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It remains a mystery when our Milky Way first formed a stellar disk component that survived and maintained its disk structure from subsequent galaxy mergers. We present a study of the age-dependent structure and star formation rate of the Milky Way's disk using high-alpha stars with significant orbital angular momentum that have precise age determinations. Our results show that the radial scale length is nearly independent of age, while the vertical scale height experienced dramatic evolution. A disk-like geometry presents even for populations older than 13 Gyr, with the scale height-to-length ratio dropping below 0.5 for populations younger than 12.5 Gyr. We dub the oldest population that has maintained a disk geometry - apparently formed over 13 Gyr ago - PanGu. With an estimated present-day stellar mass of $2 \times 10^9$ $M_\odot$, PanGu is presumed to be a major stellar component of our Galaxy in the earliest epoch. The total present-day stellar mass of the whole high-alpha disk is $2 \times 10^{10}$ $M_\odot$, mostly formed during a distinct star formation rate peak of 11 $M_\odot$ per year around 11 Gyrs ago. A comparison with Milky Way analogs in the TNG50 simulations implies that our Galaxy has experienced an exceptionally quiescent dynamical history, even before the Gaia-Enceladus merger., Comment: Published in Nature Astronomy on 10 October, 2024; This manuscript is the accepted version

Bistable mechanical metamaterials have shown promise for mitigating the harmful consequences of impact by converting kinetic energy into stored strain energy, offering an alternative and potentially synergistic approach to conventional methods of attenuating energy transmission. In this work, we numerically study the dynamic response of a one-dimensional bistable metamaterial struck by a high speed impactor (where the impactor velocity is commensurate with the sound speed), using the peak kinetic energy experienced at midpoint of the metamaterial compared to that in an otherwise identical linear system as our performance metric. We make five key findings: 1) The bistable material can counter-intuitively perform better (to nearly 1000x better than the linear system) as the viscosity decreases (but remains finite), but only when sufficiently fine discretization has been reached (i.e. the system approaches sufficiently close to the continuum limit); 2) This discretization threshold is sharp, and depends on the viscosity present; 3) The bistable materials can also perform significantly worse than linear systems (for low discretization and viscosity or zero viscosity); 4) The dependence on discretization stems from the partition of energy into trains of solitary waves that have pulse lengths proportional to the unit cell size, where, with intersite viscosity, the solitary wave trains induce high velocity gradients and thus enhanced damping compared to linear, and low-unit-cell-number bistable, materials; and 5) When sufficiently fine discretization has been reached at low viscosities, the bistable system outperforms the linear one for a wide range of impactor conditions. The first point is particularly important, as it shows the existence of a nonlinear dynamical size effect, where, given a protective layer of some thickness...

We prove a new lower bound for the Frobenius norm of the inverse of an non-negative matrix. This bound is only a modest improvement over previous results, but is sufficient for fully resolving a conjecture of Harwitz and Sloane, commonly referred to as the S-matrix conjecture, for all dimensions larger than a small constant.

We propose a quantum algorithm to tackle the quadratic nonlinearity in the Lattice Boltzmann (LB) collision operator. The key idea is to build the quantum gates based on the particle distribution functions (PDF) within the coherence time for qubits. Thus, both the operator and a state vector are linear functions of PDFs, and upon quantum state evolution, the resulting PDFs will have quadraticity. To this end, we decompose the collision operator for a $DmQn$ lattice model into a product of $2(n+1)$ operators, where $n$ is the number of lattice velocity directions. After decomposition, the $(n+1)$ operators with constant entries remain unchanged throughout the simulation, whereas the remaining $(n+1)$ will be built based on the statevector of the previous time step. Also, we show that such a decomposition is not unique. Compared to the second-order Carleman-linearized LB, the present approach reduces the circuit width by half and circuit depth by exponential order. The proposed algorithm has been verified through the one-dimensional flow discontinuity and two-dimensional Kolmogrov-like flow test cases., Comment: 5 pages, 3 figures

Stars in the Galactic disk are born on cold, nearly circular orbits with small vertical excursions. After their birth, their orbits evolve, driven by small- or large-scale perturbations in the Galactic disk's gravitational potential. Here, we study the vertical motions of young stars over their first few orbital periods, using a sample of OBA stars from \textit{Gaia} E/DR3, which includes radial velocities and ages $\tau$ from LAMOST. We constructed a parametric model for the time evolution of the stellar orbits' mean vertical actions $J_z$ as a function of Galactocentric radius, $R_{\mathrm{GC}}$. Accounting for data uncertainties, we use Markov Chain Monte Carlo (MCMC) analysis in annuli of Galactocentric radius to constrain the model parameters. Our best-fit model shows a remarkably linear increase of vertical actions with age across all Galactocentric radii examined. Orbital \textit{heating} by random scattering could offer a straightforward interpretation for this trend. However, various other dynamical aspects of the Galactic disk, such as stars being born in a warped disk, might offer alternative explanations that could be tested in the future., Comment: 10 pages, 5 figures. Draft version July 9, 2024. Typeset using LATEX default style in AASTeX631

Galaxies are not in a dynamical steady state. They continually undergo perturbations, e.g., from infalling dwarf galaxies and dark-matter substructure. After a dynamical perturbation, stars phase mix towards a new steady state; in so doing they generally form spiral structures, such as spiral density waves in galaxy disks and the Gaia Snail observed in the vertical phase-space density in the solar neighborhood. Structures in phase-space density can be hard to measure accurately, because spatially varying selection effects imprint their own patterns on the density. However, stellar labels such as metallicity, or other element abundances, or stellar masses and ages, can be measured even in the face of complex or unknown spatial selection functions. We show that if the equilibrium galaxy has phase-space gradients in these labels, any perturbation that could raise a spiral wave in the phase-space density will raise a spiral wave in the distribution of labels as well. We work out the relationship between the spiral patterns in the density and in the labels. As an example, we analyze the Gaia Snail and show that its amplitude and dynamical age as derived from elemental abundances (mainly [Mg/Fe]) follow similar patterns to those derived from the phase-space density. Our best model dates the Snail's perturbation to about 400 Myr ago although we find significant variations with angular momentum in the best-fit age. Conceptually, the ideas presented here are related to Orbital Torus Imaging, chemical tagging, and other methods that use stellar labels to trace dynamics., Comment: Submitted to ApJ, comments are welcome

We show with Gaia XP spectroscopy that extremely metal-rich stars in the Milky Way (EMR; $[M/H]_{XP} > 0.5$) - but only those - are largely confined to a tight "knot" at the center of the Galaxy. This EMR knot is round in projection, has a fairly abrupt edge near $\sim 1.5$kpc, and is a dynamically hot system. This central knot also contains very metal-rich (VMR; $+0.2\le [M/H]_{XP} \le +0.4$) stars. However, in contrast to EMR stars, the bulk of VMR stars form an extended, highly flattened distribution in the inner Galaxy ($R_{\mathrm{GC}}\lesssim 5$ kpc). We draw on TNG50 simulations of Milky Way analogs for context and find that compact, metal-rich knots confined to $<1.5$kpc are a universal feature. In typical simulated analogs, the top 5-10% most metal-rich stars are confined to a central knot; however, in our Milky Way data this fraction is only 0.1%. Dust-penetrating wide-area near-infrared spectroscopy, such as SDSS-V, will be needed for a rigorous estimate of the fraction of stars in the Galactic EMR knot. Why in our Milky Way only EMR giants are confined to such a central knot remains to be explained. Remarkably, the central few kiloparsecs of the Milky Way harbor both the highest concentration of metal-poor stars (the `poor old heart') and almost all EMR stars. This highlights the stellar population diversity at the bottom of galactic potential wells., Comment: 11 pages, 7 figures, submitted to ApJ

In recent years, the study of the Milky Way has significantly advanced due to extensive spectroscopic surveys of its stars, complemented by astroseismic and astrometric data. However, it remains disjoint from recent advancements in understanding the physics of the Galactic interstellar medium (ISM). This paper introduces a new model for the chemical evolution of the Milky Way that can be constrained on stellar data, because it combines a state-of-the-art ISM model with a Milky Way stellar disc model. Utilizing a dataset of red clump stars from APOGEE, known for their precise ages and metallicities, we concentrate on the last 6 billion years -- a period marked by Milky Way's secular evolution. We examine the oxygen abundance in the low-$\alpha$ disc stars relative to their ages and birth radii, validating or constraining critical ISM parameters that remain largely unexplored in extragalactic observations. The models that successfully reproduce the radius -- metallicity distribution and the age -- metallicity distribution of stars without violating existing ISM observations indicate a need for modest differential oxygen enrichment in Galactic outflows, meaning that the oxygen abundance of outflows is higher than the local ISM abundance, irrespective of outflow mass loading. The models also suggest somewhat elevated ISM gas velocity dispersion levels over the past 6 billion years compared to galaxies of similar mass. The extra turbulence necessary could result from energy from gas accretion onto the Galaxy, supernovae clustering in the ISM, or increased star formation efficiency per freefall time. This work provides a novel approach to constraining the Galactic ISM and outflows, leveraging the detailed insights available from contemporary Milky Way surveys., Comment: 20 pages, 9 figures. Accepted by MNRAS

In this study, we introduce a robust central Gradient-Based Reconstruction (GBR) scheme for the compressible Navier-Stokes equations. The method leverages transformation to characteristic space, allowing selective treatment of waves from the compressible Euler equations. By averaging left- and right-biased state interpolations, a central scheme is achieved for all but the acoustic waves, which require upwinding for stability. Distinct differences were observed between transformations using either primitive or conservative variables. We evaluated the method's robustness and superiority using benchmark problems, including the two-dimensional shock entropy problem, two-dimensional viscous shock tube, and three-dimensional inviscid Taylor-Green vortex. Subsequently, we assessed the method in the context of Wall Modelled Large Eddy Simulations (WMLES), where coarse grids are used to reduce computational cost but also introduce substantial numerical dissipation. Using WMLES, we simulated oblique shock impingement on a Mach 6 disturbed boundary layer and a Mach 7.7 flow over a $15^{\circ}$ compression ramp. Our findings reveal that: 1) transformation to characteristic space using conservative variables leads to more accurate results; 2) minimizing numerical dissipation through centralized interpolation is crucial. In the compression ramp case, boundary layer separation was shifted slightly upstream, and there was an over-prediction of wall heating, likely attributable to the equilibrium-assuming wall model. Overall, this work showcases the method's potential in accurately capturing complex flow dynamics with reduced numerical dissipation.

In the present contribution, we propose a quantum unitary matrix representation for the Lattice Boltzmann Method (LBM) to simulate fluid flows in the low Reynolds number ($Re$) regime. Since the particle distribution functions are encoded as probability amplitudes of the quantum state, we show that the state of the ancilla qubit must be controlled during the initial state preparation. In contrast to methods such as the linear combination of unitaries to implement non-unitary operators, we utilize the classical singular value decomposition (SVD) to decompose the collision and streaming operators into a product of unitaries. Our approach has been tested using benchmark problems such as advection-diffusion of a Gaussian hill, Poiseuille flow, Couette flow, and the lid-driven cavity problem. We report the two-qubit controlled-NOT (CNOT) and single-qubit U gate counts for test cases involving 9 to 12 qubits and grid sizes ranging from 24 to 216 points. While the gate count closely aligns with the theoretical limit, the high number of two-qubit gates on the order of $10^7$ requires special attention as it relates to circuit synthesis.

Passive transformation of waves via nonlinear systems is ubiquitous in settings ranging from acoustics to optics and electromagnetics. Passivity is of particular importance for responding rapidly to stimuli and nonlinearity enormously expands signal transformability compared to linear systems due to the breaking of superposition. It is well known that different types of nonlinearity yield vastly different effects on propagating signals, which raises the question of ``what precise nonlinearity is the best for a given wave tailoring application?'' Considering a one-dimensional spring-mass chain as a testbed, we couple the shape optimization of structures for tailored nonlinear constitutive responses with reduced-order nonlinear dynamical inverse design. Using minimization of peak kinetic energy transmission from impact as a case study, we identify ideal nonlinear constitutive responses and the geometries needed to achieve them. As part of this, we show the large sensitivity of this metric to small changes in nonlinearity, and thus the need for high precision, free-form nonlinearity tailoring. We validate our predictions using impact experiments in a chain of nonlinear springs and masses. This work sets the foundation for broader passive nonlinear mechanical wave tailoring material design, with applications to computing, signal processing, shock mitigation, and autonomous materials.

We offer a new way to look at the Large Magellanic Cloud through stellar mono-abundance and mono-age-mono-abundance maps. These maps are based on $\gtrsim 500\,000$ member stars with photo-spectroscopic [M/H] and age estimates from Gaia DR3 data, and they are the first area-complete, metallicity- and age-differentiated stellar maps of any disk galaxy. Azimuthally averaged, these maps reveal a surprisingly simple picture of the Milky Way's largest satellite galaxy. For any [M/H] below -0.1 dex, the LMC's radial profile is well described by a simple exponential, but with a scale length that steadily shrinks towards higher metallicities, from nearly 2.3~kpc at [M/H]$=-1.8$ to only 0.75~kpc at [M/H]$=-0.25$. The prominence of the bar decreases dramatically with [M/H], making it barely discernible at [M/H]$\lesssim -1.5$. Yet, even for metal-rich populations, the bar has little impact on the azimuthally averaged profile of the mono-abundance components. Including ages, we find that the scale length is a greater function of age than of metallicity, with younger populations far more centrally concentrated. At old ages, the scale length decreases with increasing metallicity; at young ages, the scale-length is independent of metallicity. These findings provide quantitative support for a scenario where the LMC built its stellar structure effectively outside in., Comment: Submitted to ApJ; constructive comments would be appreciated

Measurement science now connects strongly with engineering of quantum coherence, many-body states, and entanglement. To scale up the performance of an atomic clock using a degenerate Fermi gas loaded in a three-dimensional optical lattice, we must understand complex many-body Hamiltonians to ensure meaningful gains for metrological applications. In this work, we use a near unity filled Sr 3D lattice to study the effect of a tunable Fermi-Hubbard Hamiltonian. The clock laser introduces a spin-orbit coupling spiral phase and breaks the isotropy of superexchange interactions, changing the Heisenberg spin model into one exhibiting XXZ-type spin anisotropy. By tuning the lattice confinement and applying imaging spectroscopy we map out favorable atomic coherence regimes. With weak transverse confinement, both s- and p-wave interactions contribute to decoherence and atom loss, and their contributions can be balanced. At deep transverse confinement, we directly observe coherent superexchange interactions, tunable via on-site interaction and site-to-site energy shift, on the clock Ramsey fringe contrast over timescales of multiple seconds. This study provides a groundwork for using a 3D optical lattice clock to probe quantum magnetism and spin entanglement

In this paper, we propose a new set of midpoint-based high-order discretization schemes for computing straight and mixed nonlinear second derivative terms that appear in the compressible Navier-Stokes equations. Firstly, we detail a set of conventional fourth and sixth-order baseline schemes that utilize central midpoint derivatives for the calculation of second derivatives terms. To enhance the spectral properties of the baseline schemes, an optimization procedure is proposed that adjusts the order and truncation error of the midpoint derivative approximation while still constraining the same overall stencil width and scheme order. A new filter penalty term is introduced into the midpoint derivative calculation to help achieve high wavenumber accuracy and high-frequency damping in the mixed derivative discretization. Fourier analysis performed on the both straight and mixed second derivative terms show high spectral efficiency and minimal numerical viscosity with no odd-even decoupling effect. Numerical validation of the resulting optimized schemes is performed through various benchmark test cases assessing their theoretical order of accuracy and solution resolution. The results highlight that the present optimized schemes efficiently utilize the inherent viscosity of the governing equations to achieve improved simulation stability - a feature attributed to their superior spectral resolution in the high wavenumber range. The method is also tested and applied to non-uniform structured meshes in curvilinear coordinates, employing a supersonic impinging jet test case.

We present a comparison of the Milky Way's star formation rate (SFR) surface density ($\Sigma_{\rm SFR}$) obtained with two independent state-of-the-art observational methods. The first method infers $\Sigma_{\rm SFR}$ from observations of the dust thermal emission from interstellar dust grains in far-infrared wavelengths registered in the Herschel infrared Galactic Plane Survey (Hi-GAL). The second method determines $\Sigma_{\rm SFR}$ by modeling the current population of O-, B-, and A-type stars in a 6 kpc $\times$ 6 kpc area around the Sun. We find an agreement between the two methods within a factor of two for the mean SFRs and the SFR surface density profiles. Given the broad differences between the observational techniques and the independent assumptions in the methods for computing the SFRs, this agreement constitutes a significant advance in our understanding of the star formation of our Galaxy and implies that the local SFR has been roughly constant over the past 10\,Myr., Comment: Accepted for publication at Astronomy & Astrophysics (11SEP2023). 8 pages, 7 figures

In the Milky Way, the distribution of stars in the $[\alpha/\mathrm{Fe}]$ vs. $[\mathrm{Fe/H}]$ and $[\mathrm{Fe/H}]$ vs. age planes holds essential information about the history of star formation, accretion, and dynamical evolution of the Galactic disk. We investigate these planes by applying novel statistical methods called copulas and elicitable maps to the ages and abundances of red giants in the APOGEE survey. We find that the low- and high-$\alpha$ disk stars have a clean separation in copula space and use this to provide an automated separation of the $\alpha$ sequences using a purely statistical approach. This separation reveals that the high-$\alpha$ disk ends at the same [$\alpha$/Fe] and age at high $[\mathrm{Fe/H}]$ as the low-$[\mathrm{Fe/H}]$ start of the low-$\alpha$ disk, thus supporting a sequential formation scenario for the high- and low-$\alpha$ disks. We then combine copulas with elicitable maps to precisely obtain the correlation between stellar age $\tau$ and metallicity $[\mathrm{Fe/H}]$ conditional on Galactocentric radius $R$ and height $z$ in the range $0 < R < 20$ kpc and $|z| < 2$ kpc. The resulting trends in the age-metallicity correlation with radius, height, and [$\alpha$/Fe] demonstrate a $\approx 0$ correlation wherever kinematically-cold orbits dominate, while the naively-expected negative correlation is present where kinematically-hot orbits dominate. This is consistent with the effects of spiral-driven radial migration, which must be strong enough to completely flatten the age-metallicity structure of the low-$\alpha$ disk., Comment: 18 pages, 16 figures, Submitted to MNRAS

In this work, we propose a novel selective discontinuity sensor approach for numerical simulations of the compressible Navier-Stokes equations. Since transformation to characteristic space is already a common approach to reduce high-frequency oscillations during interpolation to cell interfaces, we exploit the characteristic wave structure of the Euler equations to selectively treat the various waves that the equations comprise. The approach uses the Ducros shock sensing criterion to detect and limit oscillations due to shocks while applying a different criterion to detect and limit oscillations due to contact discontinuities. Furthermore, the method is general in the sense that it can be applied to any method that employs characteristic transformation and shock sensors. However, in the present work, we focus on the Gradient-Based Reconstruction family of schemes. A series of inviscid and viscous test cases containing various types of discontinuities are carried out. The proposed method is shown to markedly reduce high-frequency oscillations that arise due to improper treatment of the various discontinuities; i.e., applying the Ducros shock sensor in a flow where a strong contact discontinuity is present. Moreover, the proposed method is shown to predict similar volume-averaged kinetic energy and enstrophy profiles for the Taylor-Green vortex simulation compared to the base Ducros sensor, indicating that it does not introduce unnecessary numerical dissipation when there are no contact discontinuities in the flow., Comment: 34 pages, 13 Figures

The Covid-19 pandemic has accelerated the trend of many colleges moving to test-optional, and in some cases test-blind, admissions policies. A frequent claim is that by not seeing standardized test scores, a college is able to admit a student body that it prefers, such as one with more diversity. But how can observing less information allow a college to improve its decisions? We argue that test-optional policies may be driven by social pressure on colleges' admission decisions. We propose a model of college admissions in which a college disagrees with society on which students should be admitted. We show how the college can use a test-optional policy to reduce its "disagreement cost" with society, regardless of whether this results in a preferred student pool. We discuss which students either benefit from or are harmed by a test-optional policy. In an application, we study how a ban on using race in admissions may result in more colleges going test optional or test blind.

Zirconium alloys are widely used as the fuel cladding material in pressurised water reactors, accumulating a significant population of defects and dislocations from exposure to neutrons. We present and interpret synchrotron microbeam X-ray diffraction measurements of proton-irradiated Zircaloy-4, where we identify a transient peak and the subsequent saturation of dislocation density as a function of exposure. This is explained by direct atomistic simulations showing that the observed variation of dislocation density as a function of dose is a natural result of the evolution of the dense defect and dislocation microstructure driven by the concurrent generation of defects and their subsequent stress-driven relaxation. In the dynamic equilibrium state of the material developing in the high dose limit, the defect content distribution of the population of dislocation loops, coexisting with the dislocation network, follows a power law with exponent $\alpha \approx 2.2$. This corresponds to the power law exponent of $\beta \approx 3.4$ for the distribution of loops as a function of their diameter that compares favourably with the experimentally measured values of $\beta$ in the range $ 3 \leq \beta \leq 4$.

We use the sample of 198 Milky Way (MW) and Andromeda (M31) analogs from TNG50 to quantify the level of disk flaring predicted by a modern, high-resolution cosmological hydrodynamical simulation. Disk flaring refers to the increase of vertical stellar disk height with galactocentric distance. The TNG50 galaxies are selected to have stellar disky morphology, a stellar mass in the range of $M_* = 10^{10.5 - 11.2}~\rm{M_{\odot}}$, and a MW-like Mpc-scale environment at $z=0$. The stellar disks of such TNG50 MW/M31 analogs exhibit a wide diversity of structural properties, including a number of galaxies with disk scalelength and thin and thick disk scaleheights that are comparable to those measured or inferred for the Galaxy and Andromeda. With one set of physical ingredients, TNG50 returns a large variety of flaring flavours and amounts, also for mono-age stellar populations. With this paper, we hence propose a non-parametric characterization of flaring. The typical MW/M31 analogs exhibit disk scaleheights that are $1.5-2$ times larger in the outer than in the inner regions of the disk for both old and young stellar populations, but with a large galaxy-to-galaxy variation. Which stellar population flares more, and by how much, also varies from galaxy to galaxy. TNG50 de facto brackets existing observational constraints for the Galaxy and all previous numerical findings. A link between the amount of flaring and the $z=0$ global galaxy structural properties or merger history is complex. However, a connection between the scaleheights and the local stellar vertical kinematics and gravitational potential is clearly in place., Comment: Submitted to MNRAS. Main figures: 5, 13. See presentation and data release of TNG50 MW/M31 analogs by Pillepich et al. and see also Ramesh et al. on astro-ph today