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Chaos makes isolated systems of many interacting particles quickly thermalize and forget about their past. Here, we show that quantum mechanics hinders chaos in many-body systems: although the quantum eigenstates are thermal and strongly entangled, exponentially many of them are scarred, that is, have an enlarged weight along underlying classical unstable periodic orbits. Scarring makes the system more likely to be found on an orbit it was initialized on, retaining a memory of its past and thus weakly breaking ergodicity, even at long times and despite the system being fully thermal. We demonstrate the ubiquity of quantum scarring in many-body systems by considering a large family of spin models, including some of the most popular ones from condensed matter physics. Our findings, at hand for modern quantum simulators, prove structure in spite of chaos in many-body quantum systems., Comment: 5 pages, 3 figures

The accurate reconstruction of immiscible fluid-fluid interfaces from the volume fraction field is a critical component of geometric Volume of Fluid (VOF) methods. A common strategy is the Piecewise Linear Interface Calculation (PLIC), which fits a plane in each mixed-phase computational cell. However, recent work goes beyond PLIC by using two planes or even a paraboloid. To select such planes or paraboloids, complex optimization algorithms as well as carefully crafted heuristics are necessary. Yet, the potential exists for a well-trained machine learning model to efficiently provide broadly applicable solutions to the interface reconstruction problem at lower costs. In this work, the viability of a machine learning approach is demonstrated in the context of a single plane reconstruction. A feed-forward deep neural network is used to predict the normal vector of a PLIC plane given volume fraction and phasic barycenter data in a $3\times3\times3$ stencil. The PLIC plane is then translated in its cell to ensure exact volume conservation. Our proposed neural network PLIC reconstruction (PLIC-Net) is equivariant to reflections about the Cartesian planes. Training data is analytically generated with $\mathcal{O}(10^6)$ randomized paraboloid surfaces, which allows for sampling a wide range of interface shapes. PLIC-Net is tested in multiphase flow simulations where it is compared to standard (E)LVIRA reconstruction algorithms, and the impact of training data statistics on PLIC-Net's performance is also explored. It is found that PLIC-Net greatly limits the formation of spurious planes and generates cleaner numerical break-up of the interface. Additionally, the computational cost of PLIC-Net is lower than that of (E)LVIRA. These results establish that machine learning is a viable approach to VOF interface reconstruction and is superior to current reconstruction algorithms for some cases.

In the present paper, we model the velocity disturbance generated by a regularized forcing near a planar wall, which, along with the temporal nature of the forcing, provides an estimate of the unsteady velocity disturbance of the particle near a planar wall. We use the analytical solution for a singular in-time transient Stokeslet near a planar wall (Felderhof, 2009) and derive the corresponding time-persistent Stokeslets. The velocity disturbance due to a regularized forcing is then obtained numerically via a discrete convolution with the regularization kernel. The resulting Green's functions for parallel and perpendicular regularized forcing to the wall are stored as pre-computed temporal correction maps. By storing the time-dependent particle force on the fluid as fictitious particles, we estimate the unsteady velocity disturbance generated by the particle as a scalar product between the stored forces and the pre-computed Green's functions. Since the model depends on the analytical Green's function solution of the singular Stokeslet near a planar wall, the obtained velocity disturbance exactly satisfies the no-slip condition and does not require any fitted parameters to account for the rapid decay of the disturbance near the wall. The numerical evaluation of the convolution integral makes the present method suitable for arbitrary regularization kernels. Additionally, the generation of parallel and perpendicular correction maps enables to estimate the velocity disturbance due to particle motion in arbitrary directions relative to the local flow. The convergence of the method is studied on a fixed particle near a planar wall, and verification tests are performed on a settling particle parallel to a wall and a free-falling particle perpendicular to the wall., Comment: 40 pages

In volume-filtered Euler-Lagrange simulations of particle-laden flows, the fluid forces acting on a particle are estimated using reduced models, which rely on the knowledge of the local undisturbed flow for that particle. Since the two-way coupling between the particle and the fluid creates a local flow perturbation, the filtered fluid velocity interpolated to the particle location must be corrected prior to estimating the fluid forces, so as to subtract the contribution of this perturbation and recover the local undisturbed flow with good accuracy. In this manuscript, we present a new model for estimating a particle's self-induced flow disturbance that accounts for its transient development and for inertial effects related to finite particle Reynolds numbers. The model also does not require the direction of the momentum feedback to align with the direction of the particle's relative velocity, allowing force contributions other than the steady drag force to be considered. It is based upon the linearization of the volume-filtered equations governing the particle's self-induced flow disturbance, such that their solution can be expressed as a linear combination of regularized transient Stokeslet contributions. Tested on a range of numerical cases, the model is shown to consistently estimate the particle's self-induced flow disturbance with high accuracy both in steady and highly transient flow environments, as well as for finite particle Reynolds numbers.

We use time-resolved nonlinear pump--probe measurements to reveal features of semiconductor moir\'e materials not accessible to linear spectroscopy. With an intense, red-detuned pump pulse, we generate a high density of virtual excitons or exciton--polarons in various moir\'e minibands. A broadband probe pulse in turn measures the response of all optical resonances induced by the pump-generated excitations. We generically observe a coherent blue shift originating from contact-like exciton--exciton interactions. At charge neutrality, these measurements allow us to assess the spatial overlap between different optical excitations and to observe signatures of a bound biexciton state between two different moir\'e exciton modes. In contrast to electron doped monolayers, spatially confined moir\'e attractive polarons behave as an ensemble of non-interacting two-level emitters, exhibiting an electron-density-independent ac-Stark effect. Tuning the pump laser into resonance with the attractive polaron, we demonstrate the filling of the moir\'e lattice with localized polarons and thereby realize a nonequilibrium Bose--Fermi mixture in moir\'e flat bands.

The Local Volume Complete Cluster Survey (LoVoCCS) is an on-going program to observe nearly a hundred low-redshift X-ray-luminous galaxy clusters (redshifts $0.0310^{44}$ erg/s) with the Dark Energy Camera (DECam), capturing data in $u,g,r,i,z$ bands with a $5\sigma$ point source depth of approximately 25-26th AB magnitudes. Here, we map the aperture masses in 58 galaxy cluster fields using weak gravitational lensing. These clusters span a variety of dynamical states, from nearly relaxed to merging systems, and approximately half of them have not been subject to detailed weak lensing analysis before. In each cluster field, we analyze the alignment between the 2D mass distribution described by the aperture mass map, the 2D red-sequence (RS) galaxy distribution, and the brightest cluster galaxy (BCG). We find that the orientations of the BCG and the RS distribution are strongly aligned throughout the interiors of the clusters: the median misalignment angle is 19 deg within 2 Mpc. We also observe the alignment between the orientations of the RS distribution and the overall cluster mass distribution (by a median difference of 32 deg within 1 Mpc), although this is constrained by galaxy shape noise and the limitations of our cluster sample size. These types of alignment suggest long-term dynamical evolution within the clusters over cosmic timescales., Comment: 40 pages, 16 figures, 5 tables; revised and accepted for publication in ApJ

The volume-filtering of the Navier-Stokes equations allows to consider the effect that particles have on the fluid without further assumptions, but closures arise of which the implications are not fully understood. In the present paper, we carefully study every closure in the volume-filtered fluid momentum equation and investigate their impact on the momentum and energy transfer dependent on the filtering characteristics. We provide an analytical expression for the viscous closure that arises because filter and spatial derivative in the viscous term do not commute. An analytical expression for the regularization of the particle momentum source of a single sphere in the Stokes regime is derived. Furthermore, we propose a model for the subfilter stress tensor, which originates from filtering the advective term. The model for the subfilter stress tensor is shown to agree well with the subfilter stress tensor for small filter widths relative to the size of the particle. We show that the subfilter stress tensor requires modeling and should not be neglected. For small filter widths, we find that the commonly applied Gaussian regularization of the particle momentum source is a poor approximation of the spatial distribution of the particle momentum source, but for larger filter widths the spatial distribution approaches a Gaussian. Furthermore, we propose a modified advective term in the volume-filtered momentum equation that consistently circumvents the common stability issues observed at locally small fluid volume fractions and identify inconsistencies in previous studies of the phase-averaged kinetic energy of the volume-filtered fluid velocity. Finally, we propose a generally applicable form of the volume-filtered momentum equation and its closures based on clear and well-founded assumptions and propose guidelines for point-particle simulations based on the new findings.

Over the past decades, the volume-of-fluid (VOF) method has been the method of choice for simulating atomization processes, owing to its unique ability to discretely conserve mass. Current state-of-the-art VOF methods, however, rely on the piecewise-linear interface calculation (PLIC) to represent the interface used when calculating advection fluxes. This renders the estimated curvature of the transported interface zeroth-order accurate at best, adversely impacting the simulation of surface-tension-driven flows. In the past few years, there have been several attempts at using piecewise-parabolic interface approximations instead of piecewise-linear ones for computing advection fluxes, albeit all limited to two-dimensional cases or not inherently mass conservative. In this contribution, we present our most recent work on three-dimensional piecewise-parabolic interface reconstruction and apply it in the context of the VOF method. As a result of increasing the order of the interface representation, the reconstruction of the interface and the estimation of its curvature now become a single step instead of two separate ones. The performance of this new approach is assessed both in terms of accuracy and stability and compared to the classical PLIC-VOF approach on a range of canonical test-cases and cases of surface-tension-driven instabilities.

A precondition for the deployment of a Reinforcement Learning agent to a real-world system is to provide guarantees on the learning process. While a learning algorithm will eventually converge to a good policy, there are no guarantees on the performance of the exploratory policies. We study the problem of conservative exploration, where the learner must at least be able to guarantee its performance is at least as good as a baseline policy. We propose the first conservative provably efficient model-free algorithm for policy optimization in continuous finite-horizon problems. We leverage importance sampling techniques to counterfactually evaluate the conservative condition from the data self-generated by the algorithm. We derive a regret bound and show that (w.h.p.) the conservative constraint is never violated during learning. Finally, we leverage these insights to build a general schema for conservative exploration in DeepRL via off-policy policy evaluation techniques. We show empirically the effectiveness of our methods.

Using the photometric population prediction method {\bf Red Dragon}, we characterize the Red Sequence (RS) and Blue Cloud (BC) of DES galaxies in the COSMOS field. Red Dragon (RD) uses a redshift-evolving, error-corrected Gaussian mixture model to detail the distribution of photometric colors, smoothly parameterizing the two populations with relative weights, mean colors, intrinsic scatters, and inter-color correlations. This resulting fit of RS and BC yields RS membership probabilities $P_{\rm RS}$ for each galaxy. Even when training on only DES main bands $griz$, RD selects the quiescent population (defined here as galaxies with $\lg {\rm sSFR \cdot yr} < -11$) with $\gtrsim 90\%$ balanced accuracy out to $z=2$; augmenting with extended photometry from VIRCAM improves this accuracy to $\sim 95\%$ out to $z=3$. We measure redshift evolution of sSFR and galactic age in several stellar mass bins, finding that the BC is consistently more star-forming (by $\gtrsim 1~{\rm dex}$) and typically younger (by $\gtrsim 1~{\rm Gyr}$) than the RS (up to $z \sim 1.4$). This characterization of both RS and BC as functions of redshift and stellar mass improves our understanding of both populations and opens the door to more precise galaxy population characterization in future deep optical and IR systems., Comment: 16 pages, 19 figures; comments welcome

The locally noncentrosymmetric heavy fermion superconductor CeRh$_2$As$_2$ has attracted considerable interests due to its rich superconducting phases, accompanied by a quadrupole density wave and pronounced antiferromagnetic excitations. To understand the underlying physics, we here report measurements from high-resolution angle-resolved photoemission. Our results reveal fine splittings of the conduction bands related to the locally noncentrosymmetric structure, as well as a quasi-two-dimensional Fermi surface (FS) with strong $4f$ contributions. The FS exhibits nesting with an in-plane vector $({\pi}/a, {\pi}/a)$, which is facilitated by the van Hove singularity near $\bar X$ that arises from the characteristic conduction-$f$ hybridization. The FS nesting provides a natural explanation for the observed antiferromagnetic excitations at $({\pi}/a, {\pi}/a)$, which could be intimately connected to its unconventional superconductivity. Our experimental results are well supported by density functional theory plus dynamical mean field theory calculations, which can capture the strong correlation effects. Our study not only provides spectroscopic proof of the key factors underlying the field-induced superconducting transition, but also uncovers the critical role of FS nesting and lattice Kondo effect in the intertwined spin and charge fluctuations., Comment: v1 submitted on Sep 13th 2023

Massive halos hosting groups and clusters of galaxies imprint coherent, arcminute-scale features across the spectrophotometric sky, especially optical-IR clusters of galaxies, distortions in the sub-mm CMB, and extended sources of X-ray emission. Statistical modeling of such features often rely upon the evolving space-time density of dark matter halos -- the halo mass function (HMF) -- as a common theoretical ground for cosmological, astrophysical and fundamental physics studies. We propose a compact (eight parameter) representation of the HMF with readily interpretable parameters that stem from polynomial expansions, first in terms of log-mass, then expanding those coefficients similarly in redshift. We demonstrate good ($\sim \! 5\%$) agreement of this form, referred to as the dual-quadratic (DQ-HMF), with Mira-Titan N-body emulator estimates for halo masses above $10^{13.7} h^{-1} {\rm M}_\odot$ over the redshift range $0.1 < z < 1.5$, present best-fit parameters for a Planck 2018 cosmology, and present parameter variation in the $\sigma_8 - \Omega_{\rm m}$ plane. Convolving with a minimal mass-observable relation (MOR) yields closed-form expressions for counts, mean mass, and mass variance of cluster samples characterized by some observable property. Performing information-matrix forecasts of potential parameter constraints from existing and future surveys under different levels of systematic uncertainties, we demonstrate the potential for percent-level constraints on model parameters by an LSST-like optical cluster survey of 300,000 clusters and a richness-mass variance of $0.3^2$. Even better constraints could potentially be achieved by a survey with one-tenth the sample size but with a reduced selection property variance of $0.1^2$. Potential benefits and extensions to the basic MOR parameterization are discussed., Comment: 18 pages, 9 figures

A significant computational expense and source of numerical errors in front tracking is the remeshing of the triangulated front, required due to distortion and compaction of the front following the Lagrangian advection of its vertices. Additionally, in classic front tracking, the remeshing of the front mesh is required not only due to the deformation of the front shape, but also because the vertices of the front are translated in the direction tangential to the front, induced by the front advection. We present the normal-only advection (NOA) front-tracking method with the aim of preventing the tangential motion of the front vertices and the associated vertex clustering, in order to reduce the number of remeshing operations required to retain a high-quality triangulated interface. To this end, we reformulate the velocity used to advect the front at each discrete front-vertex position. The proposed method is validated and tested against the classic front-tracking method, comparing volume conservation, shape preservation, computational costs, and the overall need for front remeshing, as well as experimental results for canonical interfacial flows. The presented results demonstrate that the NOA front-tracking method leads to a typical reduction of remeshing operations by 80 % or more compared to the classic front-tracking method for well-resolved cases, and results in a smoother front mesh, which is essential for an accurate representation of the geometrical properties of the front. The volume conservation error is reduced by approximately one order of magnitude with the proposed method compared to the classic front-tracking method, at a similar computational cost.

Quantum many-body scars (QMBS) consist of a few low-entropy eigenstates in an otherwise chaotic many-body spectrum, and can weakly break ergodicity resulting in robust oscillatory dynamics. The notion of QMBS follows the original single-particle scars introduced within the context of quantum billiards, where scarring manifests in the form of a quantum eigenstate concentrating around an underlying classical unstable periodic orbit (UPO). A direct connection between these notions remains an outstanding problem. Here, we study a many-body spinor condensate that, owing to its collective interactions, is amenable to the diagnostics of scars. We characterize the system's rich dynamics, spectrum, and phase space, consisting of both regular and chaotic states. The former are low in entropy, violate the Eigenstate Thermalization Hypothesis (ETH), and can be traced back to integrable effective Hamiltonians, whereas most of the latter are scarred by the underlying semiclassical UPOs, while satisfying ETH. We outline an experimental proposal to probe our theory in trapped spin-1 Bose-Einstein condensates., Comment: 4 pages and 4 figures with SM (11 pages, 5 figures)

Laser induced shift of atomic states due to the AC-Stark effect has played a central role in cold-atom physics and facilitated their emergence as analog quantum simulators. Here, we explore this phenomena in an atomically thin layer of semiconductor MoSe$_2$, which we embedded in a heterostructure enabling charge tunability. Shining an intense pump laser with a small detuning from the material resonances, we generate a large population of virtual collective excitations, and achieve a regime where interactions with this background population is the leading contribution to the AC-Stark shift. Using this technique we study how itinerant charges modify -- and dramatically enhance -- the interactions between optical excitations. In particular, our experiments show that the interaction between attractive polarons could be more than an order of magnitude stronger than those between bare excitons.

We propose a novel model to obtain the subgrid-scale velocity in the context of large-eddy simulation (LES) of particle-laden turbulent flows, to recover accurate particle statistics. In the new wavelet enrichment model, the subgrid-scale velocity is discretized with a divergence-free wavelet vector basis, and the coefficients of the expansion are obtained by minimizing the squared error of the linearized subfilter Navier-Stokes equations (SFNSE). The compact support of the wavelet basis is exploited to achieve continuously varying subgrid-scale velocity statistics across the domain. The performance of the new wavelet enrichment model is evaluated in single-phase and particle-laden flow simulations, comparing the results with the results of direct numerical simulations (DNS). The simulations show that the model can generate inhomogeneous and anisotropic velocity statistics, accurate strain-rotation relations, and a good approximation of the kinetic energy spectrum of the corresponding DNS. Furthermore, the model significantly improves the prediction of the particle-pair dispersion, the clustering of the particles, and the turbulence modulation by particles in two-way coupled simulations. The proposed model recovers the most important interactions between fluid turbulence and the behavior of the particles, while maintaining the computational cost on the order of a LES.

This paper derives new correlations to predict the drag, lift and torque coefficients of axi-symmetric non-spherical rod-like particles for several fluid flow regimes and velocity profiles. The fluid velocity profiles considered are locally uniform flow and locally linear shear flow. The novel correlations for the drag, lift and torque coefficients depend on the particle Reynolds number \Rep, the orientation of the particle with respect to the main fluid direction $\theta$, the aspect ratio of the rod-like particle $\alpha$, and the dimensionless local shear rate $\tilde{G}$. The effect of the linear shear flow on the hydrodynamic forces is modeled as an additional component for the resultant of forces acting on a particle in a locally uniform flow, hence the independent expressions for the drag, lift and torque coefficients of axi-symmetric particles in a locally uniform flow are also provided in this work. The data provided to fit the coefficient in the new correlation are generated using available analytical expressions in the viscous regime, and performing direct numerical simulations (DNS) of the flow past the axi-symmetric particles at finite particle Reynolds number. The DNS are performed using the direct-forcing immersed boundary method. The coefficients in the proposed drag, lift and torque correlations are determined with a high degree of accuracy, where the mean error in the prediction lies below $2\%$ for the locally uniform flow correlations, and below $1.67\%$, $5.35\%$, $6.78\%$ for the correlations accounting for the change in the drag, lift, and torque coefficients in case of a linear shear flow, respectively. The proposed correlations for the drag, lift and torque coefficients can be used in large-scale simulations performed in the Eulerian-Lagrangian framework with locally uniform and non-uniform flows.

African languages are severely under-represented in NLP research due to lack of datasets covering several NLP tasks. While there are individual language specific datasets that are being expanded to different tasks, only a handful of NLP tasks (e.g. named entity recognition and machine translation) have standardized benchmark datasets covering several geographical and typologically-diverse African languages. In this paper, we develop MasakhaNEWS -- a new benchmark dataset for news topic classification covering 16 languages widely spoken in Africa. We provide an evaluation of baseline models by training classical machine learning models and fine-tuning several language models. Furthermore, we explore several alternatives to full fine-tuning of language models that are better suited for zero-shot and few-shot learning such as cross-lingual parameter-efficient fine-tuning (like MAD-X), pattern exploiting training (PET), prompting language models (like ChatGPT), and prompt-free sentence transformer fine-tuning (SetFit and Cohere Embedding API). Our evaluation in zero-shot setting shows the potential of prompting ChatGPT for news topic classification in low-resource African languages, achieving an average performance of 70 F1 points without leveraging additional supervision like MAD-X. In few-shot setting, we show that with as little as 10 examples per label, we achieved more than 90\% (i.e. 86.0 F1 points) of the performance of full supervised training (92.6 F1 points) leveraging the PET approach., Comment: Accepted to IJCNLP-AACL 2023 (main conference)

This paper evaluates and compares the accuracy and robustness of curvature estimation methods for three-dimensional interfaces represented implicitly by discrete volume fractions on a Cartesian mesh. The height function (HF) method is compared to three paraboloid fitting methods: fitting to the piecewise linear interface reconstruction centroids (PC), fitting to the piecewise linear interface reconstruction volumetrically (PV), and volumetrically fitting (VF) the paraboloid directly to the volume fraction field. The numerical studies presented in this work find that while the curvature error from the VF method converges with second-order accuracy as with the HF method for static interfaces represented by exact volume fractions, the PV method best balances low curvature errors with low computational cost for dynamic interfaces when the interface reconstruction and advection are coupled to a two-phase Navier-Stokes solver.

Learning with Errors (LWE) is a hard math problem underpinning many proposed post-quantum cryptographic (PQC) systems. The only PQC Key Exchange Mechanism (KEM) standardized by NIST is based on module~LWE, and current publicly available PQ Homomorphic Encryption (HE) libraries are based on ring LWE. The security of LWE-based PQ cryptosystems is critical, but certain implementation choices could weaken them. One such choice is sparse binary secrets, desirable for PQ HE schemes for efficiency reasons. Prior work, SALSA, demonstrated a machine learning-based attack on LWE with sparse binary secrets in small dimensions ($n \le 128$) and low Hamming weights ($h \le 4$). However, this attack assumes access to millions of eavesdropped LWE samples and fails at higher Hamming weights or dimensions. We present PICANTE, an enhanced machine learning attack on LWE with sparse binary secrets, which recovers secrets in much larger dimensions (up to $n=350$) and with larger Hamming weights (roughly $n/10$, and up to $h=60$ for $n=350$). We achieve this dramatic improvement via a novel preprocessing step, which allows us to generate training data from a linear number of eavesdropped LWE samples ($4n$) and changes the distribution of the data to improve transformer training. We also improve the secret recovery methods of SALSA and introduce a novel cross-attention recovery mechanism allowing us to read off the secret directly from the trained models. While PICANTE does not threaten NIST's proposed LWE standards, it demonstrates significant improvement over SALSA and could scale further, highlighting the need for future investigation into machine learning attacks on LWE with sparse binary secrets., Comment: 15 pages, 6 figures, 17 tables; accepted to CCS 2023

We evaluate the effectiveness of deep learning (DL) models for reconstructing the masses of galaxy clusters using X-ray photometry data from next-generation surveys. We establish these constraints using a catalogue of realistic mock eROSITA X-ray observations which use hydrodynamical simulations to model realistic cluster morphology, background emission, telescope response, and AGN sources. Using bolometric X-ray photon maps as input, DL models achieve a predictive mass scatter of $\sigma_{\ln M_\mathrm{500c}} = 17.8\%$, a factor of two improvements on scalar observables such as richness $N_\mathrm{gal}$, 1D velocity dispersion $\sigma_\mathrm{v,1D}$, and photon count $N_\mathrm{phot}$ as well as a $32\%$ improvement upon idealised, volume-integrated measurements of the bolometric X-ray luminosity $L_X$. We then show that extending this model to handle multichannel X-ray photon maps, separated in low, medium, and high energy bands, further reduces the mass scatter to $16.2\%$. We also tested a multimodal DL model incorporating both dynamical and X-ray cluster probes and achieved marginal gains at a mass scatter of $15.9\%$. Finally, we conduct a quantitative interpretability study of our DL models and find that they greatly down-weight the importance of pixels in the centres of clusters and at the location of AGN sources, validating previous claims of DL modelling improvements and suggesting practical and theoretical benefits for using DL in X-ray mass inference., Comment: 14 pages, 9 figures, 3 tables, accepted in MNRAS

In this paper we propose a new modeling framework for large eddy simulations (LES) of particle-laden turbulent flows that captures the interaction between the particle and fluid phase on both the resolved and subgrid-scales. Unlike the vast majority of existing subgrid-scale models, the proposed framework does not only account for the influence of the sugrid-scale velocity on the particle acceleration but also considers the effect of the particles on the turbulent fluid flow. This includes the turbulence modulation of the subgrid-scales by the particles, which is taken into account by the modeled subgrid-scale stress tensor, and the effect of the unresolved particle motion on the resolved flow scales. Our new modeling framework combines a recently proposed model for enriching the resolved fluid velocity with a subgrid-scale component, with the solution of a transport equation for the subgrid-scale kinetic energy. We observe very good agreement of the particle pair separation and particle clustering compared to the corresponding direct numerical simulation (DNS). Furthermore, we show that the change of subgrid-scale kinetic energy induced by the particles can be captured by the proposed modeling framework.

A novel smooth immersed boundary method (IBM) based on a direct-forcing formulation is proposed to simulate incompressible dense particle-laden flows. This IBM relies on a regularization of the transfer function between the Eulerian grid points (to discretise the fluid governing equations) and Lagrangian markers (to represent the particle surface) to fulfill the no-slip condition at the surfaces of the particles, allowing both symmetrical and non-symmetrical interpolation and spreading supports to be used. This enables that local source term contributions to the Eulerian grid, accounting for the boundary condition enforced at a Lagrangian marker on the surface of a particle, can be present on the inside of the particle only when this is beneficial, for instance when the Lagrangian marker is near another particle surface or near a domain boundary. However, when the Lagrangian marker is not near another particle surface or a domain boundary, the interpolation and spreading operators are locally symmetrical, meaning a ``classic'' IBM scheme is adopted. This approach, named hybrid IBM (HyBM), is validated with a number of test-cases from the literature. These results show that the HyBM achieves more accurate results compared to a classical IBM framework, especially at coarser mesh resolutions, when there are Lagrangian markers close to a particle surface or a domain wall.

In particle-laden turbulence, the Fourier Lagrangian spectrum of each phase is regularly computed, and analytically derived response functions relate the Lagrangian spectrum of the fluid- and the particle phase. However, due to the periodic nature of the Fourier basis, the analysis is restricted to statistically stationary flows. In the present work, utilizing the bases of time-focalized proper orthogonal decomposition (POD), this analysis is extended to temporally non-stationary turbulence. Studying two-way coupled particle-laden decaying homogeneous isotropic turbulence for various Stokes numbers, it is demonstrated that the temporal POD modes extracted from the dispersed phase may be used for the expansion of both fluid- and particle velocities. The POD Lagrangian spectrum of each phase may thus be computed from the same set of modal building blocks, allowing the evaluation of response functions in a POD frame of reference. Based on empirical evaluations, a model for response functions in non-stationary flows is proposed. The related energies of the two phases is well approximated by simple analytical expressions dependent on the particle Stokes number. It is found that the analytical expressions closely resemble those derived through Fourier analysis of statistically stationary flows. These results suggest the existence of an inherent spectral symmetry underlying the dynamical systems consisting of particle-laden turbulence, a symmetry which spans across stationary/non-stationary particle-laden flow states., Comment: 11 pages, 10 Figures

A phase proper orthogonal decomposition (Phase POD) method is demonstrated, utilizing phase averaging for the decomposition of spatio-temporal behaviour of statistically non-stationary turbulent flows in an optimized manner. The proposed Phase POD method is herein applied to a periodically forced statistically non-stationary lid-driven cavity flow, implemented using the snapshot proper orthogonal decomposition algorithm. Space-phase modes are extracted to describe the dynamics of the chaotic flow, in which four central flow patterns are identified for describing the evolution of the energetic structures as a function of phase. The modal building blocks of the energy transport equation are demonstrated as a function of the phase. The triadic interaction term can here be interpreted as the convective transport of bi-modal interactions. Non-local energy transfer is observed as a result of the non-stationarity of the dynamical processes inducing triadic interactions spanning across a wide range of mode numbers.

Problem Roulette (PR), an online study service at the University of Michigan, offers points-free formative practice to students preparing for examinations in introductory STEM courses. Using four years of PR data involving millions of problem attempts by thousands of students, we quantify benefits of increased practice study volume in introductory physics. After conditioning mean final grade on standardized (ACT/SAT) math test score, we analyze deviations based on student study volume. We find a strong effect; mean course grade rises quadratically with the logarithm of the total number of PR questions encountered over the term ($N_{\rm Q,tot}$), with an overall gain of $0.77 \pm 0.12$ grade points between $1 < N_{\rm Q,tot} < 1000$. The gains are persistent across the range of math test score represented in our sample. While $N_{\rm Q,tot}$ surely correlates with other study habits, the benefits of increased study in general still hold. A model for final grade using test score and study volume largely accounts for demographic stratification, including by sex, parental education level, number of parents at home, nationality / underrepresented minority status, and regional income level, with two significant exceptions: students whose parents did not earn a college degree, who earn $-0.27 \pm 0.04$ grade points ($6.1\sigma$) below expectations and underrepresented minority students at $-0.14 \pm 0.04$ points ($3.6\sigma$). Residual scatter in final grade remains comparable to the maximal study gains, implying that the model is far from deterministic: individual variation trumps mean trends. Our findings can help motivate students to study more and help teachers to identify which types of students may especially need such encouragement., Comment: Accepted for publication in Physical Review Physics Education Research; 13 pages, 8 figures