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Gaia has revealed a clear signal of disequilibrium in the solar neighborhood in the form of a spiral (or snail) feature in the vertical phase-space distribution. We investigate the possibility that this structure emerges from ongoing perturbations by dark $\left(10^{6} M_{\odot} - 10^8 M_{\odot}\right)$ Galactic subhalos. We develop a probabilistic model for generating subhalo orbits based on a semi-analytic model of structure formation, and combine this framework with an approximate prescription for calculating the response of the disk to external perturbations. We also develop a phenomenological treatment for the diffusion of phase-space spirals caused by gravitational scattering between stars and giant molecular clouds, a process that erases the kinematic signatures of old ($t \gtrsim 0.6$ Gyr) events. Perturbations caused by dark subhalos are, on average, orders of magnitude weaker than those caused by luminous satellite galaxies, but the ubiquity of dark halos predicted by cold dark matter makes them a more probable source of strong perturbation to the dynamics of the solar neighborhood. Dark subhalos alone do not cause enough disturbance to explain the Gaia snail, but they excite fluctuations of $\sim 0.1-0.5 \ \rm{km} \ \rm{s^{-1}}$ in the mean vertical velocity of stars near the Galactic midplane that should persist to the present day. Subhalos also produce correlations between vertical frequency and orbital angle that could be mistaken as originating from a single past disturbance. Our results motivate investigation of the Milky Way's dark satellites by characterizing their kinematic signatures in phase-space spirals across the Galaxy., Comment: prepared for submission to ApJ, comments welcome

The asymmetric coloring number of a graph is the minimum number of colors needed to color its vertices, so that no non-trivial automorphism preserves the color classes. We investigate the asymmetric coloring number of graphs that are disjoint unions of graphs. We will derive a general relationship between the asymmetric coloring number of disjoint copies of graphs and the number of ways to color a single copy asymmetrically, and then look at particular cases such as disjoint copies of paths, stars, cycles, and hypercubes.

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