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The classical solution to the Helmholtz wave equation in spherical coordinates is well known and has found many important applications in wave propagation, scattering, and imaging in optics and acoustics. The separable solution is comprised of spherical Bessel functions in the radial direction and spherical harmonics in the angular directions. The nature of the spherical Bessel functions includes a long asymptotic oscillatory tail at large radii, not conducive to applications where a tight concentration of wave amplitude around a ring is desired, for example in toroidal configurations. However, we have found that certain practical bandpass spectral shapes, centered around a peak frequency, can create a superposition of spherical Bessel functions that effectively concentrate the wave amplitude around a defined ring at the time instant of coherent addition, avoiding the long tail asymptotic oscillations of the single frequency solution. Theoretical solutions are shown for different bandpass spectra applied to the spherical Bessel functions, along with numerical solutions of transient wave propagation using practical hemispherical source shapes. These findings introduce a framework by which ring or toroidal concentrated waves can be produced with a simple bandpass superposition applied to hemispherical source shapes and with reference to the classical solutions in spherical coordinates., Comment: 18 pages; 10 figures

We have used the multiobject mode of the Near-Infrared Spectrograph (NIRSpec) on board the James Webb Space Telescope (JWST) to obtain low-resolution 1-5um spectra of 22 brown dwarf candidates in the Orion Nebula Cluster, which were selected with archival images from the Hubble Space Telescope. One of the targets was previously classified as a Herbig-Haro (HH) object and exhibits strong emission in H I, H2, and the fundamental band of CO, further demonstrating that HH objects can have bright emission in that CO band. The remaining targets have late spectral types (M6.5 to early L) and are young based on gravity sensitive features, as expected for low-mass members of the cluster. According to theoretical evolutionary models, these objects should have masses that range from the hydrogen burning limit to 0.003-0.007 Msun. Two of the NIRSpec targets were identified as proplyds in earlier analysis of Hubble images. They have spectral types of M6.5 and M7.5, making them two of the coolest and least massive known proplyds. Another brown dwarf shows absorption bands at 3-5um from ices containing H2O, CO2, OCN-, and CO, indicating that it is either an edge-on class II system or a class I protostar. It is the coolest and least massive object that has detections of these ice features. In addition, it appears to be the first candidate for a protostellar brown dwarf that has spectroscopy confirming its late spectral type., Comment: Astronomical Journal, in press

The recent discovery of tens of Jupiter-mass binary objects (JuMBOs) in the Orion Nebula Cluster with the James Webb Space Telescope has intensified the debate on the origin of free-floating planetary mass objects within star-forming regions. The JuMBOs have masses below the opacity limit for fragmentation, but have very wide separations (10s - 100s au), suggesting that they did not form in a similar manner to other substellar mass binaries. Here, we propose that the theory of photoerosion of prestellar cores by Lyman continuum radiation from massive stars could explain the JuMBOs in the ONC. We find that for a range of gas densities the final substellar mass is comfortably within the JuMBO mass range, and that the separations of the JuMBOs are consistent with those of more massive (G- and A-type) binaries, that would have formed from the fragmentation of the cores had they not been photoeroded. The photoerosion mechanism is most effective within the HII region(s) driven by the massive star(s). The majority of the observed JuMBOs lie outside of these regions in the ONC, but may have formed within them and then subsequently migrated due to dynamical evolution., Comment: 9 pages, 4 figures, accepted for publication in ApJ

Polymers are a primary building block in many biomaterials, often interacting with anisotropic backgrounds. While previous studies have considered polymer dynamics within nematic solvents, rarely are the the effects of anisotropic viscosity and polymer elongation differentiated. Here, we study polymers embedded in nematic liquid crystals with isotropic viscosity via numerical simulations, to explicitly investigate the effect of nematicity on macromolecular conformation and how conformation alone can produce anisotropic dynamics. We employ a hybrid technique that captures nematic orientation, thermal fluctuations and hydrodynamic interactions. The coupling of the polymer backbone to the nematic field elongates the polymer, producing anisotropic diffusion even in nematic solvents with isotropic viscosity. For intermediate coupling, the competition between background anisotropy and macrmolecular entropy leads to hairpins - sudden kinks along the backbone of the polymer. Experiments of DNA embedded in a solution of rod-like fd viruses qualitatively support the role of hairpins in establishing characteristic conformational features that govern polymer dynamics. Hairpin diffusion along the backbone exponentially slows as coupling increases. Better understanding two-way coupling between polymers and their surroundings could allow the creation of more biomimetic composite materials., Comment: 13 pages, 7 figures, 2 appendices

The two main competing theories proposed to explain the formation of massive ($>10$M$_\odot$) stars -- competitive accretion and monolithic core collapse -- make different observable predictions for the environment of the massive stars during, and immediately after, their formation. Proponents of competitive accretion have long predicted that the most massive stars should have a different spatial distribution to lower-mass stars, either through the stars being mass segregated, or being in areas of higher relative densities, or sitting deeper in gravitational potential wells. We test these predictions by analysing a suite of SPH simulations where star clusters form massive stars via competitive accretion with and without feedback. We find that the most massive stars have higher relative densities, and sit in deeper potential wells, only in simulations in which feedback is not present. When feedback is included, only half of the simulations have the massive stars residing in deeper potential wells, and there are no other distinguishing signals in their spatial distributions. Intriguingly, in our simple models for monolithic core collapse, the massive stars may also end up in deeper potential wells, because if massive cores fragment the stars are still massive, and dominate their local environs. We find no robust diagnostic test in the spatial distributions of massive stars that can distinguish their formation mechanisms, and so other predictions for distinguishing between competitive accretion and monolithic collapse are required., Comment: 18 pages, 7 figures, with an Appendix containing a further 18 figures showing all the SPH simulation results. Accepted for publication in ApJ

While boundary plasmas in present day tokamaks generally fall in a fluid regime, neutral species near the boundary often require kinetic models due to long mean-free-paths compared to characteristic spatial scales in the region. Monte-Carlo (MC) methods provide a complete, high-fidelity approach to solving kinetic models, and must be coupled to fluid plasma models to simulate the full plasma-neutrals system. The statistical nature of MC methods, however, prevents convergence of coupled fluid-kinetic simulations to an exact self-consistent steady-state. Moreover, this forces the use of explicit methods that can suffer from numerical errors and require huge computational resources. Correlated Monte-Carlo (CMC) methods are expected to alleviate these issues, but have historically enjoyed only mixed success. Here, a fully implicit method for coupled plasma-neutral systems is demonstrated in 1D using the UEDGE plasma code and a homemade CMC code. In particular, it is shown that ensuring the CMC method is a differentiable function of the background plasma is sufficient to employ a Jacobian-Free Newton-Krylov solver for implicit time steps. The convergence of the implicit coupling method is explored and compared with explicit coupling and uncorrelated methods. It is shown that ensuring differentiability by controlling random seeds in the MC is sufficient to achieve convergence, and that the use of implicit time-stepping methods has the potential for improved stability and runtimes over explicit coupling methods., Comment: 6 pages, 6 figures. Comments welcome!

Given a pair of $\mathbb{Z}_2$-harmonic spinors (resp. 1-forms) on closed Riemannian 3-manifolds $(Y_1, g_1)$ and $(Y_2,g_2)$, we construct $\mathbb{Z}_2$-harmonic spinors (resp. 1-forms) on the connected sum $Y_1 \# Y_2$ and the torus sum $Y_1 \cup_{T^2} Y_2$ using a gluing argument. The main tool in the proof is a parameterized version of the Nash-Moser implicit function theorem established by Donaldson and the second author. We use these results to construct an abundance of new examples of $\mathbb Z_2$-harmonic spinors and 1-forms. In particular, we prove that for every closed 3-manifold $Y$, there exist infinitely many $\mathbb{Z}_2$-harmonic spinors with singular sets representing infinitely many distinct isotopy classes of embedded links, strengthening an existence theorem of Doan-Walpuski. Moreover, combining this with previous results, our construction implies that if $b_1(Y) > 0$, there exist infinitely many $\mathrm{spin}^c$ structures on $Y$ such that the moduli space of solutions to the two-spinor Seiberg-Witten equations is non-empty and non-compact., Comment: 38 pages, comments welcome!

In share wave elastography (SWE), the aim is to measure the velocity of shear waves, however unwanted compression waves and bulk tissue motion pose challenges in evaluating tissue stiffness. Conventional approaches often struggle to discriminate between shear and compression waves, leading to inaccurate shear wave speed (SWS) estimation. In this study, we propose a novel approach known as the difference autocorrelation estimator to accurately estimate reverberant SWS in the presence of compression waves and noise. Methods: The difference autocorrelation estimator, unlike conventional techniques, computes the subtraction of velocity between neighboring particles, effectively minimizing the impact of long wavelength compression waves and other wide-area movements such as those caused by respiration. We evaluated the effectiveness of the integrated difference autocorrelation (IDA) by: (1) using k-Wave simulations of a branching cylinder in a soft background, (2) using ultrasound elastography on a breast phantom, (3) using ultrasound elastography in the human liver-kidney region, and (4) using magnetic resonance elastography (MRE) on a brain phantom. Results: By applying IDA on the unfiltered contaminated wave fields of simulation and elastography experiments, the estimated SWSs are in good agreement with the ground truth values (i.e., less than 2% error for the simulation, 9% error for ultrasound elastography of breast phantom and 19% error for MRE). Conclusion: Our results demonstrate that IDA accurately estimates SWS, revealing the existence of a lesion, even in the presence of strong compression waves. Significance: IDA exhibits consistency in SWS estimation across different modalities and excitation scenarios, highlighting its robustness and potential clinical utility.

The architectures of extrasolar planetary systems often deviate considerably from the ``standard" model for planet formation, which is largely based on our own Solar System. In particular, gas giants on close orbits are not predicted by planet formation theory and so some process(es) are thought to move the planets closer to their host stars. Recent research has suggested that Hot Jupiter host stars display a different phase space compared to stars that do not host Hot Jupiters. This has been attributed to these stars forming in star-forming regions of high stellar density, where dynamical interactions with passing stars have perturbed the planets. We test this hypothesis by quantifying the phase space of planet-hosting stars in dynamical N-body simulations of star-forming regions. We find that stars that retain their planets have a higher phase space than non-hosts, regardless of their initial physical density. This is because an imprint of the kinematic substructure from the regions birth is retained, as these stars have experienced fewer and less disruptive encounters than stars whose planets have been liberated and become free-floating. However, host stars whose planets remain bound but have had their orbits significantly altered by dynamical encounters are also primarily found in high phase space regimes. We therefore corroborate other research in this area which has suggested the high phase space of Hot Jupiter host stars is not caused by dynamical encounters or stellar clustering, but rather reflects an age bias in that these stars are (kinematically) younger than other exoplanet host stars., Comment: 11 pages, 4 figures. Accepted for publication in ApJ

Our work examines $t$-structures in derived categories related to Noetherian schemes, establishing both classification and nonexistence results for compactly generated $t$-structures that satisfy a tensor compatibility condition. First, we classify which $t$-structures on the derived category of quasi-coherent sheaves can be restricted to the bounded derived category of coherent sheaves. This significantly generalizes Takahashi's results for CM-excellent rings of finite Krull dimension, and its sharpness is illustrated using an example of Nagata. Second, we show that there are no non-trivial tensor $t$-structures on the category of perfect complexes with cohomology supported on an irreducible closed subset if that subset is not contained in the regular locus of the scheme, which generalizes a result of Smith in the affine setting concerning a conjecture of Antieau, Gepner, and Heller., Comment: Current: Improved results, added coauthors; Previous: Initial upload, comments welcome!

Objectives- Several ultrasound measures have shown promise for assessment of steatosis compared to traditional B-scan, however clinicians may be required to integrate information across the parameters. Here, we propose an integrated multiparametric approach, enabling simple clinical assessment of key information from combined ultrasound parameters. Methods- We have measured 13 parameters related to ultrasound and shear wave elastography. These were measured in 30 human subjects under a study of liver fat. The 13 individual measures are assessed for their predictive value using independent magnetic resonance imaging-derived proton density fat fraction (MRI-PDFF) measurements as a reference standard. In addition, a comprehensive and fine-grain analysis is made of all possible combinations of sub-sets of these parameters to determine if any subset can be efficiently combined to predict fat fraction. Results- We found that as few as four key parameters related to ultrasound propagation are sufficient to generate a linear multiparametric parameter with a correlation against MRI-PDFF values of greater than 0.93. This optimal combination was found to have a classification area under the curve (AUC) approaching 1.0 when applying a threshold for separating steatosis grade zero from higher classes. Furthermore, a strategy is developed for applying local estimates of fat content as a color overlay to produce a visual impression of the extent and distribution of fat within the liver. Conclusion- In principle, this approach can be applied to most clinical ultrasound systems to provide the clinician and patient with a rapid and inexpensive estimate of liver fat content.

Observations of star-forming regions provide snapshots in time of the star formation process, and can be compared with simulation data to constrain the initial conditions of star formation. In order to make robust inferences, different metrics must be used to quantify the spatial and kinematic distributions of stars. In this paper, we assess the suitability of the INDICATE (INdex to Define Inherent Clustering And TEndencies) method as a diagnostic to infer the initial conditions of star-forming regions that subsequently undergo dynamical evolution. We use INDICATE to measure the degree of clustering in N-body simulations of the evolution of star-forming regions with different initial conditions. We find that the clustering of individual stars, as measured by INDICATE, becomes significantly higher in simulations with higher initial stellar densities, and is higher in subvirial star-forming regions where significant amounts of dynamical mixing has occurred. We then combine INDICATE with other methods that measure the mass segregation, relative stellar surface density ratio and the morphology (Q-parameter) of star-forming regions, and show that the diagnostic capability of INDICATE increases when combined with these other metrics., Comment: 17 pages (including figures), 12 Figures. Accepted for publication in MNRAS

Whilst the formation of Solar system planets is constrained by meteoritic evidence, the geophysical history of low-mass exoplanets is much less clear. The bulk composition and climate states of rocky exoplanets may vary significantly based on the composition and properties of the planetesimals they form from. An important factor influenced by planetesimal composition is water content, where the desiccation of accreting planetesimals impacts the final water content of the resultant planets. While the inner planets of the Solar system are comparatively water-poor, recent observational evidence from exoplanet bulk densities and planetary formation models suggest that rocky exoplanets engulfed by substantial layers of high-pressure ices or massive steam atmospheres could be widespread. Here we quantify variations in planetesimal desiccation due to potential fractionation of the two short-lived radioisotopes 26Al and 60Fe relevant for internal heating on planetary formation timescales. We focus on how order of magnitude variations in 60Fe can affect the water content of planetesimals, and how this may alter the formation of extrasolar ocean worlds. We find that heating by 26Al is the dominant cause of planetesimal heating in any Solar system analogue scenario, thus validating previous works focussing only on this radioisotope. However, 60Fe can become the primary heating source in the case of high levels of supernova enrichment in massive star-forming regions. These diverging scenarios can affect the formation pathways, bulk volatile budget, and climate diversity of low-mass exoplanets., Comment: 12 pages, 13 figures

Given a $\mathbb Z_2$-harmonic spinor satisfying some genericity assumptions, this article constructs a 1-parameter family of two-spinor Seiberg-Witten monopoles converging to it after renormalization. The proof is a gluing construction beginning with model solutions on a neighborhood of the $\mathbb Z_2$-harmonic spinor's singular set. The gluing is complicated by the presence of an infinite-dimensional obstruction bundle for the singular limiting linearized operator. This difficulty is overcome by introducing a generalization of Donaldson's alternating method in which a deformation of the $\mathbb Z_2$-harmonic spinor's singular set is chosen at each stage of the alternating iteration to cancel the obstruction components., Comment: 67 pages, 1 Figure. Comments welcome!

The utilization of a reverberant shear wave field in shear wave elastography has emerged as a promising technique for achieving robust shear wave speed (SWS) estimation. However, accurately measuring SWS within such a complex wave field remains challenging. This study introduces an advanced autocorrelation estimator based on angular integration known as the angular integral autocorrelation (AIA) approach to address this issue. The AIA approach incorporates all the au-tocorrelation data from various angles during measurements, resulting in enhanced robustness to both noise and imperfect distributions in SWS estimation. The effectiveness of the AIA estimator for SWS estimation is first validated using a k-Wave simulation of a stiff branching tube in a uniform background. Furthermore, the AIA estimator is applied to ultrasound elastography experiments, MRI experiments, and OCT studies across a range of different excitation frequencies on tissues and phantoms, including in vivo scans. The results verify the capacity of the AIA approach to enhance the accuracy of SWS estimation and SNR, even within an imperfect reverberant shear wave field. Compared to simple autocorrelation approaches, the AIA approach can also successfully visualize and define lesions while significantly improving the estimated SWS and SNR in homogeneous background materials, thus providing improved elastic contrast between structures within the scans. These findings demonstrate the robustness and effectiveness of the AIA approach across a wide range of applications, including ultrasound elastography, MRE, and OCE, for accurately identifying the elastic properties of biological tissues in diverse excitation scenarios.

Parahydrogen-Induced Polarization (PHIP) is a potent technique for generating target molecules with high nuclear spin polarization. The PHIP process involves a chemical reaction between parahydrogen and a target molecule, followed by the transformation of nuclear singlet spin order into magnetization of a designated nucleus through magnetic field manipulations. Although the singlet-to-magnetization polarization transfer process works effectively at moderate concentrations, it is observed to become much less efficient at high molar polarization, defined as the product of polarization and concentration. This strong dependence on the molar polarization is attributed to interference from the field produced by the sample's magnetization during polarization transfer, which leads to complex dynamics and can severely impact the scalability of the technique. We address this challenge with a pulse sequence that negates the influence of the distant dipolar field, while simultaneously achieving singlet-to-magnetization polarization transfer to the desired target spins, free from restrictions on the molar polarization.

Recently, Amnon Neeman settled a bold conjecture by Antieau, Gepner, and Heller regarding the relationship between the regularity of finite-dimensional noetherian schemes and the existence of bounded $t$-structures on their derived categories of perfect complexes. In this paper, using different methods, we prove some very general results about the existence of bounded $t$-structures on (not necessarily algebraic or topological) triangulated categories and their invariance under completion. We show that if the opposite category of an essentially small triangulated category has finite finitistic dimension in our sense, then the existence of a bounded t-structure on it forces it to be equal to its completion. We also prove a parallel result regarding the equivalence of all bounded t-structures on any intermediate triangulated category between the starting category and its completion. Our general treatment, when specialized to the case of schemes, immediately gives us Neeman's theorem as an application and significantly generalizes another remarkable theorem by Neeman about the equivalence of bounded $t$-structures on the bounded derived categories of coherent sheaves. When specialized to other cases like associative rings, nonpositive DG-rings, connective $\mathbb{E}_1$-rings, triangulated categories without models, etc., we get many other applications. Under mild finiteness assumptions, these results not only give a categorical obstruction (the singularity category in our sense) to the existence of bounded $t$-structures on a triangulated category, but also provide plenty of triangulated categories on which all bounded $t$-structures are equivalent. The strategy used in our treatment is introducing a new concept of finitistic dimension for triangulated categories and lifting $t$-structures along completions of triangulated categories., Comment: 42 pages

Objective. Limited access to breast cancer diagnosis globally leads to delayed treatment. Ultrasound, an effective yet underutilized method, requires specialized training for sonographers, which hinders its widespread use. Approach. Volume sweep imaging (VSI) is an innovative approach that enables untrained operators to capture high-quality ultrasound images. Combined with deep learning, like convolutional neural networks (CNNs), it can potentially transform breast cancer diagnosis, enhancing accuracy, saving time and costs, and improving patient outcomes. The widely used UNet architecture, known for medical image segmentation, has limitations, such as vanishing gradients and a lack of multi-scale feature extraction and selective region attention. In this study, we present a novel segmentation model known as Wavelet_Attention_UNet (WATUNet). In this model, we incorporate wavelet gates (WGs) and attention gates (AGs) between the encoder and decoder instead of a simple connection to overcome the limitations mentioned, thereby improving model performance. Main results. Two datasets are utilized for the analysis. The public "Breast Ultrasound Images" (BUSI) dataset of 780 images and a VSI dataset of 3818 images. Both datasets contained segmented lesions categorized into three types: no mass, benign mass, and malignant mass. Our segmentation results show superior performance compared to other deep networks. The proposed algorithm attained a Dice coefficient of 0.94 and an F1 score of 0.94 on the VSI dataset and scored 0.93 and 0.94 on the public dataset, respectively., Comment: N/A

We investigate the role of temperature on the topological insulating state of metal dichalcogenide monolayers, 1T$^\prime$-MX$_2$ (M=W, Mo and X=S, Se). Using first principles calculations based on density functional theory, we consider three temperature-related contributions to the topological band gap: electrons coupling with short-wavelength phonons, with long-wavelength phonons \textit{via} Fr\"ohlich coupling, and thermal expansion. We find that electron-phonon coupling promotes the topology of the electronic structures of all 1T$^\prime$-MX$_2$ monolayers, while thermal expansion acts as a counteracting effect. Additionally, we derive the band renormalization from Fr\"ohlich coupling in the two-dimensional context and observe its relatively modest contribution to 1T$^\prime$-MX$_2$ monolayers. Finally, we present a simplified physical picture to understand the "inverse Varshni" effect driven by band inversion in topological insulators. Our work reveals that, among the four 1T$^\prime$-MX$_2$ studied monolayers, MoSe$_2$ is a promising candidate for room temperature applications as its band gap displays remarkable resilience against thermal expansion, while the topological order of WS$_2$ can be tuned under the combined influence of strain and temperature. Both materials represent novel examples of temperature promoted topological insulators., Comment: 15 pages, 6 figures

Purpose: This study aims to evaluate two distinct approaches for fibre radius estimation using diffusion-relaxation MRI data acquired in biomimetic microfibre phantoms that mimic hollow axons. The methods considered are the spherical mean power-law approach and a T2-based pore size estimation technique. Theory and Methods: A general diffusion-relaxation theoretical model for the spherical mean signal from water molecules within a distribution of cylinders with varying radii was introduced, encompassing the evaluated models as particular cases. Additionally, a new numerical approach was presented for estimating effective radii (i.e., MRI-visible mean radii) from the ground truth radii distributions, not reliant on previous theoretical approximations and adaptable to various acquisition sequences. The ground truth radii were obtained from Scanning Electron Microscope images. Results: Both methods show a linear relationship between effective radii estimated from MRI data and ground-truth radii distributions, though some discrepancies were observed. The spherical mean power-law method overestimated fibre radii. Conversely, the T2-based method exhibited higher sensitivity to smaller fibre radii but faced limitations in accurately estimating the radius in one particular phantom, possibly due to material-specific relaxation changes. Conclusion: The study demonstrates the feasibility of both techniques to predict pore sizes of hollow microfibres. The T2-based technique, unlike the spherical mean power-law method, does not demand ultra-high diffusion gradients but requires calibration with known radius distributions. This research contributes to the ongoing development and evaluation of neuroimaging techniques for fibre radius estimation, highlights the advantages and limitations of both methods and provides datasets for reproducible research., Comment: 37 pages, 8 figures. Accepted in Magnetic Resonance in Medicine, Dec, 2023

This paper assesses the potential for the large language models (LLMs) GPT-4 and GPT-3.5 to aid in deriving insight from education feedback surveys. Exploration of LLM use cases in education has focused on teaching and learning, with less exploration of capabilities in education feedback analysis. Survey analysis in education involves goals such as finding gaps in curricula or evaluating teachers, often requiring time-consuming manual processing of textual responses. LLMs have the potential to provide a flexible means of achieving these goals without specialized machine learning models or fine-tuning. We demonstrate a versatile approach to such goals by treating them as sequences of natural language processing (NLP) tasks including classification (multi-label, multi-class, and binary), extraction, thematic analysis, and sentiment analysis, each performed by LLM. We apply these workflows to a real-world dataset of 2500 end-of-course survey comments from biomedical science courses, and evaluate a zero-shot approach (i.e., requiring no examples or labeled training data) across all tasks, reflecting education settings, where labeled data is often scarce. By applying effective prompting practices, we achieve human-level performance on multiple tasks with GPT-4, enabling workflows necessary to achieve typical goals. We also show the potential of inspecting LLMs' chain-of-thought (CoT) reasoning for providing insight that may foster confidence in practice. Moreover, this study features development of a versatile set of classification categories, suitable for various course types (online, hybrid, or in-person) and amenable to customization. Our results suggest that LLMs can be used to derive a range of insights from survey text.

Simulations of the effects of stellar fly-bys on planetary systems in star-forming regions show a strong dependence on subtle variations in the initial spatial and kinematic substructure of the regions. For similar stellar densities, the more substructured star-forming regions disrupt up to a factor of two more planetary systems. We extend this work to look at the effects of substructure on stellar binary populations. We present $N$-body simulations of substructured, and non-substructured (smooth) star-forming regions in which we place different populations of stellar binaries. We find that for binary populations that are dominated by close ($<$100au) systems, a higher proportion are destroyed in substructured regions. However, for wider systems ($>$100au), a higher proportion are destroyed in smooth regions. The difference is likely due to the hard-soft, or fast-slow boundary for binary destruction. Hard (fast/close) binaries are more likely to be destroyed in environments with a small velocity dispersion (kinematically substructured regions), whereas soft (slow/wide) binaries are more likely to be destroyed in environments with higher velocity dispersions (non-kinematically substructured regions). Due to the vast range of stellar binary semimajor axes in star-forming regions ($10^{-2} - 10^4$au) these differences are small and hence unlikely to be observable. However, planetary systems have a much smaller initial semimajor axis range (likely $\sim$1 -- 100au for gas giants) and here the difference in the fraction of companions due to substructure could be observed if the star-forming regions that disrupt planetary systems formed with similar stellar densities., Comment: 9 pages, 5 figures, accepted for publication in MNRAS

The dominant formation mechanism of brown dwarfs and planetary mass objects in star-forming regions is presently uncertain. Do they form like stars, via the collapse and fragmentation of cores in Giant Molecular clouds, or do they form like planets in the discs around stars and are ejected via dynamical interactions? In this paper, we quantify the spatial distribution of substellar objects in NGC1333, in particular focusing on planetary-mass objects that have been the target of recent deep imaging observations. We find that these objects have a spatial distribution that is indistinguishable from the stars, and more massive brown dwarfs. We also analyse N-body simulations and find that a population of ejected planets would have a significantly different spatial and kinematic distribution to stars, and brown dwarfs that also formed through gravitational collapse and fragmentation. We therefore conclude that the low-mass substellar objects in NGC1333 formed more like stars than planets, although we predict that a population of hitherto undetected ejected planetary mass objects may be lurking in this, and other star-forming regions., Comment: 11 pages, 8 figures, accepted for publication in MNRAS

Short-lived radioisotopes, in particular 26-Al and 60-Fe, are thought to contribute to the internal heating of the Earth, but are significantly more abundant in the Solar System compared to the Interstellar Medium. The presence of their decay products in the oldest Solar System objects argues for their inclusion in the Sun's protoplanetary disc almost immediately after the star formation event that formed the Sun. Various scenarios have been proposed for their delivery to the Solar System, usually involving one or more core-collapse supernovae of massive stars. An alternative scenario involves the young Sun encountering an evolved Asymptotic Giant Branch (AGB) star. AGBs were previously discounted as a viable enrichment scenario for the Solar System due to the presumed low probability of an encounter between an old, evolved star and a young pre-main sequence star. We report the discovery in Gaia data of an interloping AGB star in the star-forming region NGC2264, demonstrating that old, evolved stars can encounter young forming planetary systems. We use simulations to calculate the yields of 26-Al and 60-Fe from AGBs and their contribution to the long-term geophysical heating of a planet, and find that these are comfortably within the range previously calculated for the Solar System., Comment: 8 pages, 4 figures, accepted for publication in ApJL

This article studies a class of Dirac operators of the form $D_\varepsilon= D+\varepsilon^{-1}\mathcal A$, where $\mathcal A$ is a zeroth order perturbation vanishing on a subbundle. When $\mathcal A$ satisfies certain additional assumptions, solutions of the Dirac equation have a concentration property in the limit $\varepsilon\to 0$: components of the solution orthogonal to $\ker(\mathcal A)$ decay exponentially away from the locus $\mathcal Z$ where the rank of $\ker(\mathcal A)$ jumps up. These results are extended to a class of non-linear Dirac equations. This framework is then applied to study the compactness properties of moduli spaces of solutions to generalized Seiberg-Witten equations. In particular, it is shown that for sequences of solutions which converge weakly to a $\mathbb Z_2$-harmonic spinor, certain components of the solutions concentrate exponentially around the singular set of the $\mathbb Z_2$-harmonic spinor. Using these results, the weak convergence to $\mathbb Z_2$-harmonic spinors proved in existing convergence theorems is improved to $C^\infty_{loc}$., Comment: Comments welcome!

In the approaches to elastography, two mathematical operations have been frequently applied to improve the final estimate of shear wave speed and shear modulus of tissues. The vector curl operator can separate out the transverse component of a complicated displacement field, and directional filters can separate distinct orientations of wave propagation. However, there are practical limitations that can prevent the intended improvement in elastography estimates. Some simple configurations of wavefields relevant to elastography are examined against theoretical models within the semi-infinite elastic medium and guided waves in a bounded medium. The Miller-Pursey solutions in simplified form are examined for the semi-infinite medium and the Lamb wave symmetric form is considered for the guided wave structure. In both cases, wave combinations along with practical limits on the imaging plane can prevent the curl and directional filter operations from directly providing an improved measure of shear wave speed and shear modulus. Additional limits on signal-to-noise and the support of filters also restrict the applica-bility of these strategies for improving elastographic measures. Practical implementations of shear wave excitations applied to the body and to bounded structures within the body can involve waves that are not easily resolved by the vector curl operator and directional filters. These limits may be overcome by more advanced strategies or simple improvements in baseline parameters including the size of the region of interest and the number of shear waves propagated within., Comment: 11 pages, 6 figures

Context: Core accretion models of massive star formation require the existence of massive, starless cores within molecular clouds. Yet, only a small number of candidates for such truly massive, monolithic cores are currently known. Aims: Here we analyse a massive core in the well-studied infrared-dark cloud (IRDC) called the 'dragon cloud' (also known as G028.37+00.07 or 'Cloud C'). This core (C2c1) sits at the end of a chain of a roughly equally spaced actively star-forming cores near the centre of the IRDC. Methods: We present new high-angular resolution 1 mm ALMA dust continuum and molecular line observations of the massive core. Results: The high-angular resolution observations show that this region fragments into two cores C2c1a and C2c1b, which retain significant background-subtracted masses of 23 Msun and 2 Msun (31 Msun and 6 Msun without background subtraction), respectively. The cores do not appear to fragment further on the scales of our highest angular resolution images (0.200 arcsec, 0.005 pc ~ 1000 AU). We find that these cores are very dense (nH2 > 10^6 cm-3) and have only trans-sonic non-thermal motions (Ms ~ 1). Together the mass, density and internal motions imply a virial parameter of < 1, which suggests the cores are gravitationally unstable, unless supported by strong magnetic fields with strengths of ~ 1 - 10 mG. From CO line observations, we find that there is tentative evidence for a weak molecular outflow towards the lower-mass core, and yet the more massive core remains devoid of any star formation indicators. Conclusions: We present evidence for the existence of a massive, pre-stellar core, which has implications for theories of massive star formation. This source warrants follow-up higher-angular-resolution observations to further assess its monolithic and pre-stellar nature., Comment: 8+4 pages, 4+2 Figures, 2 Tables, accepted for publication in Astronomy & Astrophysics

The abundance of the short-lived radioisotopes 26-Al and 60-Fe in the early Solar system is usually explained by the Sun either forming from pre-enriched material, or the Sun's protosolar disc being polluted by a nearby supernova explosion from a massive star. Both hypotheses suffer from significant drawbacks: the former does not account for the dynamical evolution of star-forming regions, while in the latter the time for massive stars to explode as supernovae can be similar to, or even longer than, the lifetime of protoplanetary discs. In this paper, we extend the disc enrichment scenario to include the contribution of 26-Al from the winds of massive stars before they explode as supernovae. We use N-body simulations and a post-processing analysis to calculate the amount of enrichment in each disc, and we vary the stellar density of the star-forming regions. We find that stellar winds contribute to disc enrichment to such an extent that the Solar system's 26-Al/60-Fe ratio is reproduced in up to 50 per cent of discs in dense (rho = 1000Msun pc^-3) star-forming regions. When winds are a significant contributor to the SLR enrichment, we find that Solar system levels of enrichment can occur much earlier (before 2.5 Myr) than when enrichment occurs from supernovae, which start to explode at later ages (>4 Myr). We find that Solar system levels of enrichment all but disappear in low-density star-forming regions (rho < 10Msun pc^-3), implying that the Solar system must have formed in a dense, populous star-forming region if 26-Al and 60-Fe were delivered directly to the protosolar disc from massive-star winds and supernovae., Comment: 16 pages, 10 figures, 1 appendix with 3 further figures, accepted for publication in MNRAS

A $\mathbb Z_2$-harmonic spinor on a 3-manifold $Y$ is a solution of the Dirac equation on a bundle that is twisted around a submanifold $\mathcal Z$ of codimension 2 called the singular set. This article investigates the local structure of the universal moduli space of $\mathbb Z_2$-harmonic spinors over the space of parameters $(g,B)$ consisting of a metric and perturbation to the spin connection. The main result states that near a $\mathbb Z_2$-harmonic spinor with $\mathcal Z$ smooth, the universal moduli space projects to a codimension 1 submanifold in the space of parameters. The analysis is complicated by the presence of an infinite-dimensional obstruction bundle and a loss of regularity in the first variation of the Dirac operator with respect to deformations of the singular set $\mathcal Z$, necessitating the use of the Nash-Moser Implicit Function Theorem., Comment: Comments welcome!

The multi-dimensional phase space density (both position and velocity) of star-forming regions may encode information on the initial conditions of star and planet formation. Recently, a new metric based on the Mahalanobis distance has been used to show that hot Jupiters are more likely to be found around exoplanet host-stars in high 6D phase space density, suggesting a more dynamic formation environment for these planets. However, later work showed that this initial result may be due to a bias in the age of hot Jupiters and the kinematics of their host stars. We test the ability of the Mahalanobis distance and density to differentiate more generally between star-forming regions with different morphologies by applying it to static regions that are either substructured or smooth and centrally concentrated. We find that the Mahalanobis distance is unable to distinguish between different morphologies, and that the initial conditions of the N-body simulations cannot be constrained using only the Mahalanobis distance or density. Furthermore, we find that the more dimensions in the phase space the less effective the Mahalanobis density is at distinguishing between different initial conditions. We show that a combination of the mean three-dimensional (x, y, z) Mahalanobis density and the Q-parameter for a region can constrain its initial virial state. However this is due to the discriminatory power of the Q-parameter and not from any extra information imprinted in the Mahalanobis density. We therefore recommend continued use of multiple diagnostics for determining the initial conditions of star-forming regions, rather than relying on a single multi-dimensional metric., Comment: 13 pages + appendices, 10 figures, accepted for publication in MNRAS