arXiv subjects

Xiang Yang

Publications and source records attributed to Xiang Yang.

At least 37 records · Page 2Linked to original sources

arXiv2022

Theoretical and computational analysis of the electrophoretic polymer mobility inversion induced by charge correlations

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.

cond-mat.soft↗

arXiv2022

Data-driven quantification of model-form uncertainty in Reynolds-averaged simulations of wind farms

Computational fluid dynamics using the Reynolds-averaged Navier-Stokes (RANS) remains the most cost-effective approach to study wake flows and power losses in wind farms. The underlying assumptions associated with turbulence closures are one of the biggest sources of errors and uncertainties in the model predictions. This work aims to quantify model-form uncertainties in RANS simulations of wind farms at high Reynolds numbers under neutrally stratified conditions by perturbing the Reynolds stress tensor through a data-driven machine-learning technique. To this end, a two-step feature-selection method is applied to determine key features of the model. Then, the extreme gradient boosting algorithm is validated and employed to predict the perturbation amount and direction of the modeled Reynolds stress toward the limiting states of turbulence on the barycentric map. This procedure leads to a more accurate representation of the Reynolds stress anisotropy. The data-driven model is trained on high-fidelity data obtained from large-eddy simulation of a specific wind farm, and it is tested on two other (unseen) wind farms with distinct layouts to analyze its performance in cases with different turbine spacing and partial wake. The results indicate that, unlike the data-free approach in which a uniform and constant perturbation amount is applied to the entire computational domain, the proposed framework yields an optimal estimation of the uncertainty bounds for the RANS-predicted quantities of interest, including the wake velocity, turbulence intensity, and power losses in wind farms.

physics.flu-dyn↗

arXiv2022

Modified Poisson-Boltzmann theory for polyelectrolytes in monovalent salt solutions with finite-size ions

We present a soft-potential-enhanced Poisson-Boltzmann (SPB) theory to efficiently capture ion distributions and electrostatic potential around rodlike charged macromolecules. The SPB model is calibrated with a coarse-grained particle-based model for polyelectrolytes (PEs) in monovalent salt solutions as well as compared to a full atomistic molecular dynamics simulations with explicit solvent. We demonstrate that our modification enables the SPB theory to accurately predict monovalent ion distributions around a rodlike PE in a wide range of ion and charge distribution conditions in the weak-coupling regime. These include excess salt concentrations up to 1 M, and ion sizes ranging from small ions, such as Na or Cl, to softer and larger ions with size comparable to the PE diameter. The work provides a simple way to implement an enhancement that effectively captures the influence of ion size and species into the PB theory in the context of PEs in aqueous salt solutions.

cond-mat.soft↗

arXiv2022

Interaction between two polyelectrolytes in monovalent aqueous salt solutions

We use the recently developed soft-potential-enhanced Poisson-Boltzmann (SPB) theory to study the interaction between two parallel polyelectrolytes (PEs) in monovalent ionic solutions in the weak-coupling regime. The SPB theory is fitted to ion distributions from coarse-grained molecular dynamics (MD) simulations and benchmarked against all-atom MD modelling for poly(diallyldimethylammonium) (PDADMA). We show that the SPB theory is able to accurately capture the interactions between two PEs at distances beyond the PE radius. For PDADMA positional correlations between the charged groups lead to locally asymmetric PE charge and ion distributions. This gives rise to small deviations from the SPB prediction that appear as short-range oscillations in the potential of mean force. Our results suggest that the SPB theory can be an efficient way to model interactions in chemically specific complex PE systems.

cond-mat.soft↗

arXiv2021

Model-form uncertainty quantification in RANS simulations of wakes and power losses in wind farms

Reynolds-averaged Navier-Stokes (RANS) is one of the most cost-efficient approaches to simulate wind-farm-atmosphere interactions. However, the applicability of RANS-based methods is always limited by the accuracy of turbulence closure models, which introduce various uncertainties into the models. In this study, we estimate model-form uncertainties in RANS simulations of wind farms. For this purpose, we compare different RANS models to a large-eddy simulation (LES). We find that the realizable k-epsilon model is a representative RANS model for predicting the mean velocity, the turbulence intensity, and the power losses within the wind farm. We then investigate the model-form uncertainty associated with this turbulence model by perturbing the Reynolds stress tensor. The focus is placed on perturbing the shape of the tensor represented by its eigenvalues. The results show that the perturbed RANS model successfully estimates the region bounding the LES results for quantities of interest (QoIs). We also discuss the effect of perturbation magnitude on various QoIs.

physics.flu-dyn↗

arXiv2021

Second Moment Closure Modeling and DNS of Stratified Shear Layers

Buoyant shear layers are encountered in many engineering and environmental applications and have been studied by researchers in the context of experiments and modeling for decades. Often, these flows have high Reynolds and Richardson numbers, and this leads to significant/intractable space-time resolution requirements for DNS or LES modeling. On the other hand, many of the important physical mechanisms in these systems, such as stress anisotropy, wake stabilization, and regime transition, inherently render eddy viscosity-based RANS modeling inappropriate. Accordingly, we pursue second-moment closure (SMC), i.e., full Reynolds stress/flux/variance modeling, for moderate Reynolds number non-stratified and stratified shear layers for which DNS is possible. A range of sub-model complexity is pursued for the diffusion of stresses, density fluxes and variance, pressure strain and scrambling, and dissipation. These sub-models are evaluated in terms of how well they are represented by DNS in comparison to the exact Reynolds averaged terms, and how well they impact the accuracy of the full RANS closure. For the non-stratified case, the SMC model predicts the shear layer growth rate and Reynolds shear stress profiles accurately. Stress anisotropy and budgets are captured only qualitatively. Comparing DNS of exact and modeled terms, inconsistencies in model performance and assumptions are observed, including inaccurate prediction of individual statistics, non-negligible pressure diffusion, and dissipation anisotropy. For the stratified case, shear layer and gradient Richardson number growth rates, and stress, flux, and variance decay rates, are captured with less accuracy than corresponding flow parameters in the non-stratified case. These studies lead to several recommendations for model improvement.

physics.flu-dyn↗

arXiv2021

The diverse nature of small-scale turbulence

The self-similar Richardson cascade admits two logically possible scenarios of small-scale turbulence at high Reynolds numbers. In the first scenario, eddies' population densities vary as a function of eddies' scales. As a result, one or a few eddy types dominate at small scales, and small-scale turbulence lacks diversity. In the second scenario, eddies' population densities are scale-invariant across the inertial range, resulting in small-scale diversity. That is, there are as many types of eddies at the small scales as at the large scales. In this letter, we measure eddies' population densities in three-dimensional isotropic turbulence and determine the nature of small-scale turbulence. The result shows that eddies' population densities are scale-invariant.

physics.flu-dyn↗

arXiv2021

3D flow motions in the viscous sublayer

We employ novel digital Fresnel reflection holography to capture the 3D flows within the viscous sublayer of a smooth-wall turbulent channel flow at Reτ=400. The measurements reveal unsteady and diverse flow patterns in the sublayer including nearly uniform high and low speed flows and strong small-scale (on the order of viscous wall units) spanwise meandering motions. The probability density functions (PDFs) of wall shear stresses show a clear discrepancy in high stress range with those from direct numerical simulation (DNS), which is attributed to the unresolved streamwise and spanwise motions by DNS. Moreover, the PDF of Lagrangian particle accelerations yields a stretched exponential shape like that in homogenous isotropic turbulence, indicating strong intermittency in the sublayer. We find a significant fraction of high accelerations is associated with the small-scale meandering motions. Our study helps explain the effect of sublayer-scale roughness on reducing drag and flow separation reported in the literature.

physics.flu-dyn↗

arXiv2021

Determining a priori a RANS model's applicable range via global epistemic uncertainty quantification

Calibrating a Reynolds-averaged Navier-Stokes (RANS) model against data leads to an improvement. Determining {\it a priori} if such an improvement generalizes to flows outside the calibration data is an outstanding challenge. This work attempts to address this challenge via global epistemic Uncertainty Quantification (UQ). Unlike the available epistemic UQ methods that are local and tell us a model's uncertainty at one specific flow condition, the global epistemic UQ method presented in this work tells us also whether a perturbation of the original model would generalize. Specifically, the global epistemic UQ method evaluates a potential improvement in terms of its "effectiveness" and "inconsistency". Any improvement can be put in one of the following four quadrants: first, high effectiveness, low inconsistency; second, high effectiveness, high inconsistency; third, low effectiveness, low inconsistency; and fourth, low effectiveness, high inconsistency. An improvement would generalize if and only if it is in the high effectiveness and low inconsistency quadrant. To demonstrate the concept, we apply the global epistemic UQ to full Reynolds stress modeling of a stratified shear layer. The global epistemic UQ results point to a model coefficient in the pressure-strain correlation closure (among others) as effective and consistent for predicting the quantity of interest of shear layer's growth. We calibrate the model coefficient such that our RANS matches direct numerical simulation data at one flow condition. We show that the calibrated model generalizes to several other test flow conditions. On the other hand, when calibrating a high inconsistency term, we get a model that works at only the calibrated condition.

physics.flu-dyn↗

arXiv2020

Shuffle-Exchange Brings Faster: Reduce the Idle Time During Communication for Decentralized Neural Network Training

As a crucial scheme to accelerate the deep neural network (DNN) training, distributed stochastic gradient descent (DSGD) is widely adopted in many real-world applications. In most distributed deep learning (DL) frameworks, DSGD is implemented with Ring-AllReduce architecture (Ring-SGD) and uses a computation-communication overlap strategy to address the overhead of the massive communications required by DSGD. However, we observe that although $O(1)$ gradients are needed to be communicated per worker in Ring-SGD, the $O(n)$ handshakes required by Ring-SGD limits its usage when training with many workers or in high latency network. In this paper, we propose Shuffle-Exchange SGD (SESGD) to solve the dilemma of Ring-SGD. In the cluster of 16 workers with 0.1ms Ethernet latency, SESGD can accelerate the DNN training to $1.7 \times$ without losing model accuracy. Moreover, the process can be accelerated up to $5\times$ in high latency networks (5ms).

cs.DC↗

arXiv2020

Bifurcation and multiple states in plane Couette flow with spanwise rotation

We present a derivation that begins with the Navier--Stokes equation and ends with a prediction of multiple statistically stable states identical to those observed in a spanwise rotating plane Couette flow. This derivation is able to explain the presence of multiple states in fully developed turbulence and the selection of one state over the other by differently sized computational domains and different initial conditions. According to the present derivation, two and only two statistically stable states are possible in an infinitely large plane Couette flow with spanwise rotation, and that multiple states are not possible at very slow or very rapid rotation speeds. We also show the existence of limit cycles near statistically stable states.

physics.flu-dyn↗

arXiv2019

Robust boundary flow in chiral active fluid

We perform experiments on an active chiral fluid system of self-spinning rotors in confining boundary. Along the boundary, actively rotating rotors collectively drives a unidirectional material flow. We systematically vary rotor density and boundary shape; boundary flow robustly emerges under all conditions. Flow strength initially increases then decreases with rotor density (quantified by area fraction $ϕ$); peak strength appears around a density $ϕ=0.65$. Boundary curvature plays an important role: flow near a concave boundary is stronger than that near a flat or convex boundary in the same confinements. Our experimental results in all cases can be reproduced by a continuum theory with single free fitting parameter, which describes the frictional property of the boundary. Our results support the idea that boundary flow in active chiral fluid is topologically protected; such robust flow can be used to develop materials with novel functions.

cond-mat.soft↗

arXiv2019

Diffusion of Colloidal Rods in Corrugated Channels

In many natural and artificial devices diffusive transport takes place in confined geometries with corrugated boundaries. Such boundaries cause both entropic and hydrodynamic effects, which have been studied only for the case of spherical particles. Here we experimentally investigate diffusion of particles of elongated shape confined into a corrugated quasi-two-dimensional channel. Elongated shape causes complex excluded-volume interactions between particle and channel walls which reduce the accessible configuration space and lead to novel entropic free energy effects. The extra rotational degree of freedom also gives rise to a complex diffusivity matrix that depends on both the particle location and its orientation. We further show how to extend the standard Fick-Jacobs theory to incorporate combined hydrodynamic and entropic effects, so as, for instance, to accurately predict experimentally measured mean first passage times along the channel. Our approach can be used as a generic method to describe translational diffusion of anisotropic particles in corrugated channels.

cond-mat.soft↗

arXiv2019

Resolvent-based estimation of space-time flow statistics

We develop a method to estimate space-time flow statistics from a limited set of known data. While previous work has focused on modeling spatial or temporal statistics independently, space-time statistics carry fundamental information about the physics and coherent motions of the flow and provide a starting point for low-order modeling and flow control efforts. The method is derived using a statistical interpretation of resolvent analysis. The central idea of our approach is to use known data to infer the statistics of the nonlinear terms that constitute a forcing on the linearized Navier-Stokes equations, which in turn imply values for the remaining unknown flow statistics through application of the resolvent operator. Rather than making an a priori rank-1 assumption, our method allows the known input data to select the most relevant portions of the resolvent operator for describing the data, making it well-suited for high-rank turbulent flows. We demonstrate the predictive capabilities of the method using two examples: the Ginzburg-Landau equation, which serves as a convenient model for a convectively unstable flow, and a turbulent channel flow at low Reynolds number.

physics.flu-dyn↗

arXiv2017

Scale Adaptive Clustering of Multiple Structures

We propose the segmentation of noisy datasets into Multiple Inlier Structures with a new Robust Estimator (MISRE). The scale of each individual structure is estimated adaptively from the input data and refined by mean shift, without tuning any parameter in the process, or manually specifying thresholds for different estimation problems. Once all the data points were classified into separate structures, these structures are sorted by their densities with the strongest inlier structures coming out first. Several 2D and 3D synthetic and real examples are presented to illustrate the efficiency, robustness and the limitations of the MISRE algorithm.

cs.CV↗

arXiv2017

Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels

In the absence of advection, confined diffusion characterizes transport in many natural and artificial devices, such as ionic channels, zeolites, and nanopores. While extensive theoretical and numerical studies on this subject have produced many important predictions, experimental verifications of the predictions are rare. Here, we experimentally measure colloidal diffusion times in microchannels with periodically varying width and contrast results with predictions from the Fick-Jacobs theory and Brownian dynamics simulation. While the theory and simulation correctly predict the entropic effect of the varying channel width, they fail to account for hydrodynamic effects, which include both an overall decrease and a spatial variation of diffusivity in channels. Neglecting such hydrodynamic effects, the theory and simulation underestimate the mean and standard deviation of first passage times by 40\% in channels with a neck width twice the particle diameter. We further show that the validity of the Fick-Jakobs theory can be restored by reformulating it in terms of the experimentally measured diffusivity. Our work thus demonstrates that hydrodynamic effects play a key role in diffusive transport through narrow channels and should be included in theoretical and numerical models.

cond-mat.soft↗

arXiv2017

Robust Estimation of Multiple Inlier Structures

The robust estimator presented in this paper processes each structure independently. The scales of the structures are estimated adaptively and no threshold is involved in spite of different objective functions. The user has to specify only the number of elemental subsets for random sampling. After classifying all the input data, the segmented structures are sorted by their strengths and the strongest inlier structures come out at the top. Like any robust estimators, this algorithm also has limitations which are described in detail. Several synthetic and real examples are presented to illustrate every aspect of the algorithm.

cs.CV↗

arXiv2015

Dynamic Clustering in Suspension of Motile Bacteria

Bacteria suspension exhibits a wide range of collective phenomena arising from interactions between individual cells. Here we show Serratia marcescens cells near an air-liquid interface spontaneously aggregate into dynamic clusters through surface-mediated hydrodynamic interactions. These long-lived clusters translate randomly and rotate in the counter-clockwise direction; they continuously evolve, merge with others and split into smaller ones. Measurements indicate that long-ranged hydrodynamic interactions have strong influences on cluster properties. Bacterial clusters change material and fluid transport near the interface and hence may have environmental and biological consequences.

cond-mat.soft↗