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We report direct numerical simulation (DNS) results of the rough-wall channel, focusing on roughness with high $k_{rms}/k_a$ statistics but small to negative $Sk$ statistics, and we study the implications of this new dataset on rough-wall modelling. Here, $k_{rms}$ is the root-mean-square, $k_a$ is the first order moment of roughness height, and $Sk$ is the skewness. The effects of packing density, skewness and arrangement of roughness elements on mean streamwise velocity, equivalent roughness height ($z_0$) and Reynolds and dispersive stresses have been studied. We demonstrate that two-point correlation lengths of roughness height statistics play an important role in characterizing rough surfaces with identical moments of roughness height but different arrangements of roughness elements. Analysis of the present as well as historical data suggests that the task of rough-wall modelling is to identify geometric parameters that distinguish the rough surfaces within the calibration dataset. We demonstrate a novel feature selection procedure to determine these parameters. Further, since there is not a finite set of roughness statistics that distinguish between all rough surfaces, we argue that obtaining a universal rough-wall model for making equivalent sand-grain roughness ($k_s$) predictions would be challenging, and that each rough-wall model would have its applicable range. This motivates the development of group-based rough-wall models. The applicability of multi-variate polynomial regression and feedforward neural networks for building such group-based rough-wall models using the selected features has been shown., Comment: 34 pages, 29 figures

An analytic calculation is given for binary star evaporation under the tidal perturbation from randomly distributed, spatially extended dark objects. In particular, the Milky Way's wide binary star population are susceptible to such disruption from dark matter solitons of comparable and larger sizes. We identify high-probability `halo-like' wide binaries in GAIA EDR3 with separations larger than 0.1 parsec. Survival of the farthest-separated candidates will provide a novel gravitational probe to dark matter in the form of solitons. In case of dilute axion-like solitons, the observational sensitivity is shown to extend into the axion mass range $m_a \sim 10^{-17}-10^{-15}$ eV., Comment: 15 pages, 4 figures, 3 tables

Turbulent flow physics regulates the aerodynamic properties of lifting surfaces, the thermodynamic efficiency of vapor power systems, and exchanges of natural and anthropogenic quantities between the atmosphere and ocean, to name just a few applications. The dynamics of turbulent flows are described via numerical integration of the non-linear Navier-Stokes equation -- a procedure known as computational fluid dynamics (CFD). At the dawn of scientific computing in the late 1950s, it would be many decades before terms such as ``carbon footprint'' or ``sustainability'' entered the lexicon, and longer still before these themes attained national priority throughout advanced economies. This paper introduces a framework designed to calculate the carbon footprint of CFD and its contribution to carbon emission reduction strategies. We will distinguish between "hero" and "routine" calculations, noting that the carbon footprint of hero calculations is largely determined by the energy source mix utilized. We will also review CFD of flows where turbulence effects are modeled, thus reducing the degrees of freedom. Estimates of the carbon footprint are presented for such fully- and partially-resolved simulations as functions of turbulence activity and calculation year, demonstrating a reduction in carbon emissions by two to five orders of magnitude at practical conditions. Beyond analyzing CO2 emissions, we quantify the benefits of applying CFD towards overall carbon emission reduction. The community's effort to avoid redundant calculations via turbulence databases merits particular attention, with estimates indicating that a single database could potentially reduce CO2 emissions by approximately O(1) million metric tons. Additionally, implementing CFD in the fluids industry has markedly decreased dependence on wind tunnel testing, which is anticipated to lead to CO2 emission reduction., Comment: 18 pages, 6 figures

We present a comprehensive investigation on the mass function (MF) of a snake-like stellar structure in the solar neighbourhood, building on our previous discovery. To ensure the reliability of the data, we reselect the member stars of the Stellar ``Snake'' in the latest {\it Gaia} Data Release 3 using the same approach as the initial series of articles. We also precisely measure the physical parameters of the clusters within the Stellar Snake. In light of the high completeness of the member stars in the cluster regions, we develop a simulated model color-magnitude diagram-based inference method to derive the mass function, binary fraction, and mass-ratio distribution of the clusters in the Stellar Snake. Notably, despite their similar ages and metallicity, we discover systematic variations in the MFs along the elongation direction of the Snake in the mass range of 0.5 to 2.0 M$_\odot$. The ``head'' of the Snake conforms to a canonical initial mass function with a power-law slope of $\alpha\sim-2.3$. Extending towards the ``tail,'' the MF becomes more top-light, indicating a deficiency of massive stars within these clusters. This result provides evidence for the delayed formation of massive stars in the clusters. Such clues give support to the hypothesis that the Stellar Snake constitutes as a hierarchically primordial structure., Comment: 19 pages, 15 figures, Accepted for publication on MNRAS

This work aims to incorporate basic calibrations of Reynolds-averaged Navier-Stokes (RANS) models as part of machine learning (ML) frameworks. The ML frameworks considered are tensor-basis neural network (TBNN), physics-informed machine learning (PIML), and field inversion & machine learning (FIML) in J. Fluid Mech., 2016, 807, 155-166, Phys. Rev. Fluids, 2017, 2(3), 034603 and J. Comp. Phys., 2016, 305, 758-774, and the baseline RANS models are the one-equation Spalart-Allmaras model, the two-equation $k$-$\omega$ model, and the seven-equation Reynolds stress transport models. ML frameworks are trained against plane channel flow and shear-layer flow data. We compare the ML frameworks and study whether the machine-learned augmentations are detrimental outside the training set. The findings are summarized as follows. The augmentations due to TBNN are detrimental. PIML leads to augmentations that are beneficial inside the training dataset but detrimental outside it. These results are not affected by the baseline RANS model. FIML's augmentations to the two eddy viscosity models, where an inner-layer treatment already exists, are largely neutral. Its augmentation to the seven-equation model, where an inner-layer treatment does not exist, improves the mean flow prediction in a channel. Furthermore, these FIML augmentations are mostly non-detrimental outside the training dataset. In addition to reporting these results, the paper offers physical explanations of the results. Last, we note that the conclusions drawn here are confined to the ML frameworks and the flows considered in this study. More detailed comparative studies and validation & verification studies are needed to account for developments in recent years.

We examine and benchmark the emerging idea of applying the large-eddy simulation (LES) formalism to unconventionally coarse grids where RANS would be considered more appropriate at first glance. We distinguish this idea from very-large-eddy-simulation (VLES) and detached-eddy-simulation (DES), which require switching between RANS and LES formalism. LES on RANS grid is appealing because first, it requires minimal changes to a production code; second, it is more cost-effective than LES; third, it converges to LES; and most importantly, it accurately predicts flows with separation. This work quantifies the benefit of LES on RANS-like grids as compared to RANS on the same grids. Three canonical cases are considered: periodic hill, backward-facing step, and jet in cross flow. We conduct direct numerical simulation (DNS), proper LES on LES grids, LES on RANS-quality grids, and RANS. We show that while the LES solutions on the RANS-quality grids are not grid converged, they are twice as accurate as the RANS on the same grids.

The constants and functions in Reynolds-averaged Navier Stokes (RANS) turbulence models are coupled. Consequently, modifications of a RANS model often negatively impact its basic calibrations, which is why machine-learned augmentations are often detrimental outside the training dataset. A solution to this is to identify the degrees of freedom that do not affect the basic calibrations and only modify these identified degrees of freedom when re-calibrating the baseline model to accommodate a specific application. This approach is colloquially known as the "rubber-band" approach, which we formally call "constrained model re-calibration" in this article. To illustrate the efficacy of the approach, we identify the degrees of freedom in the Spalart-Allmaras (SA) model that do not affect the log law calibration. By subsequently interfacing data-based methods with these degrees of freedom, we train models to solve historically challenging flow scenarios, including the round-jet/plane-jet anomaly, airfoil stall, secondary flow separation, and recovery after separation. In addition to good performance inside the training dataset, the trained models yield similar performance as the baseline model outside the training dataset.

Assessing the compliance of a white-box turbulence model with known turbulent knowledge is straightforward. It enables users to screen conventional turbulence models and identify apparent inadequacies, thereby allowing for a more focused and fruitful validation and verification. However, comparing a black-box machine-learning model to known empirical scalings is not straightforward. Unless one implements and tests the model, it would not be clear if a machine-learning model, trained at finite Reynolds numbers preserves the known high Reynolds number limit. This is inconvenient, particularly because model implementation involves retraining and re-interfacing. This work attempts to address this issue, allowing fast a priori screening of machine-learning models that are based on feed-forward neural networks (FNN). The method leverages the mathematical theorems we present in the paper. These theorems offer estimates of a network's limits even when the exact weights and biases are unknown. For demonstration purposes, we screen existing machine-learning wall models and RANS models for their compliance with the log layer physics and the viscous layer physics in a priori manner. In addition, the theorems serve as essential guidelines for future machine-learning models.

This study presents a methodology focusing on the use of computational model and experimental data fusion to improve the Spalart-Allmaras (SA) closure model for Reynolds-averaged Navier-Stokes solutions. In particular, our goal is to develop a technique that not only assimilates sparse experimental data to improve turbulence model performance, but also preserves generalization for unseen cases by recovering classical SA behavior. We achieve our goals using data assimilation, namely the Ensemble Kalman filtering approach (EnKF), to calibrate the coefficients of the SA model for separated flows. A holistic calibration strategy is implemented via the parameterization of the production, diffusion, and destruction terms. This calibration relies on the assimilation of experimental data collected in the form of velocity profiles, skin friction, and pressure coefficients. Despite using observational data from a single flow condition around a backward-facing step (BFS), the recalibrated SA model demonstrates generalization to other separated flows, including cases such as the 2D NASA wall mounted hump (2D-WMH) and modified BFS. Significant improvement is observed in the quantities of interest, i.e., skin friction coefficient ($C_f$) and pressure coefficient ($C_p$) for each flow tested. Finally, it is also demonstrated that the newly proposed model recovers SA proficiency for flows, such as a NACA-0012 airfoil and axisymmetric jet (ASJ), and that the individually calibrated terms in the SA model target specific flow-physics wherein the calibrated production term improves the re-circulation zone while destruction improves the recovery zone.

Carbon, as one of the most common element in the earth, constructs hundreds of allotropic phases to present rich physical nature. In this work, by combining the ab inito calculations and symmetry analyses method, we systematically study a large number of allotropes of carbon (703), and discovered 315 ideal topological phononic materials and 32 topological electronic materials. The ideal topological phononic nature includes single, charge-two, three, four Weyl honons, the Dirac or Weyl nodal lines phonons, and nodal surfaces phonons. And the topological electron nature ncludes topological insulator, (Type-II) Dirac points, triple nodal points, the Dirac (Weyl) nodal lines, quadratic nodal lines and so on. For convenience, we take the uni in SG 178 and pbg in SG 230 as the examples to describe the topological features in the main. We find that it is the coexistence of single pair Weyl phonons and one-nodal surfaces phonons in the uni in SG 178, which can form the single surface arc in the (100) surface BZ and isolated double-helix surface states (IDHSSs)in the (110) surface BZ. In topological semimetal pbg in SG 230, we find that the perfect triple degenerate nodal point can be found in the near Fermi level, and it can form the clear surface states in the (001) and (110) surface BZ. Our work not only greatly expands the topological features in all allotropes of carbon, but also provide many ideal platforms to study the topological electrons and phonons.

This paper explores the similarity of the streamwise velocity fluctuations in a channel. In the analysis, we employ a one-dimensional scalar variant of the proper orthogonal decomposition (POD). This approach naturally motivates the introduction of two different levels of similarity which we will refer to as strong and weak similarity. Strong similarity requires that the two-point correlation, and thus, all POD modes, show Reynolds number similarity, while weak similarity only requires that the first few POD modes show similarity. As POD concerns information at more than one location, these similarities are more general than various similarities found in the literature concerning single-point flow statistics. We examine flows at $Re_\tau=$180, 540, 1000, and 5200. Strong similarity is observed in the viscous layer and the wake region, and weak similarity is found in both the viscous wall region and the outer part of the logarithmic layer. The presence of weak similarity suggests the existence of an extension to the law of the wall (LoW). We propose such an extension based on the results from the one-dimensional POD analysis. The usefulness of the LoW extension is then assessed by comparing flow reconstructions according to the conventional equilibrium LoW and the extended LoW. We show that the extended LoW provides accurate flow reconstructions in the wall layer, capturing fine-scale motions that are entirely missed by the equilibrium LoW., Comment: 17 pages, 16 figures

Deep Neural Networks (DNNs) have significantly improved the accuracy of intelligent applications on mobile devices. DNN surgery, which partitions DNN processing between mobile devices and multi-access edge computing (MEC) servers, can enable real-time inference despite the computational limitations of mobile devices. However, DNN surgery faces a critical challenge: determining the optimal computing resource demand from the server and the corresponding partition strategy, while considering both inference latency and MEC server usage costs. This problem is compounded by two factors: (1) the finite computing capacity of the MEC server, which is shared among multiple devices, leading to inter-dependent demands, and (2) the shift in modern DNN architecture from chains to directed acyclic graphs (DAGs), which complicates potential solutions. In this paper, we introduce a novel Decentralized DNN Surgery (DDS) framework. We formulate the partition strategy as a min-cut and propose a resource allocation game to adaptively schedule the demands of mobile devices in an MEC environment. We prove the existence of a Nash Equilibrium (NE), and develop an iterative algorithm to efficiently reach the NE for each device. Our extensive experiments demonstrate that DDS can effectively handle varying MEC scenarios, achieving up to 1.25$\times$ acceleration compared to the state-of-the-art algorithm., Comment: Under Review

One major challenge of disentanglement learning with variational autoencoders is the trade-off between disentanglement and reconstruction fidelity. Previous studies, which increase the information bottleneck during training, tend to lose the constraint of disentanglement, leading to the information diffusion problem. In this paper, we present a novel framework for disentangled representation learning, DeVAE, which utilizes hierarchical latent spaces with decreasing information bottlenecks across these spaces. The key innovation of our approach lies in connecting the hierarchical latent spaces through disentanglement-invariant transformations, allowing the sharing of disentanglement properties among spaces while maintaining an acceptable level of reconstruction performance. We demonstrate the effectiveness of DeVAE in achieving a balance between disentanglement and reconstruction through a series of experiments and ablation studies on dSprites and Shapes3D datasets. Code is available at https://github.com/erow/disentanglement_lib/tree/pytorch#devae.

This paper focuses on the use of reinforcement learning (RL) as a machine-learning (ML) modeling tool for near-wall turbulence. RL has demonstrated its effectiveness in solving high-dimensional problems, especially in domains such as games. Despite its potential, RL is still not widely used for turbulence modeling and is primarily used for flow control and optimization purposes. A new RL wall model (WM) called VYBA23 is developed in this work, which uses agents dispersed in the flow near the wall. The model is trained on a single Reynolds number ($Re_\tau = 10^4$) and does not rely on high-fidelity data, as the back-propagation process is based on a reward rather than output error. The states of the RLWM, which are the representation of the environment by the agents, are normalized to remove dependence on the Reynolds number. The model is tested and compared to another RLWM (BK22) and to an equilibrium wall model, in a half-channel flow at eleven different Reynolds numbers ($Re_\tau \in [180;10^{10}]$). The effects of varying agents' parameters such as actions range, time-step, and spacing are also studied. The results are promising, showing little effect on the average flow field but some effect on wall-shear stress fluctuations and velocity fluctuations. This work offers positive prospects for developing RLWMs that can recover physical laws, and for extending this type of ML models to more complex flows in the future., Comment: arXiv admin note: text overlap with arXiv:2211.03614

Insights gained from modal analysis are invoked for predictive large-eddy simulation (LES) wall modeling. Specifically, we augment the law of the wall (LoW) by an additional mode based on a one-dimensional proper orthogonal decomposition (POD) applied to a 2D turbulent channel. The constructed wall model contains two modes, i.e., the LoW mode and the POD-based mode, and the model matches with the LES at two, instead of one, off-wall locations. To show that the proposed model captures non-equilibrium effects, we perform a-priori and a-posteriori tests in the context of both equilibrium and non-equilibrium flows. The a-priori tests show that the proposed wall model captures extreme wall-shear stress events better than the equilibrium wall model. The model also captures non-equilibrium effects due to adverse pressure gradients. The a-posteriori tests show that the wall model captures the rapid decrease and the initial decrease of the streamwise wall-shear stress in channels subjected to suddenly imposed adverse and transverse pressure gradients, respectively, both of which are missed by currently available wall models. These results show promise in applying modal analysis for turbulence wall modeling. In particular, the results show that employing multiple modes helps in the modeling of non-equilibrium flows.

Electrophoretic (EP) mobility reversal is commonly observed for strongly charged macromolecules in multivalent salt solutions. This curious effect takes place, e.g., when a charged polymer, such as DNA, adsorbs excess counterions so that the counterion-dressed surface charge reverses its sign, leading to the inversion of the polymer drift driven by an external electric field. In order to characterize this seemingly counterintuitive phenomenon that cannot be captured by electrostatic mean-field theories, we adapt here a previously developed strong-coupling-dressed Poisson-Boltzmann approach to the cylindrical geometry of the polyelectrolyte-salt system. Within the framework of this formalism, we derive an analytical polymer mobility formula dressed by charge correlations. In qualitative agreement with polymer transport experiments, this mobility formula predicts that the increment of the monovalent salt, the decrease of the multivalent counterion valency, and the increase of the dielectric permittivity of the background solvent, suppress charge correlations and increase the multivalent bulk counterion concentration required for EP mobility reversal. These results are corroborated by coarse-grained molecular dynamics simulations showing how multivalent counterions induce mobility inversion at dilute concentrations and suppress the inversion effect at large concentrations. This re-entrant behavior, previously observed in the aggregation of like-charged polymer solutions, calls for verification by polymer transport experiments., Comment: 14 pages, 9 figures