity among feature ranking techniques as well as their individual stability. A comparative analysis is carried out between the most relevant features found out in this study and features provided by the experts according to the state-of-the-art knowledge. Results The two best performance results in terms of Area Under the ROC Curve (AUC) are achieved with a SVM classifier using the top-41 features selected by the SVM wrapper approach (AUC=0.693) and Logistic Regression with the top-40 features selected by the Pearson (AUC=0.689). Experiments showed that performing feature selection contributes to classification performance with a 3.9% and 1.9% improvement in AUC for the SVM and Logistic Regression classifier, respectively, with respect to the results using the full feature set. The visual approach proposed in this work allows to see that the Neural Network-based wrapper ranking is the most unstable while the Random Forest is the most stable.

Here I present a summarised description of the general behavior of waves near turning points. I show that when asymptotic matching to a prescribed incident wavefield is performed, the solution changes from being the Airy function to being more generally the hyperbolic umbilic function. This solution accounts for (de-)focusing of the incident wavefield due to gradient-index lensing in addition to the familiar Airy physics, which importantly do not superimpose. Possible applications to fusion research are discussed., Comment: Proceeding for 2023 EPS plasma physics conference

We present new Atacama Large (sub)Millimeter Array 0.98 mm observations of the continuum emission and several molecular lines toward the high-mass protostellar system GGD27-MM1, driving the HH 80-81 radio-jet. The detailed analysis of the continuum and the CH$_3$CN molecular emission allows us to separate the contributions from the dust content of the disk (extending up to 190 au), the molecular content of the disk (extending from 140 to 360 au), and the content of the envelope, revealing the presence of several possible accretion streamers (also seen in other molecular tracers, such as CH$_3$OH). We analyze the physical properties of the system, producing temperature and column density maps, and radial profiles for the disk and the envelope. We qualitatively reproduce the trajectories and line-of-sight velocities of the possible streamers using a theoretical model approach. An ad-hoc model of a flared disk comprising a hot dust disk embedded in cold gas fits the H$_2$S emission, which revealed the molecular disk as crescent-shape with a prominent central absorption. Another fit to the central absorption spectrum suggests that the absorption is probably caused by different external cold layers from the envelope or the accretion streamers. Finally, the analysis of the rotation pattern of the different molecular transitions in the molecular disk, suggests that there is an inner zone devoid of molecular content., Comment: 36 pages, 28 figures, 6 tables. Accepted by the ApJ

An $(r,z,k)$-mixed graph $G$ has every vertex with undirected degree $r$, directed in- and out-degree $z$, and diameter $k$. In this paper, we study the case $r=z=1$, proposing some new constructions of $(1,1,k)$-mixed graphs with a large number of vertices $N$. Our study is based on computer techniques for small values of $k$ and the use of graphs on alphabets for general $k$. In the former case, the constructions are either Cayley or lift graphs. In the latter case, some infinite families of $(1,1,k)$-mixed graphs are proposed with diameter of the order of $2\log_2 N$.

A wave near an isolated turning point is typically assumed to have an Airy function profile with respect to the separation distance. This description is incomplete, however, and is insufficient to describe the behavior of more realistic wavefields that are not simple plane waves. Asymptotic matching to a prescribed incoming wavefield generically introduces a phasefront curvature term that changes the characteristic wave behavior from the Airy function to that of the hyperbolic umbilic function. This function, which is one of the seven classic 'elementary' functions from catastrophe theory along with the Airy function, can be understood intuitively as the solution for a linearly focused Gaussian beam propagating in a linearly varying density profile, as we show. The morphology of the caustic lines that govern the intensity maxima of the diffraction pattern as one alters the density lengthscale of the plasma, the focal length of the incident beam, and also the injection angle of the incident beam are presented in detail. This morphology includes a Goos-H\"anchen shift and focal shift at oblique incidence that do not appear in a reduced ray-based description of the caustic. The enhancement of the intensity swelling factor for a focused wave compared to the typical Airy solution is highlighted, and the impact of finite lens aperture is discussed. Collisional damping and finite beam waist are included in the model and appear as complex components to the arguments of the hyperbolic umbilic function. The observations presented here on the behavior of waves near turning points should aid the development of improved reduced wave models to be used, for example, in designing modern nuclear fusion experiments., Comment: 12 pages, 7 figures, 3 appendices

Almost Moore mixed graphs\/} appear in the context of the degree/diameter problem as a class of extremal mixed graphs, in the sense that their order is one unit less than the Moore bound for such graphs. The problem of their existence has been considered just for diameter $2$. In this paper, we give a complete characterization of these extremal mixed graphs for diameters 2 and 3. We also derive some optimal constructions for other diameters.

The optimization of radiofrequency-wave (RF) systems for fusion experiments is often performed using ray-tracing codes, which rely on the geometrical-optics (GO) approximation. However, GO fails at caustics such as cutoffs and focal points, erroneously predicting the wave intensity to be infinite. This is a critical shortcoming of GO, since the caustic wave intensity is often the quantity of interest, e.g. RF heating. Full-wave modeling can be used instead, but the computational cost limits the speed at which such optimizations can be performed. We have developed a less expensive alternative called metaplectic geometrical optics (MGO). Instead of evolving waves in the usual $\textbf{x}$ (coordinate) or $\text{k}$ (spectral) representation, MGO uses a mixed $\textbf{X} \equiv \textsf{A}\textbf{x} + \textsf{B}\textbf{k}$ representation. By continuously adjusting the matrix coefficients $\textsf{A}$ and $\textsf{B}$ along the rays, one can ensure that GO remains valid in the $\textbf{X}$ coordinates without caustic singularities. The caustic-free result is then mapped back onto the original $\textbf{x}$ space using metaplectic transforms. Here, we overview the MGO theory and review algorithms that will aid the development of an MGO-based ray-tracing code. We show how using orthosymplectic transformations leads to considerable simplifications compared to previously published MGO formulas. We also prove explicitly that MGO exactly reproduces standard GO when evaluated far from caustics (an important property which until now has only been inferred from numerical simulations), and we relate MGO to other semiclassical caustic-removal schemes published in the literature. This discussion is then augmented by an explicit comparison of the computed spectrum for a wave bounded between two cutoffs., Comment: Invited paper for APS DPP 2021. 21 pages, 6 figures, 5 appendices

This paper introduces the Scrape-Off-Layer Fast Ion (SOLFI) code, which is a new and versatile full-orbit Monte Carlo particle tracer developed to follow fast ion orbits inside and outside the separatrix in tokamaks. SOLFI is benchmarked in a simple straight mirror geometry, showing that the code conserves particle energy and magnetic moment, obtains the correct passing boundary for particles moving in the magnetic mirror field with an imposed electrostatic field, and correctly observes equal ion and electron current at the ambipolar potential predicted from analytical theory. This result has consequences for collisionless scrape-off-layers in spherical tokamaks. We then utilize SOLFI for fundamental physics studies in novel tokamak geometries, exploring the effect of shaping on the trapped particle fraction and bounce locations in tokamaks and demonstrating that negative triangularity can be used to maximize the fraction of particles bouncing in the good-curvature region, potentially leading to enhanced confinement., Comment: 14 pages, 10 figures

A wide range of n- and p-type doping levels in GaAs layers grown by chemical beam epitaxy is achieved using H$_{2}$-diluted DTBSi and CBr$_{4}$ as gas precursors for Si and C. We show that the doping level can be varied by modifying either the concentration or the flux of the diluted precursor. Specifically, we demonstrate carrier concentrations of 6$\times$10$^{17}$-1.2$\times$10$^{19}$ cm$^{-3}$ for Si, and 9$\times$10$^{16}$-3.7$\times$10$^{20}$ cm$^{-3}$ for C, as determined by Hall effect measurements. The incorporation of Si and C as a function of the flux of the corresponding diluted precursor is found to follow, respectively, a first and a fourth order power law. The dependence of the electron and hole mobility values on the carrier concentration as well as the analysis of the layers by low-temperature (12 K) photoluminescence spectroscopy indicate that the use of H$_{2}$ for diluting DTBSi or CBr$_{4}$ has no effect on the electrical and optical properties of GaAs.

The metaplectic transform (MT), a generalization of the Fourier transform sometimes called the linear canonical transform, is a tool used ubiquitously in modern optics, for example, when calculating the transformations of light beams in paraxial optical systems. The MT is also an essential ingredient of the geometrical-optics modeling of caustics that was recently proposed by the authors. In particular, this application relies on the near-identity MT (NIMT); however, the NIMT approximation used so far is not exactly unitary and leads to numerical instability. Here, we develop a discrete MT that is exactly unitary, and approximate it to obtain a discrete NIMT that is also unitary and can be computed in linear time. We prove that the discrete NIMT converges to the discrete MT when iterated, thereby allowing the NIMT to compute MTs that are not necessarily near-identity. We then demonstrate the new algorithms with a series of examples., Comment: 10 pages, 3 figures, 1 appendix

B-fields are predicted to play a role in the formation of filamentary structures and their fragmentation process. We aim at investigating the role of the B-field in the process of core fragmentation toward the hub-filament systems in the IRDC G14.2, which present different fragmentation level. We performed observations of the thermal dust polarization at 350 {\mu}m using the CSO toward the hubs. We applied the polarization--intensity-gradient method to estimate the significance of the B-field over the G-force. The B-field in Hub-N shows a uniform structure along the E-W orientation, perpendicular to the major axis of the hub-filament system. The I-gradient in Hub-N displays a local minimum coinciding with the dust core MM1a detected with interferometric observations. The B-field orientation is perturbed when approaching the dust core. Hub-S shows 2 local minima, reflecting the bimodal distribution of the B-field. In Hub-N, both E and W of the hub-filament system, the I-gradient and the B-field are parallel whereas they tend to be perpendicular when penetrating the filaments and hub. The analysis of the {\delta}- and {\Sigma} B-maps indicate that, the B-field cannot prevent the collapse, suggesting that the B-field is initially dragged by the infalling motion and aligned with it, or is channeling material toward the central ridge from both sides. Values of {\Sigma} B > 1 are found toward a N-S ridge encompassing the dust emission peak, indicating that in this region B-field dominates over G-force, or that with the current angular resolution we cannot resolve an hypothetical more complex structure. We estimated the B-field strength, the MtF ratio and the A-M number, and found differences between the 2 hubs. The different levels of fragmentation observed in these 2 hubs could arise from the differences in the B-field properties rather than from different intensity of the G-field., Comment: 14 pages, 9 figures

As an approximate theory that is highly regarded for its computational efficiency, geometrical optics (GO) is widely used for modeling waves in various areas of physics. However, GO fails at caustics, which significantly limits its applicability. A new framework, called metaplectic geometrical optics (MGO), has recently been developed that allows caustics of certain types to be modeled accurately within the GO framework. Here, we extend MGO to the most general case. To illustrate our new theory, we also apply it to several sample problems, including calculations of two-dimensional wavefields near fold and cusp caustics. In contrast with traditional-GO solutions, the corresponding MGO solutions are finite everywhere and approximate well the true wavefield near these caustics., Comment: 14 pages, 3 figures, 3 appendices. Complete derivations in supplementary pdf

The Mondrian problem consists of dissecting a square of side length $n\in \NN$ into non-congruent rectangles with natural length sides such that the difference $d(n)$ between the largest and the smallest areas of the rectangles partitioning the square is minimum. In this paper, we compute some bounds on $d(n)$ in terms of the number of rectangles of the square partition. These bounds provide us optimal partitions for some values of $n \in \NN$. We provide a sequence of square partitions such that $d(n)/n^2$ tends to zero for $n$ large enough. For the case of `perfect' partitions, that is, with $d(n)=0$, we show that, for any fixed powers $s_1,\ldots, s_m$, a square with side length $n=p_1^{s_1}\cdots p_m^{s_m}$, can have a perfect Mondrian partition only if $p_1$ satisfies a given lower bound. Moreover, if $n(x)$ is the number of side lengths $x$ (with $n\le x$) of squares not having a perfect partition, we prove that its `density' $\frac{n(x)}{x}$ is asymptotic to $\frac{(\log(\log(x))^2}{2\log x}$, which improves previous results.

In this paper, we deal with a simple geometric problem: Is it possible to partition a rectangle into $k$ non-congruent rectangles of equal area? This problem is motivated by the so-called `Mondrian art problem' that asks a similar question for dissections with rectangles of integer sides. Here, we generalize the Mondrian problem by allowing rectangles of real sides. In this case, we show that the minimum value of $k$ for a rectangle to have a `perfect Mondrian partition' (that is, with non-congruent equal-area rectangles) is seven. Moreover, we prove that such a partition is unique (up to symmetries) and that there exist exactly two proper perfect Mondrian partitions for $k=8$. Finally, we also prove that any square has a perfect Mondrian decomposition for $k\ge 7$.

The massive star-forming region W75N~(B) is thought to host a cluster of massive protostars (VLA~1, VLA~2, and VLA~3) undergoing different evolutionary stages. In this work, we present radio continuum data with the highest sensitivity and angular resolution obtained to date in this region, using the VLA-A and covering a wide range of frequencies (4-48~GHz), which allowed us to study the morphology and the nature of the emission of the different radio continuum sources. We also performed complementary studies with multi-epoch VLA data and ALMA archive data at 1.3 mm wavelength. We find that VLA~1 is driving a thermal radio jet at scales of $\approx$0.1 arcsec ($\approx$130 au), but also shows signs of an incipient hyper-compact HII region at scales of $\lesssim$ 1 arcsec ($\lesssim$ 1300~au). VLA~3 is also driving a thermal radio jet at scales of a few tenths of arcsec (few hundred of au). We conclude that this jet is shock-exciting the radio continuum sources Bc and VLA~4 (obscured HH objects), which show proper motions moving outward from VLA~3 at velocities of $\approx$112--118~km/s. We have also detected three new weak radio continuum sources, two of them associated with millimeter continuum cores observed with ALMA, suggesting that these two sources are also embedded YSOs in this massive star-forming region., Comment: 14 pages, 7 figures. Accepted for publication in MNRAS

We consider the case in which mixed graphs (with both directed and undirected edges) are Cayley graphs of Abelian groups. In this case, some Moore bounds were derived for the maximum number of vertices that such graphs can attain. We first show these bounds can be improved if we know more details about the order of some elements of the generating set. Based on these improvements, we present some new families of mixed graphs. For every fixed value of the degree, these families have an asymptotically large number of vertices as the diameter increases. In some cases, the results obtained are shown to be optimal., Comment: arXiv admin note: text overlap with arXiv:1908.00245

Geometrical optics (GO) is often used to model wave propagation in weakly inhomogeneous media and quantum-particle motion in the semiclassical limit. However, GO predicts spurious singularities of the wavefield near reflection points and, more generally, at caustics. We present a new formulation of GO, called metaplectic geometrical optics (MGO), that is free from these singularities and can be applied to any linear wave equation. MGO uses sequenced metaplectic transforms of the wavefield, corresponding to symplectic transformations of the ray phase space, such that caustics disappear in the new variables, and GO is reinstated. The Airy problem and the quantum harmonic oscillator are studied analytically using MGO for illustration. In both cases, the MGO solutions are remarkably close to the exact solutions and remain finite at cutoffs, unlike the usual GO solutions., Comment: 19 pages, 9 figures, 3 appendices. This is the version of the article before peer review or editing, as submitted by an author to New Journal of Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1367-2630/aba91a

Recent high-angular resolution (40 mas) ALMA observations at 1.14 mm resolve a compact (R~200 au) flattened dust structure perpendicular to the HH 80-81 jet emanating from the GGD 27-MM1 high-mass protostar, making it a robust candidate for a true accretion disk. The jet/disk system (HH 80-81 / GGD 27-MM1) resemble those found in association with low- and intermediate-mass protostars. We present radiative transfer models that fit the 1.14 mm ALMA dust image of this disk which allow us to obtain its physical parameters and predict its density and temperature structure. Our results indicate that this accretion disk is compact (Rdisk~170 au) and massive (5Msun), about 20% of the stellar mass of 20 Msun. We estimate the total dynamical mass of the star-disk system from the molecular line emission finding a range between 21 and 30 Msun, which is consistent with our model. We fit the density and temperature structures found by our model with power law functions. These results suggest that accretion disks around massive stars are more massive and hotter than their low-mass siblings, but they still are quite stable. We also compare the temperature distribution in the GGD 27-MM1 disk with that found in low- and intermediate-mass stars and discuss possible implications on the water snow line. We have also carried about a study of the distance based on Gaia DR2 data and the population of young stellar objects (YSOs) in this region, and from the extinction maps. We conclude that the source distance is in within 1.2 and 1.4 kpc, closer than what was derived in previous studies (1.7 kpc)., Comment: 20 pages, 15 figures

Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case in which such graphs are Cayley graphs of Abelian groups. These groups can be constructed by using a generalization to $\mathbb{Z}^n$ of the concept of congruence in $\mathbb{Z}$. Here we use this approach to present some families of mixed graphs, which, for every fixed value of the degree, have an asymptotically large number of vertices as the diameter increases. In some cases, the results obtained are shown to be optimal.

The metaplectic transform (MT), also known as the linear canonical transform, is a unitary integral mapping which is widely used in signal processing and can be viewed as a generalization of the Fourier transform. For a given function $\psi$ on an $N$-dimensional continuous space $\textbf{q}$, the MT of $\psi$ is parameterized by a rotation (or more generally, a linear symplectic transformation) of the $2N$-dimensional phase space $(\textbf{q},\textbf{p})$, where $\textbf{p}$ is the wavevector space dual to $\textbf{q}$. Here, we derive a pseudo-differential form of the MT. For small-angle rotations, or near-identity transformations of the phase space, it readily yields asymptotic \textit{differential} representations of the MT, which are easy to compute numerically. Rotations by larger angles are implemented as successive applications of $K \gg 1$ small-angle MTs. The algorithm complexity scales as $O(K N^3 N_p)$, where $N_p$ is the number of grid points. We present a numerical implementation of this algorithm and discuss how to mitigate the associated numerical instabilities., Comment: 16 pages, 9 figures, 4 appendices \copyright 2019 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited

We used ALMA to observe the star-forming region GGD27 at 1.14 mm with an unprecedented angular resolution, 40 mas (56 au) and sensitivity (0.002 Msun). We detected a cluster of 25 continuum sources, most of which are likely tracing disks around Class 0/I protostars. Excluding the two most massive objects, disks masses are in the range 0.003-0.05 Msun. The analysis of the cluster properties indicates that GGD27 displays moderate subclustering. This result combined with the dynamical timescale of the radio jet (10000 years) suggests the youthfulness of the cluster. The lack of disk mass segregation signatures may support this too. We found a clear paucity of disks with Rdisk >100 au. The median value of the radius is 34 au, smaller than the median of 92 au for Taurus but comparable to the value found in Ophiuchus and in the Orion Nebula Cluster. In GGD27 there is no evidence of a distance-dependent disk mass distribution (i. e., disk mass depletion due to external photoevaporation), most likely due to the cluster youth. There is a clear deficit of disks for distances <0.02 pc. Only for distances >0.04 pc stars can form larger and more massive disks, suggesting that dynamical interactions far from the cluster center are weaker, although the small disks found could be the result of disk truncation. This work demonstrates the potential to characterize disks from low-mass YSOs in distant and massive (still deeply embedded) clustered environments., Comment: Accepted for publication in Astronomy & Astrophysics Letters

In spherical tokamaks, the electron plasma frequency is greater than the electron cyclotron frequency. Electromagnetic waves in the electron cyclotron range of frequencies are unsuitable for directly heating such plasmas due to their reduced accessibility. However, mode-conversion of the extraordinary wave to the electron Bernstein wave (X-B mode-conversion) at the upper hybrid resonance makes it possible to efficiently couple externally-launched electromagnetic wave energy into an overdense plasma core. Traditional mode-conversion models describe an X-mode wave propagating in a potential containing two cutoffs that bracket a single wave resonance. Often, however, the mode-conversion region is in the edge, where turbulent fluctuations and blobs can generate abrupt cutoffs and scattering of the incident X-mode wave. We present a new framework for studying the X-B mode-conversion which makes the inclusion of these fluctuations analytically tractable. In the new approach, the high-field cutoff is modelled as an infinite barrier, which manifests as a boundary condition applied to a wave equation involving only one cutoff adjacent to the resonance on the low-field side. The new model reproduces the main features of the previous approach, yet is more suitable for analyzing experimental observations and extrapolating to higher dimensions. We then develop an analytical estimate for the effect of small-amplitude, quasi-monochromatic density fluctuations on the X-B mode-conversion efficiency using perturbation theory. We find that Bragg backscattering of the launched X-mode wave reduces the mode-conversion efficiency significantly when the fluctuation wavenumber is resonant with the wavenumber of the incident X-mode wave. These analytical results are corroborated by numerically integrating the mode-conversion equations., Comment: 35 pages, 10 figures

Here we present deep (16 mumJy), very high (40 mas) angular resolution 1.14 mm, polarimetric, Atacama Large Millimeter/submillimeter Array (ALMA) observations towards the massive protostar driving the HH 80-81 radio jet. The observations clearly resolve the disk oriented perpendicular to the radio jet, with a radius of ~0.171 arcsec (~291 au at 1.7 kpc distance). The continuum brightness temperature, the intensity profile, and the polarization properties clearly indicate that the disk is optically thick for a radius of R<170 au. The linear polarization of the dust emission is detected almost all along the disk and its properties suggest that dust polarization is produced mainly by self-scattering. However, the polarization pattern presents a clear differentiation between the inner (optically thick) part of the disk and the outer (optically thin) region of the disk, with a sharp transition that occurs at a radius of 0.1 arcsec (~170 au). The polarization characteristics of the inner disk suggest that dust settling has not occurred yet with a maximum dust grain size between 50 and 500 mum. The outer part of the disk has a clear azimuthal pattern but with a significantly higher polarization fraction compared to the inner disk. This pattern is broadly consistent with self-scattering of a radiation field that is beamed radially outward, as expected in the optically thin outer region, although contribution from non-spherical grains aligned with respect to the radiative flux cannot be excluded., Comment: Accepted for publication in the Astrophysical Journal Letters

Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite. As main results, we show that in this context the Moore-like bound is attained in the case of diameter $k=3$, and that bipartite mixed graphs of diameter $k\ge 4$ do not exist.