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The cylindrical algebraic covering method was originally proposed to decide the satisfiability of a set of non-linear real arithmetic constraints. We reformulate and extend the cylindrical algebraic covering method to allow for checking the truth of arbitrary non-linear arithmetic formulas, adding support for both quantifiers and Boolean structure. Furthermore, we also propose a variant to perform quantifier elimination on such formulas. After introducing the algorithm, we elaborate on various extensions, optimizations and heuristics. Finally, we present an experimental evaluation of our implementation and provide a comparison with state-of-the-art SMT solvers and quantifier elimination tools.

We generalise the classical Bass-Heller-Swan decomposition for the K-theory of (twisted) Laurent algebras to a splitting for general localising invariants of certain categories of twisted automorphisms. As an application, we obtain splitting formulas for Waldhausen's A-theory of mapping tori and for the K-theory of certain tensor algebras. We identify the Nil-terms appearing in this splitting in two ways. Firstly, as the reduced K-theory of twisted endomorphisms. Secondly, as the reduced K-theory of twisted nilpotent endomorphisms. Finally, we generalise classical vanishing results for Nil-terms of regular rings to our setting., Comment: 30 pages. Comments welcome!

Fluid transport across nanometric channels induced by electric, pressure and concentration gradients is ubiquitous in biological systems and fosters various applications. In this context, computer simulation setups with well-defined open-boundary equilibrium starting states are essential in understanding and assisting experimental studies. However, open-boundary computational methods are scarce and typically do not satisfy all the equilibrium conditions imposed by reality. Namely, in the absence of external gradients, 1) the system of interest (SoI) must be at thermodynamic and chemical equilibrium with an infinite reservoir of particles, 2) the fluctuations of the SoI in equilibrium should sample the grand canonical ensemble, 3) the local solvation thermodynamics, which is extremely sensitive to finite-size effects due to solvent depletion, should be correctly described. This point is particularly relevant for out-of-equilibrium systems. Finally, 4) the method should be robust enough to deal with phase transitions and coexistence conditions in the SoI. In this study, we demonstrate with prototypical liquid systems embedded into a reservoir of ideal gas particles that the adaptive resolution simulation (AdResS) method, coupled with particle insertion/deletion steps, satisfies all these requirements. Therefore, this AdResS setup is suitable for performing equilibrium and non-equilibrium simulations of open systems.

Tidal disruption events (TDEs) are an important way to probe the properties of stellar populations surrounding supermassive black holes. Observed spectra of several TDEs, such as ASASSN-14li, show high nitrogen to carbon abundance ratios, leading to questions about their progenitors. Disrupting an intermediate- or high-mass star that has undergone CNO processing, increasing the nitrogen in its core, could lead to an enhanced nitrogen TDE. Galactic nuclei present a conducive environment for high-velocity stellar collisions that can lead to high mass loss, stripping the carbon- and hydrogen-rich envelopes of the stars and leaving behind the enhanced nitrogen cores. TDEs of these stripped stars may therefore exhibit even more extreme nitrogen enhancement. Using the smoothed particle hydrodynamics code StarSmasher, we provide a parameter space study of high-velocity stellar collisions involving intermediate-mass stars, analyzing the composition of the collision products. We conclude that high-velocity stellar collisions can form products that have abundance ratios similar to those observed in the motivating TDEs. Furthermore, we show that stars that have not experienced high CNO processing can yield low-mass collision products that retain even higher nitrogen to carbon abundance ratios. We analytically estimate the mass fallback for a typical TDE of several collision products to demonstrate consistency between our models and TDE observations. Lastly, we discuss how the extended collision products, with high central to average density ratios, can be related to repeated partial TDEs like ASASSN-14ko and G objects in the Galactic Center., Comment: 26 pages, 10 figures, 3 tables, submitted to ApJ

Dynamical interactions in dense star clusters could significantly influence the properties of black holes, leaving imprints on their gravitational-wave signatures. While previous studies have mostly focused on repeated black hole mergers for spin and mass growth, this work examines the impact of physical collisions and close encounters between black holes and (non-compact) stars. Using Monte Carlo N-body models of dense star clusters, we find that a large fraction of black holes retained upon formation undergo collisions with stars. Within our explored cluster models, the proportion of binary black hole mergers affected by stellar collisions ranges from $10\%$ to $60\%$. If all stellar-mass black holes are initially non-spinning, we find that up to $40\%$ of merging binary black holes may have components with dimensionless spin parameter $\chi\gtrsim 0.2$ because of prior stellar collisions, while typically about $10\%$ have spins near $\chi = 0.7$ from prior black hole mergers. We demonstrate that young star clusters are especially important environments as they can produce collisions of black holes with very massive stars, allowing significant spin up of the black holes through accretion. Our predictions for black hole spin distributions from these stellar collisions highlight their sensitivity to accretion efficiency, underscoring the need for detailed hydrodynamic calculations to better understand the accretion physics following these interactions., Comment: 16 pages, 8 figures, 2 tables. Submitted to ApJ

To search for a conceptual picture describing the magnetization plateau phenomenon, we surveyed the crystal structures and the spin lattices of those magnets exhibiting plateaus in their magnetization vs. magnetic field curves by probing the three questions: (a) why only certain magnets exhibit magnetization plateaus, (b) why there occur several different types of magnetization plateaus, and (c) what controls the widths of magnetization plateaus. We show that the answers to these questions lie in how the magnets under field absorb Zeeman energy hence changing their magnetic structures. The magnetic structure of a magnet insulator is commonly described in terms of its spin lattice, which requires the determination of the spin exchanges nonnegligible strengths between the magnetic ions. Our work strongly suggests that a magnet under magnetic field partitions its spin lattice into antiferromagnetic (AFM) or ferrimagnetic fragments by breaking its weak magnetic bonds. Our supposition of the field-induced partitioning of spin lattice into magnetic fragments is supported by the anisotropic magnetization plateaus of Ising magnets and by the highly anisotropic width of the 1/3-magnetization plateau in azurite. The answers to the three questions (a) - (c) emerge naturally by analyzing how these fragments are formed under magnetic field., Comment: A survey of the magnetization plateau phenomenon; 128 pages including the Supporting Information

Wide, highly eccentric ($e>0.9$) compact binaries can naturally arise as progenitors of gravitational wave (GW) mergers. These systems are expected to have a significant population in the mHz band, with their GW signals characterized by ``repeated bursts" emitted upon each pericenter passage. In this study, we show that the detection of mHz GW signals from highly eccentric stellar mass binaries in the local universe can strongly constrain their orbital parameters. Specifically, it can achieve a relative measurement error of $\sim 10^{-6}$ for orbital frequency and $\sim 1\%$ for eccentricity (as $1-e$) in most of the detectable cases. On the other hand, the binary's mass ratio, distance, and intrinsic orbital inclination may be less precisely determined due to degeneracies in the GW waveform. We also perform mock LISA data analysis to evaluate the realistic detectability of highly eccentric compact binaries. Our results show that highly eccentric systems could be efficiently identified when multiple GW sources and stationary Gaussian instrumental noise are present in the detector output. This work highlights the potential of extracting the signal of ``bursting'' LISA sources to provide valuable insights into their orbital evolution, surrounding environment, and formation channels., Comment: 16+10 pages, 6+4 figures. Submitted to PRD

Alongside the population of several hundred radio millisecond pulsars currently known in Milky Way globular clusters, a subset of six slowly spinning pulsars (spin periods $0.3-4$\,s) are also observed. With inferred magnetic fields $\gtrsim 10^{11}\,$G and characteristic ages $\lesssim10^8\,$yr, explaining the formation of these apparently young pulsars in old stellar populations poses a major challenge. One popular explanation is that these objects are not actually young but instead have been partially spun up via accretion from a binary companion. In this scenario, accretion in a typical low-mass X-ray binary is interrupted by a dynamical encounter with a neighboring object in the cluster. Instead of complete spin up to millisecond spin periods, the accretion is halted prematurely, leaving behind a ``partially recycled'' neutron star. In this Letter, we use a combination of analytic arguments motivated by low-mass X-ray binary evolution and $N$-body simulations to show that this partial-recycling mechanism is not viable. Realistic globular clusters are not sufficiently dense to interrupt mass transfer on the short timescales required to achieve such slow spin periods. We argue that collapse of massive white dwarfs and/or neutron star collisions are more promising ways to form slow pulsars in old globular clusters., Comment: 9 pages, 2 figures. Submitted to ApJL. Comments welcome!

We study the Volterra Volterra Cox-Ingersoll-Ross process on $\mathbb{R}_+$ and its stationary version. Based on a fine asymptotic analysis of the corresponding Volterra Riccati equation combined with the affine transformation formula, we first show that the finite-dimensional distributions of this process are asymptotically independent. Afterwards, we prove a law-of-large numbers in $L^p$(\Omega)$ with $p \geq 2$ and show that the stationary process is ergodic. As an application, we prove the consistency of the method of moments and study the maximum-likelihood estimation for continuous and discrete high-frequency observations., Comment: arXiv admin note: substantial text overlap with arXiv:2404.05554

We consider slow-roll inflation in the context of a modified Brans-Dicke dilaton gravity. From a two self-interacting potentials $V(\phi)$, we reproduce a Starobinsky-like potential and, commonly in syperstring models, an exponential tail potential $V(\phi)\sim(1-e^{\alpha_0\phi})$, with $\alpha_0$ being a constant coefficient related to the Brans-Dicke parameter $\omega$. Using the observational bounds on the spectral index $n_s$ and tensor-to-scalar ratio $r$ imposed by Planck-CMB baseline data and the BICEP2/Keck collaboration with combination with Planck 2018 and the Baryonic Acoustic Oscillations(BAO), we obtain for both models a good agreement with current observations with $n_s = 0.960 - 0.972$ and $r<0.02$. In addition, the resulting large values of $\omega$ suggests a possible linkage of the inflationary regime and today's solar system bounds., Comment: revised version, updated references

In this companion article to [HKK24], we apply the theory of equivariant Poincar\'e duality developed there in the special case of cyclic groups $C_p$ of prime order to remove, in a special case, a technical condition given by Davis--L\"uck [DL24] in their work on the Nielsen realisation problem for aspherical manifolds. Along the way, we will also give a complete characterisation of $C_p$--Poincar\'e spaces as well as introduce a genuine equivariant refinement of the classical notion of virtual Poincar\'e duality groups which might be of independent interest., Comment: 30 pages. Comments welcome!

The widespread application of Artificial Intelligence (AI) techniques has significantly influenced the development of new therapeutic agents. These computational methods can be used to design and predict the properties of generated molecules. Multi-target Drug Discovery (MTDD) is an emerging paradigm for discovering drugs against complex disorders that do not respond well to more traditional target-specific treatments, such as central nervous system, immune system, and cardiovascular diseases. Still, there is yet to be an established benchmark suite for assessing the effectiveness of AI tools for designing multi-target compounds. Standardized benchmarks allow for comparing existing techniques and promote rapid research progress. Hence, this work proposes an evaluation framework for molecule generation techniques in MTDD scenarios, considering brain diseases as a case study. Our methodology involves using large language models to select the appropriate molecular targets, gathering and preprocessing the bioassay datasets, training quantitative structure-activity relationship models to predict target modulation, and assessing other essential drug-likeness properties for implementing the benchmarks. Additionally, this work will assess the performance of four deep generative models and evolutionary algorithms over our benchmark suite. In our findings, both evolutionary algorithms and generative models can achieve competitive results across the proposed benchmarks., Comment: 8 pages, 1 figure, published in 2024 IEEE Congress on Evolutionary Computation (CEC)

A kinetic theory for moderately dense gases of inelastic and rough spherical molecules is developed from the Enskog equation where a macroscopic state is characterized by 29 scalar fields which correspond to the moments of the distribution function: mass density, hydrodynamic velocity, pressure tensor, absolute temperature, translational and rotational heat fluxes, hydrodynamic angular velocity and angular velocity flux. The balance equations for the 29 scalar fields are obtained from a transfer equation derived from the Enskog equation where the kinetic and potential parts of the new moments of the distribution function and production terms are calculated from Grad's distribution function for the basic fields. The transition from the 29 field theory to an eight field theory -- with mass density, hydrodynamic velocity, absolute temperature and hydrodynamic angular velocity -- leads to the determination of the transport coefficients of the Navier-Stokes and Fourier laws. The transport coefficients are functions of the normal and tangential restitution coefficients and of the local equilibrium radial distribution function. The transport coefficients in the limiting case of elastic rough spheres is also determined., Comment: 20 pages

The existence of compact stellar remnants in the mass range $2-5\,M_{\odot}$ has long been debated. This so-called lower mass gap was initially suggested by the lack of low-mass X-ray binary observations with accretors about $2-5\,M_{\odot}$, but it has recently been called into question following newer observations, including a lower-mass-gap candidate with a millisecond pulsar companion in the dense globular cluster NGC 1851. Here we model NGC 1851 with a grid of similar dense star clusters utilizing the state-of-the-art Monte Carlo $N$-body code \texttt{CMC}, and we specifically study the formation of lower-mass-gap black holes. We demonstrate that both massive star evolution and dynamical interactions can contribute to forming lower-mass-gap black holes. In general, the collapse of massive remnants formed through mergers of neutron stars or massive white dwarfs produces the largest number of lower-mass-gap black holes among all formation channels. However, in more massive clusters, supernova core collapse can contribute comparable numbers. Our NGC 1851-like models can reproduce millisecond pulsar -- lower-mass-gap black hole binaries similar to the observed system. Additionally, the lower-mass-gap black holes can also become components of dynamically assembled binaries, and some will be in merging black hole - neutron star systems similar to the recently detected gravitational wave source GW230529. However, the corresponding merger rate is probably $\lesssim 1~{\rm Gpc^{-3}\,yr^{-1}}$., Comment: 18 pages, 7 figures, 3 tables. Published at ApJ

This paper explores artificial intelligence (AI) methods for the approximate compiling of unitaries, focusing on the use of fixed two-qubit gates and arbitrary single-qubit rotations typical in superconducting hardware. Our approach involves three main stages: identifying an initial template that approximates the target unitary, predicting initial parameters for this template, and refining these parameters to maximize the fidelity of the circuit. We propose AI-driven approaches for the first two stages, with a deep learning model that suggests initial templates and an autoencoder-like model that suggests parameter values, which are refined through gradient descent to achieve the desired fidelity. We demonstrate the method on 2 and 3-qubit unitaries, showcasing promising improvements over exhaustive search and random parameter initialization. The results highlight the potential of AI to enhance the transpiling process, supporting more efficient quantum computations on current and future quantum hardware.

The perovskite oxide EuTiO3 (ETO) has attracted increased scientific interest due to its potential multiferroic properties and magnetic activity above and below its structural phase transition at TS=282K. Various experiments have indirectly evidenced that this transition is neither a cubic tetragonal nor the only one occurring in ETO. Here, we show new results demonstrating two further instabilities below TS based on lattice dynamics and spin-phonon interactions combined with a Landau free energy model with coupled order parameters. The new transition temperatures perfectly agree with available experimental data where further instabilities have been anticipated., Comment: 14 pages, 5 figures

The superposition of frequency-shifted Laguerre-Gauss modes can produce a rotating saddle-like intensity profile. When spinning fast enough, the optical forces produced by this structured light saddle generate a dynamically stable equilibrium point capable of trapping nanoparticles in a high vacuum, akin to a Paul trap but with its unique characteristics. We analyze the stability conditions and center-of-mass motion, dynamics and cooling of a nanoparticle levitated in the optical saddle trap. We expect the optical saddle to find applications in levitated optomechanics experiments requiring fast parametric modulation and inverted squeezing potential landscapes.

Competing interactions in low-dimensional materials can produce nearly degenerate electronic and structural phases. We investigate the staircase of structural phase transitions in layered IrTe$_2$ for which a number of potential transition mechanisms have been postulated. The spatial coexistence of multiple phases on the micron scale has prevented a detailed analysis of the electronic structure. By exploiting micro-ARPES obtained with synchrotron radiation we extract the electronic structure of the multiple structural phases in IrTe$_2$ in order to address the mechanism underlying the phase transitions. We find direct evidence of lowered energy states that appear in the low-temperature phases, states previously predicted by \textit{ab initio} calculations and extended here. Our results validate a proposed scenario of bonding and anti-bonding states as the driver of the phase transitions., Comment: None

We report the discovery of a high velocity, very low-mass star or brown dwarf whose kinematics suggest it is unbound to the Milky Way. CWISE J124909.08+362116.0 was identified by citizen scientists in the Backyard Worlds: Planet 9 program as a high proper motion ($\mu$ $=$ 0''9/yr) faint red source. Moderate resolution spectroscopy with Keck/NIRES reveals it to be a metal-poor early L subdwarf with a large radial velocity ($-$103$\pm$10 km/s), and its estimated distance of 125$\pm$8 pc yields a speed of 456$\pm$27 km/s in the Galactic rest frame, near the local escape velocity for the Milky Way. We explore several potential scenarios for the origin of this source, including ejection from the Galactic center $\gtrsim$3 Gyr in the past, survival as the mass donor companion to an exploded white dwarf. acceleration through a three-body interaction with a black hole binary in a globular cluster, and accretion from a Milky Way satellite system. CWISE J1249+3621 is the first hypervelocity very low mass star or brown dwarf to be found, and the nearest of all such systems. It may represent a broader population of very high velocity, low-mass objects that have undergone extreme accelerations., Comment: 17 pages, 3 figures, accepted for publication in Astrophysical Journal Letters

Quantum programs are typically developed using quantum Software Development Kits (SDKs). The rapid advancement of quantum computing necessitates new tools to streamline this development process, and one such tool could be Generative Artificial intelligence (GenAI). In this study, we introduce and use the Qiskit HumanEval dataset, a hand-curated collection of tasks designed to benchmark the ability of Large Language Models (LLMs) to produce quantum code using Qiskit - a quantum SDK. This dataset consists of more than 100 quantum computing tasks, each accompanied by a prompt, a canonical solution, a comprehensive test case, and a difficulty scale to evaluate the correctness of the generated solutions. We systematically assess the performance of a set of LLMs against the Qiskit HumanEval dataset's tasks and focus on the models ability in producing executable quantum code. Our findings not only demonstrate the feasibility of using LLMs for generating quantum code but also establish a new benchmark for ongoing advancements in the field and encourage further exploration and development of GenAI-driven tools for quantum code generation.

Code Large Language Models (Code LLMs) have emerged as powerful tools, revolutionizing the software development landscape by automating the coding process and reducing time and effort required to build applications. This paper focuses on training Code LLMs to specialize in the field of quantum computing. We begin by discussing the unique needs of quantum computing programming, which differ significantly from classical programming approaches or languages. A Code LLM specializing in quantum computing requires a foundational understanding of quantum computing and quantum information theory. However, the scarcity of available quantum code examples and the rapidly evolving field, which necessitates continuous dataset updates, present significant challenges. Moreover, we discuss our work on training Code LLMs to produce high-quality quantum code using the Qiskit library. This work includes an examination of the various aspects of the LLMs used for training and the specific training conditions, as well as the results obtained with our current models. To evaluate our models, we have developed a custom benchmark, similar to HumanEval, which includes a set of tests specifically designed for the field of quantum computing programming using Qiskit. Our findings indicate that our model outperforms existing state-of-the-art models in quantum computing tasks. We also provide examples of code suggestions, comparing our model to other relevant code LLMs. Finally, we introduce a discussion on the potential benefits of Code LLMs for quantum computing computational scientists, researchers, and practitioners. We also explore various features and future work that could be relevant in this context.

The origins and mergers of supermassive black holes (BHs) remain a mystery. We describe a scenario from a novel multi-physics simulation featuring rapid ($\lesssim 1\,$Myr) hyper-Eddington gas capture by a $\sim 1000\,{\rm M}_{\odot}$ ``seed'' BH up to supermassive ($\gtrsim 10^{6}\,M_{\odot}$) masses, in a massive, dense molecular cloud complex typical of high-redshift starbursts. Due to the high cloud density, stellar feedback is inefficient and most of the gas turns into stars in star clusters which rapidly merge hierarchically, creating deep potential wells. Relatively low-mass BH seeds at random positions can be ``captured'' by merging sub-clusters and migrate to the center in $\sim1$ free-fall time (vastly faster than dynamical friction). This also efficiently produces a paired BH binary with $\sim 0.1$\,pc separation. The centrally-concentrated stellar density profile (akin to a ``proto-bulge'') allows the cluster as a whole to capture and retain gas and build up a large (pc-scale) circum-binary accretion disk with gas coherently funnelled to the central BH (even when the BH radius of influence is small). The disk is ``hyper-magnetized'' and ``flux-frozen'': dominated by a toroidal magnetic field with plasma $\beta \sim 10^{-3}$, with the fields amplified by flux-freezing. This drives hyper-Eddington inflow rates $\gtrsim 1\,\rm M_\odot yr^{-1}$, which also drive the two BHs to nearly-equal masses. The late-stage system appears remarkably similar to recently-observed high-redshift ``little red dots.'' This scenario can provide an explanation for rapid SMBH formation, growth and mergers in high-redshift galaxies., Comment: 9 pages, 5 figures, final version matching the publication

In this article, we introduce and develop the notion of parametrised Poincar\'{e} duality in the formalism of parametrised higher category theory by Martini-Wolf, in part generalising Cnossen's theory of twisted ambidexterity to the nonpresentable setting. We prove several basechange results, allowing us to move between different coefficient categories and ambient topoi. We then specialise the general framework to yield a good theory of equivariant Poincar\'{e} duality spaces for compact Lie groups and apply our basechange results to obtain a suite of isotropy separation methods. Finally, we employ this theory to perform various categorical Smith-theoretic manoeuvres to prove, among other things, a generalisation of a theorem of Atiyah-Bott and Conner-Floyd on group actions with single fixed points., Comment: 97 pages. Comments welcome!

This paper demonstrates the integration of Reinforcement Learning (RL) into quantum transpiling workflows, significantly enhancing the synthesis and routing of quantum circuits. By employing RL, we achieve near-optimal synthesis of Linear Function, Clifford, and Permutation circuits, up to 9, 11 and 65 qubits respectively, while being compatible with native device instruction sets and connectivity constraints, and orders of magnitude faster than optimization methods such as SAT solvers. We also achieve significant reductions in two-qubit gate depth and count for circuit routing up to 133 qubits with respect to other routing heuristics such as SABRE. We find the method to be efficient enough to be useful in practice in typical quantum transpiling pipelines. Our results set the stage for further AI-powered enhancements of quantum computing workflows.

The detection of supermassive black holes (SMBHs) in high-redshift luminous quasars may require a phase of rapid accretion, and as a precondition, substantial gas influx toward seed black holes (BHs) from kilo-parsec or parsec scales. Our previous research demonstrated the plausibility of such gas supply for BH seeds within star-forming giant molecular clouds (GMCs) with high surface density ($\sim 10^4\,{\rm {\rm M_\odot}\, pc}^{-2}$), facilitating ``hyper-Eddington'' accretion via efficient feeding by dense clumps which are driven by turbulence and stellar feedback. This article investigates the impacts of feedback from accreting BHs on this process, including radiation, mechanical jets, and highly relativistic cosmic rays. We run a suite of numerical simulations to explore diverse parameter spaces of BH feedback, including the sub-grid accretion model, feedback energy efficiency, mass loading factor, and initial metallicity. Utilizing radiative feedback models inferred from the slim disk, we find that hyper-Eddington accretion is still achievable, yielding BH bolometric luminosities as high as $10^{41}$ -- $10^{44}\,\rm erg/s$, depending on the GMC properties and specific feedback model assumed. We find the maximum possible mass growth of seed BHs ($\Delta M_{\rm BH}^{\rm max}$) is regulated by the momentum deposition rate from BH feedback, $\dot{p}_{\rm feedback}/(\dot{M}_{\rm BH} c)$, which leads to an analytic scaling that agrees well with simulations. This scenario predicts the rapid formation of $\sim 10^4\,\rm M_\odot$ intermediate-massive BHs (IMBHs) from stellar-mass BHs within $\sim \rm Myr$. Furthermore, we examine the impacts of sub-grid accretion models and how BH feedback may influence star formation within these cloud complexes., Comment: Updated version; accepted to A&A

Instrumental variable (IV) regression can be approached through its formulation in terms of conditional moment restrictions (CMR). Building on variants of the generalized method of moments, most CMR estimators are implicitly based on approximating the population data distribution via reweightings of the empirical sample. While for large sample sizes, in the independent identically distributed (IID) setting, reweightings can provide sufficient flexibility, they might fail to capture the relevant information in presence of corrupted data or data prone to adversarial attacks. To address these shortcomings, we propose the Sinkhorn Method of Moments, an optimal transport-based IV estimator that takes into account the geometry of the data manifold through data-derivative information. We provide a simple plug-and-play implementation of our method that performs on par with related estimators in standard settings but improves robustness against data corruption and adversarial attacks.

Context. The star-black hole (S-BH) binary known as Gaia BH3, discovered by the Gaia Collaboration is chemically and kinematically associated with the metal-poor ED-2 stream in the Milky Way halo. Aims. We explore the possibility that Gaia BH3 was assembled dynamically in the progenitor globular cluster (GC) of the ED-2 stream. Methods. We used a public suite of star-by-star dynamical Monte Carlo models to identify S-BH binaries in GCs with different initial masses and (half-mass) radii. Results. We show that a likely progenitor of the ED-2 stream was a relatively low-mass ($\lesssim10^5M_\odot$) GC with an initial half-mass radius of ~4 pc. Such a GC can dynamically retain a large fraction of its BH population and dissolve on the orbit of ED-2. From the suite of models we find that GCs produce ~ 3 - 30 S-BH binaries, approximately independent of initial GC mass and inversely correlated with initial cluster radius. Scaling the results to the Milky Way GC population, we find that ~75% of the S-BH binaries formed in GCs are ejected from their host GC, all in the early phases of evolution ($\lesssim1$ Gyr); these are expected to no longer be close to streams. The ~25% of S-BH binaries retained until dissolution are expected to form part of streams, such that for an initial mass of the progenitor of ED-2 of a few $10^4M_\odot$, we expect ~2-3 S-BH to end up in the stream. GC models with metallicities similar to Gaia BH3 ($\lesssim1\%$ solar) include S-BH binaries with similar BH masses ($\gtrsim30M_\odot$), orbital periods, and eccentricities. Conclusions. We predict the Galactic halo contains of order $10^5$ S-BH binaries that formed dynamically in GCs, a fraction of which may readily be detected in Gaia DR4. The detection of these sources provides valuable tests of BH dynamics in clusters and the possible role in formation of gravitational wave sources., Comment: 5 pages, 3 figures, accepted in A&A

Very massive stars (VMSs) formed via a sequence of stellar collisions in dense star clusters have been proposed as the progenitors of massive black hole seeds. VMSs could indeed collapse to form intermediate-mass black holes (IMBHs), which would then grow by accretion to become the supermassive black holes observed at the centers of galaxies and powering high-redshift quasars. Previous studies have investigated how different cluster initial conditions affect the formation of a VMS, including mass segregation, stellar collisions, and binaries, among others. In this study, we investigate the growth of VMSs with a new grid of Cluster Monte Carlo (CMC) star cluster simulations -- the most expansive to date. The simulations span a wide range of initial conditions, varying the number of stars, cluster density, stellar initial mass function (IMF), and primordial binary fraction. We find a gradual shift in the mass of the most massive collision product across the parameter space; in particular, denser clusters born with top-heavy IMFs provide strong collisional regimes that form VMSs with masses easily exceeding 1000 solar masses. Our results are used to derive a fitting formula that can predict the typical mass of a VMS formed as a function of the star cluster properties. Additionally, we study the stochasticity of this process and derive a statistical distribution for the mass of the VMS formed in one of our models, recomputing the model 50 times with different initial random seeds., Comment: Accepted for ApJ. Comments welcome. 19 pages, 10 figures

Epitaxial growth of WTe$_2$ offers significant advantages, including the production of high-qualityfilms, possible long range in-plane ordering and precise control over layer thicknesses. However,the mean island size of WTe$_2$ grown by molecular beam epitaxy (MBE) in litterature is only a fewtens of nanometers, which is not suitable for an implementation of devices at large lateral scales.Here we report the growth of Td-WTe$_2$ ultrathin films by MBE on monolayer (ML) graphenereaching a mean flake size of $\cong$110nm, which is, on overage, more than three time larger thanprevious results. WTe$_2$ films thicker than 5nm have been successfully synthesized and exhibit theexpected Td-phase atomic structure. We rationalize epitaxial growth of Td-WTe$_2$ and propose asimple model to estimate the mean flake size as a function of growth parameters that can be appliedto other transition metal dichalcogenides (TMDCs). Based on nucleation theory and Kolmogorov-Johnson-Meh-Avrami (KJMA) equation, our analytical model supports experimental data showinga critical coverage of 0.13ML above which WTe$_2$ nucleation becomes negligible. The quality ofmonolayer WTe$_2$ films is demonstrated from electronic band structure analysis using angle-resolved photoemission spectroscopy (ARPES) in agreement with first-principle calculationsperformed on free-standing WTe$_2$ and previous reports., Comment: ACS Applied Materials and Interfaces, 2024

Recently, we demonstrated self-consistent formation of strongly-magnetized quasar accretion disks (QADs) from cosmological radiation-magnetohydrodynamic-thermochemical galaxy-star formation simulations, including the full STARFORGE physics shown previously to produce a reasonable IMF under typical ISM conditions. Here we study star formation and the stellar IMF in QADs, on scales from 100 au to 10 pc from the SMBH. We show it is critical to include physics often previously neglected, including magnetic fields, radiation, and (proto)stellar feedback. Closer to the SMBH, star formation is suppressed, but the (rare) stars that do form exhibit top-heavy IMFs. Stars can form only in special locations (e.g. magnetic field switches) in the outer QAD. Protostars accrete their natal cores rapidly but then dynamically decouple from the gas and wander, ceasing accretion on timescales ~100 yr. Their jets control initial core accretion, but the ejecta are swept up into the larger-scale QAD flow without much dynamical effect. The strong tidal environment strongly suppresses common-core multiplicity. The IMF shape depends sensitively on un-resolved dynamics of protostellar disks (PSDs), as the global dynamical times can become incredibly short ($\ll$ yr) and tidal fields are incredibly strong, so whether PSDs can efficiently transport angular momentum or fragment catastrophically at $\lesssim 10$ au scales requires novel PSD simulations to properly address. Most analytic IMF models and analogies with planet formation in PSDs fail qualitatively to explain the simulation IMFs, though we discuss a couple of viable models., Comment: 39 pages, 23 figures, replaced with version accepted to the Open Journal of Astrophysics. Additional images and movies from the simulations available at http://www.tapir.caltech.edu/~phopkins/Site/animations/Movies_zoom.html

We study statistical inference of the drift parameters for the Volterra Ornstein-Uhlenbeck process on R in the ergodic regime. For continuous-time observations, we derive the corresponding maximum likelihood estimators and show that they are strongly consistent and asymptotically normal locally uniformly in the parameters. For the case of discrete high-frequency observations, we prove similar results by discretization of the continuous-time maximum likelihood estimator. Finally, for discrete low-frequency observations, we show that the method of moments is consistent. Our proofs are crucially based on the law of large numbers., Comment: The old version has been split into two separate articles. This identifier contains part one on the Volterra Ornstein-Uhlenbeck process, while the other one focuses on the Volterra Cox-Ingersoll-Ross process