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Machine learning has become ubiquitous in materials modelling and now routinely enables large-scale atomistic simulations with quantum-mechanical accuracy. However, developing machine-learned interatomic potentials requires high-quality training data, and the manual generation and curation of such data can be a major bottleneck. Here, we introduce an automated framework for the exploration and fitting of potential-energy surfaces, implemented in an openly available software package that we call autoplex (`automatic potential-landscape explorer'). We discuss design choices, particularly the interoperability with existing software architectures, and the ability for the end user to easily use the computational workflows provided. We show wide-ranging capability demonstrations: for the titanium-oxygen system, SiO2, crystalline and liquid water, as well as phase-change memory materials. More generally, our study illustrates how automation can speed up atomistic machine learning -- with a long-term vision of making it a genuine mainstream tool in physics, chemistry, and materials science.

In this paper, we present a concise development of the well-studied theory of trace class operators on infinite dimensional (separable) Hilbert spaces suitable for an advanced undergraduate, as well as a construction of the inverse Laplacian on closed manifolds. With these developments acting as prerequisite, we present original trace computations involving the inverse Laplacian on the (flat) torus, generalizing computations done by R. Grady and O. Gwilliam within the context of topological quantum field theory., Comment: 31 pages

We report the first measurement of the azimuthal anisotropy of J$/\psi$ at forward rapidity ($1.2<|\eta|<2.2$) in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV at the Relativistic Heavy Ion Collider. The data were collected by the PHENIX experiment in 2014 and 2016 with integrated luminosity of 14.5~nb$^{-1}$. The second Fourier coefficient ($v_2$) of the azimuthal distribution of $J/\psi$ is determined as a function of the transverse momentum ($p_T$) using the event-plane method. The measurements were performed for several selections of collision centrality: 0\%--50\%, 10\%--60\%, and 10\%-40\%. We find that in all cases the values of $v_2(p_T)$, which quantify the elliptic flow of J$/\psi$, are consistent with zero. The results are consistent with measurements at midrapidity, indicating no significant elliptic flow of the J$/\psi$ within the quark-gluon-plasma medium at collision energies of $\sqrt{s_{_{NN}}}=200$ GeV., Comment: 369 authors from 72 institutions, 12 pages, 7 figures, 5 tables. v1 is version submitted to Physical Review C. HEPdata tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.html

We present the first forward-rapidity measurements of elliptic anisotropy of open-heavy-flavor muons at the BNL Relativistic Heavy Ion Collider. The measurements are based on data samples of Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV collected by the PHENIX experiment in 2014 and 2016 with integrated luminosity of 14.5~nb$^{-1}$. The measurements are performed in the pseudorapidity range $1.2<|\eta|<2$ and cover transverse momenta $1

Uncertainty is inherent to most data, including vector field data, yet it is often omitted in visualizations and representations. Effective uncertainty visualization can enhance the understanding and interpretability of vector field data. For instance, in the context of severe weather events such as hurricanes and wildfires, effective uncertainty visualization can provide crucial insights about fire spread or hurricane behavior and aid in resource management and risk mitigation. Glyphs are commonly used for representing vector uncertainty but are often limited to 2D. In this work, we present a glyph-based technique for accurately representing 3D vector uncertainty and a comprehensive framework for visualization, exploration, and analysis using our new glyphs. We employ hurricane and wildfire examples to demonstrate the efficacy of our glyph design and visualization tool in conveying vector field uncertainty.

This paper introduces the Kernel Neural Operator (KNO), a novel operator learning technique that uses deep kernel-based integral operators in conjunction with quadrature for function-space approximation of operators (maps from functions to functions). KNOs use parameterized, closed-form, finitely-smooth, and compactly-supported kernels with trainable sparsity parameters within the integral operators to significantly reduce the number of parameters that must be learned relative to existing neural operators. Moreover, the use of quadrature for numerical integration endows the KNO with geometric flexibility that enables operator learning on irregular geometries. Numerical results demonstrate that on existing benchmarks the training and test accuracy of KNOs is higher than popular operator learning techniques while using at least an order of magnitude fewer trainable parameters. KNOs thus represent a new paradigm of low-memory, geometrically-flexible, deep operator learning, while retaining the implementation simplicity and transparency of traditional kernel methods from both scientific computing and machine learning., Comment: 10 pages + 5 page appendix, 8 figures

In this note, we use recent advances concerning the K-stability of $\mathbb{Q}$-Fano varieties to provide settings for which Vojta's conjecture holds., Comment: 11 pages, comments welcome!

We introduce the $\textit{Macaulay2}$ package $\texttt{OIGroebnerBases}$ for working with OI-modules over Noetherian polynomial OI-algebras. The main methods implement OI-analogues of Buchberger's algorithm and Schreyer's theorem to compute Gr\"obner bases, syzygies and free resolutions of submodules of free OI-modules., Comment: 7 pages

We construct a theory of motivic cohomology for quasi-compact, quasi-separated schemes of equal characteristic, which is related to non-connective algebraic $K$-theory via an Atiyah--Hirzebruch spectral sequence, and to \'etale cohomology in the range predicted by Beilinson and Lichtenbaum. On smooth varieties over a field our theory recovers classical motivic cohomology, defined for example via Bloch's cycle complex. Our construction uses trace methods and (topological) cyclic homology. As predicted by the behaviour of algebraic $K$-theory, the motivic cohomology is in general sensitive to singularities, including non-reduced structure, and is not $\mathbb{A}^1$-invariant. It nevertheless has good geometric properties, satisfying for example the projective bundle formula and pro cdh descent. Further properties of the theory include a Nesterenko--Suslin comparison isomorphism to Milnor $K$-theory, and a vanishing range which simultaneously refines Weibel's conjecture about negative $K$-theory and a vanishing result of Soul\'e for the Adams eigenspaces of higher algebraic $K$-groups. We also explore the relation of the theory to algebraic cycles, showing in particular that the Levine--Weibel Chow group of zero cycles on a surface arises as a motivic cohomology group.

The structure of amorphous silicon is widely thought of as a fourfold-connected random network, and yet it is defective atoms, with fewer or more than four bonds, that make it particularly interesting. Despite many attempts to explain such "dangling-bond" and "floating-bond" defects, respectively, a unified understanding is still missing. Here, we show that atomistic machine-learning methods can reveal the complex structural and energetic landscape of defects in amorphous silicon. We study an ultra-large-scale, quantum-accurate structural model containing a million atoms, and more than ten thousand defects, allowing reliable defect-related statistics to be obtained. We combine structural descriptors and machine-learned local atomic energies to develop a universal classification of the different types of defects in amorphous silicon. The results suggest a revision of the established floating-bond model by showing that fivefold-coordinated atoms in amorphous silicon exhibit a wide range of local environments, and it is shown that fivefold (but not threefold) coordination defects tend to cluster together. Our study provides new insights into one of the most widely studied amorphous solids, and has general implications for modelling and understanding defects in disordered materials beyond silicon alone.

When a viscous fluid partially fills a Hele--Shaw channel, and is pushed by a pressure difference, the fluid interface is unstable due to the Saffman--Taylor instability. We consider the evolution of a fluid region of finite extent, bounded between two interfaces, in the limit the interfaces are close, that is, when the fluid region is a thin liquid filament separating two gases of different pressure. In this limit, we derive a second-order `thin filament' model that describes the normal velocity of the filament centreline, and evolution of the filament thickness, as functions of the thickness, centreline curvature and their derivatives. We show that the second-order terms in this model, that include the effect of transverse flow along the filament, are necessary to regularise the instability. Numerical simulation of the thin filament model is shown to be in accordance with level-set computations of the complete two-interface model. Solutions ultimately evolve to form a bubble of rapidly increasing radius and decreasing thickness.

Machine learning (ML) models for molecules and materials commonly rely on a decomposition of the global target quantity into local, atom-centered contributions. This approach is convenient from a computational perspective, enabling large-scale ML-driven simulations with a linear-scaling cost, and also allow for the identification and post-hoc interpretation of contributions from individual chemical environments and motifs to complicated macroscopic properties. However, even though there exist practical justifications for these decompositions, only the global quantity is rigorously defined, and thus it is unclear to what extent the atomistic terms predicted by the model can be trusted. Here, we introduce a quantitative metric, which we call the local prediction rigidity (LPR), that allows one to assess how robust the locally decomposed predictions of ML models are. We investigate the dependence of LPR on the aspects of model training, particularly the composition of training dataset, for a range of different problems from simple toy models to real chemical systems. We present strategies to systematically enhance the LPR, which can be used to improve the robustness, interpretability, and transferability of atomistic ML models.

PHENIX presents a simultaneous measurement of the production of direct $\gamma$ and $\pi^0$ in $d$$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV over a $p_T$ range of 7.5 to 18 GeV/$c$ for different event samples selected by event activity, i.e. charged-particle multiplicity detected at forward rapidity. Direct-photon yields are used to empirically estimate the contribution of hard-scattering processes in the different event samples. Using this estimate, the average nuclear-modification factor $R_{d\rm Au,EXP}^{\gamma^{\rm dir}}$ is $0.925{\pm}0.023({\rm stat}){\pm}0.15^{\rm (scale)}$, consistent with unity for minimum-bias (MB) $d$$+$Au events. For event classes with moderate event activity, $R_{d\rm Au,EXP}^{\gamma^{\rm dir}}$ is consistent with the MB value within 5\% uncertainty. These results confirm that the previously observed enhancement of high-$p_T$ $\pi^0$ production found in small-system collisions with low event activity is a result of a bias in interpreting event activity within the Glauber framework. In contrast, for the top 5\% of events with the highest event activity, $R_{d\rm Au,EXP}^{\gamma^{\rm dir}}$ is suppressed by 20\% relative to the MB value with a significance of $4.5\sigma$, which may be due to final-state effects., Comment: 279 authors from 69 institutions, 8 pages, 3 figures, v2 is version accepted for publication in Physical Review Letters. HEPdata tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.html

Given a sequence of related modules $M_n$ defined over a sequence of related polynomial rings, one may ask how to simultaneously compute a finite Gr\"obner basis for each $M_n$. Furthermore, one may ask how to simultaneously compute the module of syzygies of each $M_n$. In this paper we address both questions. Working in the setting of OI-modules over a Noetherian polynomial OI-algebra, we provide OI-analogues of Buchberger's Criterion, Buchberger's Algorithm for computing Gr\"obner bases, and Schreyer's Theorem for computing syzygies. We also establish a stabilization result for Gr\"obner bases., Comment: 16 pages; some modifications

The displacement of a viscous liquid by a gas within a Hele-Shaw cell is a classical problem. The gas-liquid interface is hydrodynamically unstable, forming striking finger-like patterns that have been the subject of intense focus. Generally, both the gas and liquid phases are taken to be incompressible, with the capillary number being the key parameter that determines the severity of the instability. Here, we consider a radially outward displacement driven by the steady compression of a gas reservoir. The associated gas injection rate is then unsteady due to the compressibility of the gas. We identify a second nondimensional parameter, the compressibility number, that plays a strong role in the development of the fingering pattern. We use an axisymmetric model to study the impact of compressibility number on the unsteady evolution of injection rate and gas pressure. We use linear stability analysis to show that increasing the compressibility number delays the onset of finger development relative to the corresponding incompressible case. Finally, we present and compare a series of experiments and fully nonlinear simulations over a broad range of capillary and compressibility numbers. These results show that increasing the compressibility number systematically decreases the severity of the fingering pattern at high capillary number. Our results provide an unprecedented comparison of experiments with simulations for viscous fingering, a comprehensive understanding of the role of compressibility in unstable gas-liquid displacement flows, and insight into a new mechanism for controlling the development of fingering patterns.

We study integral points on varieties with infinite \'etale fundamental groups. More precisely, for a number field $F$ and $X/F$ a smooth projective variety, we prove that for any geometrically Galois cover $\varphi\colon Y \to X$ of degree at least $2\dim(X)^2$, there exists an ample line bundle $\mathscr{L}$ on $Y$ such that for a general member $D$ of the complete linear system $|\mathscr{L}|$, $D$ is geometrically irreducible and any set of $\varphi(D)$-integral points on $X$ is finite. We apply this result to varieties with infinite \'etale fundamental group to give new examples of irreducible, ample divisors on varieties for which finiteness of integral points is provable., Comment: v2: 10 pages. Fixed an error in previous version and strengthened results. Final version

Machine learning (ML) approaches enable large-scale atomistic simulations with near-quantum-mechanical accuracy. With the growing availability of these methods there arises a need for careful validation, particularly for physically agnostic models - that is, for potentials which extract the nature of atomic interactions from reference data. Here, we review the basic principles behind ML potentials and their validation for atomic-scale materials modeling. We discuss best practice in defining error metrics based on numerical performance as well as physically guided validation. We give specific recommendations that we hope will be useful for the wider community, including those researchers who intend to use ML potentials for materials "off the shelf".

Electronic structure calculations on small systems such as H$_2$, H$_2$O, LiH, and BeH$_2$ with chemical accuracy are still a challenge for the current generation of the noisy intermediate-scale quantum (NISQ) devices. One of the reasons is that due to the device limitations, only minimal basis sets are commonly applied in quantum chemical calculations, which allow one to keep the number of qubits employed in the calculations at minimum. However, the use of minimal basis sets leads to very large errors in the computed molecular energies as well as potential energy surface shapes. One way to increase the accuracy of electronic structure calculations is through the development of small basis sets better suited for quantum computing. In this work, we show that the use of adaptive basis sets, in which exponents and contraction coefficients depend on molecular structure, provide an easy way to dramatically improve the accuracy of quantum chemical calculations without the need to increase the basis set size and thus the number of qubits utilized in quantum circuits. As a proof of principle, we optimize an adaptive minimal basis set for quantum computing calculations on an H$_2$ molecule, in which exponents and contraction coefficients depend on the H-H distance, and apply it to the generation of H$_2$ potential energy surface on IBM-Q quantum devices. The adaptive minimal basis set reaches the accuracy of the double-zeta basis sets, thus allowing one to perform double-zeta quality calculations on quantum devices without the need to utilize twice as many qubits in simulations. This approach can be extended to other molecular systems and larger basis sets in a straightforward manner., Comment: 31 pages, 10 figures, 1 table, and 75 references

Let $k$ be an algebraically closed field of characteristic zero, and let $X/k$ be a projective variety. The conjectures of Demailly--Green--Griffiths--Lang posit that every integral subvariety of $X$ is of general type if and only if $X$ is algebraically hyperbolic i.e., for any ample line bundle $\mathcal{L}$ on $X$ there is a real number $\alpha(X,\mathcal{L})$, depending only on $X$ and $\mathcal{L}$, such that for every smooth projective curve $C/k$ of genus $g(C)$ and every $k$-morphism $f\colon C\to X$, $\text{deg}_Cf^*\mathcal{L} \leq \alpha(X,\mathcal{L})\cdot g(C) $ holds. In this work, we prove that if $X/k$ is a projective variety such that every integral subvariety is of general type, then for every ample line bundle $\mathcal{L}$ on $X$ and every integer $g\geq 0$, there is an integer $\alpha(X,\mathcal{L},g)$, depending only on $X,\mathcal{L},$ and $g$, such that for every smooth projective curve $C/k$ of genus $g$ and every $k$-morphism $f\colon C\to X$, the inequality $\text{deg}_Cf^*\mathcal{L} \leq \alpha(X,\mathcal{L},g)$ holds, or equivalently, the Hom-scheme $\underline{\text{Hom}}_k(C,X)$ is projective., Comment: v2: 41 pages. Significant updates throughout to address several mistakes in previous version. Results remain unchanged. Comments are welcome!

We use the $p$-divisible group attached to a 1-motive to generalize the conjugate $p$-adic uniformization of Iovita--Morrow--Zaharescu to arbitrary $p$-adic formal semi-abelian schemes or $p$-divisible groups over the ring of integers in a $p$-adic field. This mirrors a mixed Hodge theory construction of the inverse uniformization map for complex semi-abelian varieties. We also highlight the geometric structure of the target of the conjugate uniformization map, which is an \'{e}tale cover of a negative Banach--Colmez space in the sense of Fargues--Scholze., Comment: 21 pages; comments welcome!

Traditional mathematical models of Hele--Shaw flow consider the injection (or withdrawal) of an air bubble into (or from) an infinite body of viscous fluid. The most commonly studied feature of such a model is how the Saffman-Taylor instability drives viscous fingering patterns at the fluid/air interface. Here we consider a more realistic model, which assumes the viscous fluid is finite, covering a doubly connected two-dimensional region bounded by two fluid/air interfaces. For the case in which the flow is driven by a pressure difference across the two interfaces, we explore this model numerically, highlighting the development of viscous fingering patterns on the interface with the higher pressure. Our numerical scheme is based on the level set method, where each interface is represented as a separate level set function. We show that the scheme is able to reproduce the characteristic finger patterns observed experimentally up to the point at which one of the interfaces bursts through the other. The simulations are shown to compare well with experimental results. Further, we consider a model for the problem in which an annular body of fluid is evolving in a rotating Hele--Shaw cell. In this case, our simulations explore how either one or both of the interfaces can be unstable and develop fingering patterns, depending on the rotation rate and the volume of fluid present.

Let $p$ be a rational prime, let $F$ denote a finite, unramified extension of $\mathbb{Q}_p$, let $K$ be the completion of the maximal unramified extension of $\mathbb{Q}_p$, and let $\overline{K}$ be some fixed algebraic closure of $K$. Let $A$ be an abelian variety defined over $F$, with good reduction, let $\mathcal{A}$ denote the N\'eron model of $A$ over ${\rm Spec}(\mathcal{O}_F)$, and let $\widehat{\mathcal{A}}$ be the formal completion of $\mathcal{A}$ along the identity of its special fiber, i.e. the formal group of $A$. In this work, we prove two results concerning the ramification of $p$-power torsion points on $\widehat{\mathcal{A}}$. One of our main results describes conditions on $\widehat{\mathcal{A}}$, base changed to $\text{Spf}(\mathcal{O}_K) $, for which the field $K(\widehat{\mathcal{A}}[p])/K$ is a tamely ramified extension where $\widehat{\mathcal{A}}[p]$ denotes the group of $p$-torsion points of $\widehat{\mathcal{A}}$ over $\mathcal{O}_{\overline{K}}$. This result generalizes previous work when $A$ is $1$-dimensional and work of Arias-de-Reyna when $A$ is the Jacobian of certain genus 2 hyperelliptic curves., Comment: 15 pages, comments welcome! arXiv admin note: substantial text overlap with arXiv:2107.09165

The variety of robotic hand designs and actuation schemes makes it difficult to measure a hand's graspable volume. For end-users, this lack of standardized measurements makes it challenging to determine a priori if a robot hand is the right size for grasping an object. We propose a practical hand measurement standard, based on precision and power grasps, that is applicable to a wide variety of robot hand designs. The resulting measurements can be used to both determine if an object will fit in the hand and characterize the size of an object with respect to the hand. Our measurement procedure uses a functional approach, based on grasping a hypothetical cylinder, that allows the measurer choose the exact hand orientation and finger configurations that are used for the measurements. This ensures that the measurements are functionally comparable while relying on the human to determine the finger configurations that best match the intended grasp. We demonstrate using our measurement standard with three commercial robot hand designs and objects from the YCB data set., Comment: Significantly changed second version of arXiv:2106.10402. Paper originally submitted to Robotics Automation Letters

Single photon emitters (SPEs) are often identified with a Hanbury Brown and Twiss intensity interferometer (HBTII) consisting of a 50:50 beamsplitter and two time-correlated single photon counters. For an SPE, the cross-correlation of photon arrival time between the two detectors, $g^{(2)}(\tau)$, shows a hallmark dip to zero at $\tau=0$. One common heuristic for identifying SPEs is by measuring a system to have $g^{(2)}(0)<1/2$. Here in, we use stochastic methods to simulate the case of a SPE observed with non-ideal detectors and optics. We show that identification of SPEs is thwarted when the detectors have asymmetric detection efficiency, and when detector background noise is more than half the true SPE signal rate.

Recently, the PHENIX Collaboration has published second- and third-harmonic Fourier coefficients $v_2$ and $v_3$ for midrapidity ($|\eta|<0.35$) charged hadrons in 0\%--5\% central $p$$+$Au, $d$$+$Au, and $^3$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV utilizing three sets of two-particle correlations for two detector combinations with different pseudorapidity acceptance [Phys. Rev. C {\bf 105}, 024901 (2022)]. This paper extends these measurements of $v_2$ to all centralities in $p$$+$Au, $d$$+$Au, and $^3$He$+$Au collisions, as well as $p$$+$$p$ collisions, as a function of transverse momentum ($p_T$) and event multiplicity. The kinematic dependence of $v_2$ is quantified as the ratio $R$ of $v_2$ between the two detector combinations as a function of event multiplicity for $0.5$$<$$p_T$$<$$1$ and $2$$<$$p_T$$<$$2.5$ GeV/$c$. A multiphase-transport (AMPT) model can reproduce the observed $v_2$ in most-central to midcentral $d$$+$Au and $^3$He$+$Au collisions. However, the AMPT model systematically overestimates the measurements in $p$$+$$p$, $p$$+$Au, and peripheral $d$$+$Au and $^3$He$+$Au collisions, indicating a higher nonflow contribution in AMPT than in the experimental data. The AMPT model fails to describe the observed $R$ for $0.5$$<$$p_T$$<$$1$ GeV/$c$, but there is qualitative agreement with the measurements for $2$$<$$p_T$$<$$2.5$ GeV/$c$., Comment: 393 authors from 72 institutions, 14 pages, 10 figures, 2014, 2015, and 2016 data. v2 is version accepted for publication in Physical Review C. HEPdata tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.html

We establish various properties of the p-adic algebraic K-theory of smooth algebras over perfectoid rings living over perfectoid valuation rings. In particular, the p-adic K-theory of such rings is homotopy invariant, and coincides with the p-adic K-theory of the p-adic generic fibre in high degrees. In the case of smooth algebras over perfectoid valuation rings of mixed characteristic the latter isomorphism holds in all degrees and generalises a result of Nizio{\l}., Comment: comments welcome

Like many young adults transitioning into the next phase of their life, young adults with autism desire increased independence and autonomy and want to feel confident in their ability to succeed. However, young adults with autism are often less financially independent compared to other youth, including other peers with special health care needs. Financial literacy is often not taught in high schools, with only 21 US states requiring students to take a course that integrates personal finance. This results in many young adults having limited knowledge of money management. Transition services for high school students with ASD often lack a personal finance component as well. This "Autism at-a-Glance" is designed to support practitioners and family members in developing and promoting money management skills for young adults on the autism spectrum.

The probability that a random permutation in $S_n$ is a derangement is well known to be $\displaystyle\sum\limits_{j=0}^n (-1)^j \frac{1}{j!}$. In this paper, we consider the conditional probability that the $(k+1)^{st}$ point is fixed, given there are no fixed points in the first $k$ points. We prove that when $n \neq 3$ and $k \neq 1$, this probability is a decreasing function of both $k$ and $n$. Furthermore, it is proved that this conditional probability is well approximated by $\frac{1}{n} - \frac{k}{n^2(n-1)}$. Similar results are also obtained about the more general conditional probability that the $(k+1)^{st}$ point is fixed, given that there are exactly $d$ fixed points in the first $k$ points., Comment: 16 pages, 2 figures. To be published in Transactions on Combinatorics

Analyte response is convoluted with instrument response in time resolved fluorescence data. Decoding the desired analyte information from the measurement usually requires iterative numerical convolutions. Here in, we show that time resolved data can be completely, analytically reconstructed without numerical convolutions. Our strategy relies on a summation of exponentially modified Gaussians which encode all convolutions within easily evaluated complementary error functions. Compared to a numerical convolution strategy implemented with Python, this new method is computationally cheaper and scales less steeply with the number of temporal points in the experimental dataset.

Various biological and chemical processes lead to the nucleation and growth of non-wetting fluid bubbles within the pore space of a granular medium, such as the formation of gas bubbles in liquid-saturated lake-bed sediments. In sufficiently soft porous materials, the non-wetting nature of these bubbles can result in the formation of open cavities within the granular solid skeleton. Here, we consider this process through the lens of phase separation, where thermomechanics govern the separation of the non-wetting phase from a fluid-fluid-solid mixture. We construct a phase-field model informed by large-deformation poromechanics, in which two immiscible fluids interact with a poroelastic solid skeleton. Our model captures the competing effects of elasticity and fluid-fluid-solid interactions. We use a phase-field damage model to capture the mechanics of the granular solid. As a model problem, we consider an initial distribution of non-wetting fluid in the pore space that separates into multiple cavities. We use simulations and linear-stability analysis to identify the key parameters that control phase separation, the conditions that favour the formation of cavities, and the characteristic size of the resulting cavities.

Machine learning (ML) based interatomic potentials are emerging tools for materials simulations but require a trade-off between accuracy and speed. Here we show how one can use one ML potential model to train another: we use an existing, accurate, but more computationally expensive model to generate reference data (locations and labels) for a series of much faster potentials. Without the need for quantum-mechanical reference computations at the secondary stage, extensive reference datasets can be easily generated, and we find that this improves the quality of fast potentials with less flexible functional forms. We apply the technique to disordered silicon, including a simulation of vitrification and polycrystalline grain formation under pressure with a system size of a million atoms. Our work provides conceptual insight into the machine learning of interatomic potential models, and it suggests a route toward accelerated simulations of condensed-phase systems and nanostructured materials.

The relationship between dietary habits and microbiota composition during adolescence has not been well examined. This is a crucial knowledge gap to fill considering that diet-microbiota interactions influence neurodevelopment, immune system maturation and metabolic regulation. This study examined the associations between diet and the gut microbiota in a school-based sample of 136 adolescents(M[subscript age] = 12·1 years; age range 11-13 years; 48% female; 47% Black, 38% non-Hispanic White, 15% Hispanic or other minorities) from urban, suburban and rural areas in the Southeast USA. Adolescents completed the Rapid Eating Assessment for Participants and provided stool samples for 16S ribosomal RNA gene sequencing. Parents reported their child and family socio-demographic characteristics. The associations between diet and socio-demographics with gut microbiota diversity and abundance were analyzed using multivariable regression models. Child race and ethnicity, sex, socio-economic status and geographic locale contributed to variation within microbiota composition ([Beta]-diversity). Greater consumption of processed meat was associated with a lower microbial [alpha]-diversity after adjusting for socio-demographic variables. Multi-adjusted models showed that frequent consumption of nutrient-poor, energy-dense foods (e.g. sugar-sweetened beverages, fried foods, sweets) was negatively associated with abundances of genera in the family "Lachnospiraceae" ("Anaerostipes," "Fusicatenibacter" and "Roseburia"), which are thought to play a beneficial role in host health through their production of short-chain fatty acids (SCFAs). These results provide new insights into the complex relationships among socio-demographic factors, diet and gut microbiota during adolescence. Adolescence may represent a critical window of opportunity to promote healthy eating practices that shape a homoeostatic gut microbiota with life-long benefits. [This is the online version of an article published in "British Journal of Nutrition."]

Transition metal dichalcogenide heterostructures can host interlayer excitons (IXs), which consist of electrons and holes spatially separated in different layers. IXs possess permanent dipoles and have proven to offer a wealth of novel physics. We develop a discrete, random-walk model which includes annihilation and repulsion interactions among IXs. Using this model, we simulate the trapping of IXs in traps of different depths, densities, and shapes. Our results show that dipole-dipole interactions play an important role in regulating IX trapping. The effects of dipole interactions can be mitigated with small, deep traps which are realizable with atomic defects and moire potentials.

Let $p$ be a rational prime, let $F$ denote a finite, unramified extension of $\mathbb{Q}_p$, $K$ the maximal unramified extension of $\mathbb{Q}_p$, $\overline{K}$ some fixed algebraic closure of $K$, and $\mathbb{C}_p$ the completion of $\overline{K}$. Let $G_F$ the absolute Galois group of $F$. Let $A$ be an abelian variety defined over $F$, with good reduction. Classically, the Fontaine integral was seen as a Hodge--Tate comparison morphism, i.e. as a map $\varphi_{A} \otimes 1_{\mathbb{C}_p}\colon T_p(A)\otimes_{\mathbb{Z}_p}\mathbb{C}_p\to \text{Lie}(A)(F)\otimes_F\mathbb{C}_p(1)$, and as such it is surjective and has a large kernel. The present article starts with the observation that if we do not tensor $T_p(A)$ with $\mathbb{C}_p$, then the Fontaine integral is often injective. In particular, it is proved that if $T_p(A)^{G_K} = 0$, then $\varphi_A$ is injective. As an application, we extend the Fontaine integral to a perfectoid like universal cover of $A$ and show that if $T_p(A)^{G_K} = 0$, then $A(\overline{K})$ has a type of $p$-adic uniformization, which resembles the classical complex uniformization., Comment: v3: 25 pages, final version

There is strong evidence for the formation of small droplets of quark-gluon plasma in $p/d/^{3}$He+Au collisions at the Relativistic Heavy Ion Collider (RHIC) and in $p$+$p$/Pb collisions at the Large Hadron Collider. In particular, the analysis of data at RHIC for different geometries obtained by varying the projectile size and shape has proven insightful. In the present analysis, we find excellent agreement with the previously published PHENIX at RHIC results on elliptical and triangular flow with an independent analysis via the two-particle correlation method, which has quite different systematic uncertainties and an independent code base. In addition, the results are extended to other detector combinations with different kinematic (pseudorapidity) coverage. These results provide additional constraints on contributions from nonflow and longitudinal decorrelations., Comment: 383 authors from 70 institutions, 13 pages, 12 figures, 4 tables, 2014,15,16 data (and supplemental material of 9 pages with 6 figures and 16 tables). v2 is version accepted for publication in Physical Review C. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.html

The varied landscape of robotic hand designs makes it difficult to set a standard for how to measure hand size and to communicate the size of objects it can grasp. Defining consistent workspace measurements would greatly assist scientific communication in robotic grasping research because it would allow researchers to 1) quantitatively communicate an object's relative size to a hand's and 2) approximate a functional subspace of a hand's kinematic workspace in a human-readable way. The goal of this paper is to specify a measurement procedure that quantitatively captures a hand's workspace size for both a precision and power grasp. This measurement procedure uses a {\em functional} approach -- based on a generic grasping scenario of a hypothetical object -- in order to make the procedure as generalizable and repeatable as possible, regardless of the actual hand design. This functional approach lets the measurer choose the exact finger configurations and contact points that satisfy the generic grasping scenario, while ensuring that the measurements are {\em functionally} comparable. We demonstrate these functional measurements on seven hand configurations. Additional hand measurements and instructions are provided in a GitHub Repository., Comment: Submitted to IROS 2021, waiting for response

Given the profound and uncritiqued changes that have been implemented in Aotearoa New Zealand education since the 1990s, this paper provides a critical commentary on the characterising features of the New Zealand mathematics' curriculum in the context of the first stage of a study. The emphasis is on the importance of research design that begins with an explicit, evidence-based hypothesis. To that end, we describe evidence that informs and identifies the study's hypothesised problem and causes. The study itself will show whether or not the hypothesis is justified; that is, is the absence of standardised prescribed content in New Zealand mathematics' curriculum the reason for the country's declining mathematics rankings? The study aims to increase understanding in the field of mathematics education by exploring the effects on New Zealand year 7 public school teachers' mathematics curriculum selection and design practices, teaching practices, and subsequently student achievement., Comment: Submitted to the New Zealand Journal of Educational Studies, 12 June 2021

As the proportion of variable inverter-based renewable energy generation in electricity systems increases from a minority to the majority of total supply, the complexity and cost of providing ancillary system services increases in parallel. Australia is experiencing this shift now - from having the third most carbon-intensive electricity sector in the world in 2010, to now having penetrations of variable renewable energy (VRE) regularly reaching 100 percent in some regions, with world-leading uptake of distributed energy resources (DER). This paper presents pioneering work exploring new technical, economic and regulatory frameworks for the provision of Essential System Services (ESS), also known as ancillary services, in power systems dominated by variable inverter-based renewable energy resources. We explore the recent application of the concept of demand curves and nomograms to the procurement of ESS, and emerging design principles for frameworks in facilitating the evolution from default provision of system services by synchronous generation, to co-optimisation of services through unit commitment, to independent provision of services through inverter based resources. The paper also analyses the recent technical and financial success of the world's largest battery, the Hornsdale Power Reserve in South Australia, and its ability to inform how future electricity market frameworks may incentivize and accommodate new technological capability, both first and Nth of a kind systems. Finally, the paper reviews emerging energy system technological capability, including the provision of synthetic inertia and RoCoF control, grid-forming inverters, and advanced DER aggregation in providing ESS and system restart capability for secure, resilient and island-able grids., Comment: 26 pages, 8 figures

Let $K$ be an algebraically closed, complete, non-Archimedean valued field of characteristic zero, and let $\mathscr{X}$ be a $K$-analytic space (in the sense of Huber). In this work, we pursue a non-Archimedean characterization of Campana's notion of specialness. We say $\mathscr{X}$ is $K$-analytically special if there exists a connected, finite type algebraic group $G/K$, a dense open subset $\mathscr{U}\subset G^{\text{an}}$ with $\text{codim}(G^{\text{an}}\setminus \mathscr{U}) \geq 2$, and an analytic morphism $\mathscr{U} \to \mathscr{X}$ which is Zariski dense. With this definition, we prove several results which illustrate that this definition correctly captures Campana's notion of specialness in the non-Archimedean setting. These results inspire us to make non-Archimedean counterparts to conjectures of Campana. As preparation for our proofs, we prove auxiliary results concerning the indeterminacy locus of a meromorphic mapping between $K$-analytic spaces, the notion of pseudo-$K$-analytically Brody hyperbolic, and extensions of meromorphic maps from smooth, irreducible $K$-analytic spaces to the analytification of a semi-abelian variety., Comment: 31 pages; comments welcome!

Let $E/\mathbb{Q}$ be an elliptic curve, let $\overline{\mathbb{Q}}$ be a fixed algebraic closure of $\mathbb{Q}$, and let $G_{\mathbb{Q}}=\text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ be the absolute Galois group of $\mathbb{Q}$. The action of $G_{\mathbb{Q}}$ on the adelic Tate module of $E$ induces the adelic Galois representation $\rho_E\colon G_{\mathbb{Q}} \to \text{GL}(2,\widehat{\mathbb{Z}}).$ The goal of this paper is to explain how the image of $\rho_E$ can be smaller than expected. To this end, we offer a group theoretic categorization of different ways in which an entanglement between division fields can be explained and prove several results on elliptic curves (and more generally, principally polarized abelian varieties) over $\mathbb{Q}$ where the entanglement occurs over an abelian extension., Comment: 33 pages; v4: corrected a mistake in Definition 3.3

"Autism at-a-Glance" is a series of practitioner and family-friendly documents created by the Center on Secondary Education for Students with ASD (CSESA) designed for high school staff members supporting students on the autism spectrum, as well as family members of adolescents with ASD. The purpose of the "Autism at-a-Glance" series is to provide a current summary of topics relevant to high school students with ASD as well as practical tips and resources for school and community personnel and family members. This "Autism at-a-Glance" was designed to support parents and other family members in supporting adolescents on the autism spectrum as they develop their literacy at home and in the community.

The classical model for studying one-phase Hele-Shaw flows is based on a highly nonlinear moving boundary problem with the fluid velocity related to pressure gradients via a Darcy-type law. In a standard configuration with the Hele-Shaw cell made up of two flat stationary plates, the pressure is harmonic. Therefore, conformal mapping techniques and boundary integral methods can be readily applied to study the key interfacial dynamics, including the Saffman-Taylor instability and viscous fingering patterns. As well as providing a brief review of these key issues, we present a flexible numerical scheme for studying both standard and non-standard Hele-Shaw flows. Our method consists of using a modified finite difference stencil in conjunction with the level set method to solve the governing equation for pressure on complicated domains and track the location of the moving boundary. Simulations show that our method is capable of reproducing the distinctive morphological features of the Saffman-Taylor instability on a uniform computational grid. By making straightforward adjustments, we show how our scheme can easily be adapted to solve for a wide variety of non-standard configurations, including cases where the gap between the plates is linearly tapered, the plates are separated in time, and the entire Hele-Shaw cell is rotated at a given angular velocity.

We study the mod $p^r$ Milnor $K$-groups of $p$-adically complete and $p$-henselian rings, establishing in particular a Nesterenko-Suslin style description in terms of the Milnor range of syntomic cohomology. In the case of smooth schemes over complete discrete valuation rings we prove the mod $p^r$ Gersten conjecture for Milnor $K$-theory locally in the Nisnevich topology. In characteristic $p$ we show that the Bloch-Kato-Gabber theorem remains true for valuation rings, and for regular formal schemes in a pro sense.

We present a measurement of the transverse single-spin asymmetry for $\pi^0$ and $\eta$ mesons in $p^\uparrow$$+$$p$ collisions in the pseudorapidity range $|\eta|<0.35$ and at a center-of-mass energy of 200 GeV with the PHENIX detector at the Relativistic Heavy Ion Collider. In comparison with previous measurements in this kinematic region, these results have a factor of 3 smaller uncertainties. As hadrons, $\pi^0$ and $\eta$ mesons are sensitive to both initial- and final-state nonperturbative effects for a mix of parton flavors. Comparisons of the differences in their transverse single-spin asymmetries have the potential to disentangle the possible effects of strangeness, isospin, or mass. These results can constrain the twist-3 trigluon collinear correlation function as well as the gluon Sivers function., Comment: 314 authors from 66 institutions, 10 pages, 5 figures, 2 tables, 2015 data. v2 is version accepted for publication in Phys. Rev. D. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.html