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We analyze the interaction between a self-diffusiophoretic spherical Janus motor and an inert spherical cargo particle in an axisymmetric configuration in the Stokes regime. To study the different configurations of the two spheres and their motions, we develop an analog to the twin multipole approach to numerically determine the axisymmetric stream function for the flow field. We verify the validity and accuracy of this approach using existing literature and COMSOL Multiphysics. We study the effects of the size of the Janus cap, the relative ratio of sizes of the two spheres, and their separation distance on their interactions. For the case of a stationary cargo, we identify the existence of a distinct regime where the Janus motor hovers at a finite separation distance from the cargo and summarize the results using a phase diagram. In the presence of a freely moving cargo, we analyze the steady terminal velocities of the Janus motor and the cargo to identify distinct conditions at which the two spheres can translate with equal velocities while maintaining a finite separation distance.

In the age of digital healthcare, passively collected physical activity profiles from wearable sensors are a preeminent tool for evaluating health outcomes. In order to fully leverage the vast amounts of data collected through wearable accelerometers, we propose to use quantile functional regression to model activity profiles as distributional outcomes through quantile responses, which can be used to evaluate activity level differences across covariates based on any desired distributional summary. Our proposed framework addresses two key problems not handled in existing distributional regression literature. First, we use spline mixed model formulations in the basis space to model nonparametric effects of continuous predictors on the distributional response. Second, we address the underlying missingness problem that is common in these types of wearable data but typically not addressed. We show that the missingness can induce bias in the subject-specific distributional summaries that leads to biased distributional regression estimates and even bias the frequently used scalar summary measures, and introduce a nonparametric function-on-function modeling approach that adjusts for each subject's missingness profile to address this problem. We evaluate our nonparametric modeling and missing data adjustment using simulation studies based on realistically simulated activity profiles and use it to gain insights into adolescent activity profiles from the Teen Environment and Neighborhood study.

Bayesian Cox semiparametric regression is an important problem in many clinical settings. Bayesian procedures provide finite-sample inference and naturally incorporate prior information if MCMC algorithms and posteriors are well behaved. Survival analysis should also be able to incorporate multilevel modeling such as case weights, frailties and smoothing splines, in a straightforward manner. To tackle these modeling challenges, we propose the Cox-Polya-Gamma (Cox-PG) algorithm for Bayesian multilevel Cox semiparametric regression and survival functions. Our novel computational procedure succinctly addresses the difficult problem of monotonicity constrained modeling of the nonparametric baseline cumulative hazard along with multilevel regression. We develop two key strategies. First, we exploit an approximation between Cox models and negative binomial processes through the Poisson process to reduce Bayesian computation to iterative Gaussian sampling. Next, we appeal to sufficient dimension reduction to address the difficult computation of nonparametric baseline cumulative hazard, allowing for the collapse of the Markov transition within the Gibbs sampler based on beta sufficient statistics. In addition, we explore conditions for uniform ergodicity of the Cox-PG algorithm. We demonstrate our multilevel modeling approach using open source data and simulations. We provide software for our Bayesian procedure in the supplement.

The onset and growth of rigid clusters in a two-dimensional (2D) suspension in shear flow are studied by numerical simulations. The suspension exhibits the lubricated-to-frictional rheology transition, but the key results here are for stresses above the levels that cause extreme shear-thickening. At large solid fraction, $\phi$, but below the stress-dependent jamming fraction, we find a critical $\phi_{c}\left(\sigma,\mu\right)$ where $\sigma$ is a dimensionless shear stress and $\mu$ is the interparticle friction coefficient. For $\phi>\phi_c$, the proportion of particles in rigid clusters grows sharply, as $f_{\rm rig} \sim \left\vert\phi-\phi_{c}\right\vert^{\beta}$ with $\beta=1/8$, as do the fluctuations in the fraction of rigid particles, with a susceptibility measure $\chi_{\rm rig} \sim \left\vert\phi-\phi_{c}\right\vert^{-\gamma}$ with $\gamma = 7/4$. The system is thus found to exhibit criticality. The results are shown to depend on an effective field $h\left(\mu\right)$, which provides data collapse near $\phi_c$ for both $f_{\rm rig}$ and $\chi_{\rm rig}$. This behavior occurs over a range of stresses, with $\phi_c\left(\sigma,\mu\right)$ increasing as the stress decreases.

We propose a new method for the simultaneous selection and estimation of multivariate sparse additive models with correlated errors. Our method called Covariance Assisted Multivariate Penalized Additive Regression (CoMPAdRe) simultaneously selects among null, linear, and smooth non-linear effects for each predictor while incorporating joint estimation of the sparse residual structure among responses, with the motivation that accounting for inter-response correlation structure can lead to improved accuracy in variable selection and estimation efficiency. CoMPAdRe is constructed in a computationally efficient way that allows the selection and estimation of linear and non-linear covariates to be conducted in parallel across responses. Compared to single-response approaches that marginally select linear and non-linear covariate effects, we demonstrate in simulation studies that the joint multivariate modeling leads to gains in both estimation efficiency and selection accuracy, of greater magnitude in settings where signal is moderate relative to the level of noise. We apply our approach to protein-mRNA expression levels from multiple breast cancer pathways obtained from The Cancer Proteome Atlas and characterize both mRNA-protein associations and protein-protein subnetworks for each pathway. We find non-linear mRNA-protein associations for the Core Reactive, EMT, PIK-AKT, and RTK pathways.

The emergence of novel infectious agents presents challenges to statistical models of disease transmission. These challenges arise from limited, poor-quality data and an incomplete understanding of the agent. Moreover, outbreaks manifest differently across regions due to various factors, making it imperative for models to factor in regional specifics. In this work, we offer a model that effectively utilizes constrained data resources to estimate disease transmission rates at the local level, especially during the early outbreak phase when primarily infection counts and aggregated local characteristics are accessible. This model merges a pathogen transmission methodology based on daily infection numbers with regression techniques, drawing correlations between disease transmission and local-area factors, such as demographics, health policies, behavior, and even climate, to estimate and forecast daily infections. We incorporate the quasi-score method and an error term to navigate potential data concerns and mistaken assumptions. Additionally, we introduce an online estimator that facilitates real-time data updates, complemented by an iterative algorithm for parameter estimation. This approach facilitates real-time analysis of disease transmission when data quality is suboptimal and knowledge of the infectious pathogen is limited. It is particularly useful in the early stages of outbreaks, providing support for local decision-making.

Exponential family models, generalized linear models (GLMs), generalized linear mixed models (GLMMs) and generalized additive models (GAMs) are widely used methods in statistics. However, many scientific applications necessitate constraints be placed on model parameters such as shape and linear inequality constraints. Constrained estimation and inference of parameters remains a pervasive problem in statistics where many methods rely on modifying rigid large sample theory assumptions for inference. We propose a flexible slice sampler Gibbs algorithm for Bayesian GLMMs and GAMs with linear inequality and shape constraints. We prove our posterior samples follow a Markov chain central limit theorem (CLT) by proving uniform ergodicity of our Markov chain and existence of the a moment generating function for our posterior distributions. We use our CLT results to derive joint bands and multiplicity adjusted Bayesian inference for nonparametric functional effects. Our rigorous CLT results address a shortcoming in the literature by obtaining valid estimation and inference on constrained parameters in finite sample settings. Our algorithmic and proof techniques are adaptable to a myriad of important statistical modeling problems. We apply our Bayesian GAM to a real data analysis example involving proportional odds regression for concussion recovery in children with shape constraints and smoothed nonparametric effects. We obtain multiplicity adjusted inference on monotonic nonparametric time effect to elucidate recovery trends in children as a function of time.

Although inertial particle-laden flows occur in a wide range of industrial and natural processes, there is both a lack of fundamental understanding of these flows and continuum-level governing equations needed to predict transport and particle distribution. Towards this effort, the Taylor-Couette flow (TCF) system has been used recently to study the flow behavior of particle-laden fluids under inertia. This article provides an overview of experimental, theoretical, and computational work related to the TCF of neutrally buoyant non-Brownian suspensions, with an emphasis on the effect of finite-sized particles on the series of flow transitions and flow structures. Particles, depending on their size and concentration, cause several significant deviations from Newtonian fluid behavior, including shifting the Reynolds number corresponding to transitions in flow structure and changing the possible structures present in the flow. Furthermore, particles may also migrate depending on the flow structure, leading to hysteretic effects that further complicate the flow behavior. The current state of theoretical and computational modeling efforts to describe the experimental observations is discussed, and suggestions for potential future directions to improve the fundamental understanding of inertial particle-laden flows are provided.

In this paper, we introduce a new Bayesian approach for analyzing task fMRI data that simultaneously detects activation signatures and background connectivity. Our modeling involves a new hybrid tensor spatial-temporal basis strategy that enables scalable computing yet captures nearby and distant intervoxel correlation and long-memory temporal correlation. The spatial basis involves a composite hybrid transform with two levels: the first accounts for within-ROI correlation, and second between-ROI distant correlation. We demonstrate in simulations how our basis space regression modeling strategy increases sensitivity for identifying activation signatures, partly driven by the induced background connectivity that itself can be summarized to reveal biological insights. This strategy leads to computationally scalable fully Bayesian inference at the voxel or ROI level that adjusts for multiple testing. We apply this model to Human Connectome Project data to reveal insights into brain activation patterns and background connectivity related to working memory tasks.

Shear thickening of suspensions is studied by discrete-particle simulation, accounting for hydrodynamic, repulsive, and contact forces. The contact forces, including friction, are activated when the imposed shear stress $\sigma$ is able to overcome the repulsive force. The simulation method captures strong continuous and discontinuous shear thickening (CST and DST) in the range of solid volume fraction $0.54 \le \phi\le 0.56$ studied here. This work presents characteristics of the contact force network developed in the suspension under shear. The number of frictional contacts per particle $Z$ is shown to have a one-to-one relationship with the suspension stress, and the conditions for simple percolation of frictional contacts are found to deviate strongly from those of a random network model. The stress is shown to have important correlations with topological invariant metrics of the contact network known as $k$-cores; the $k$-cores are maximal subgraphs (`clusters') in which all member particles have $k$ or more frictional contacts to other members of the same subgraph. Only $k\le 3$ is found in this work at solid volume fractions $\phi \le 0.56$. Distinct relationships between the suspension rheology and the $k$-cores are found. One is that the stress susceptibility, defined as $\partial \sigma/\partial \dot{\gamma}$ where $\dot{\gamma}$ is the shear rate, is found to peak at the condition of onset of the $3$-core, regardless of whether the system exhibits CST or DST. A second is that the stress per particle within cores of different $k$ increases sharply with increase of $k$ at the onset of DST; in CST, the difference is mild., Comment: 38 pages, 19 figures

We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs to vary over the functional domain. The model involves estimation of graphical models that evolve functionally in a nonparametric fashion while accounting for within-functional correlations and borrowing strength across functional positions so contiguous locations are encouraged but not forced to have similar graph structure and edge strength. We utilize a strategy that combines nonparametric basis function modeling with modified Bayesian graphical regularization techniques, which induces a new class of hypoexponential normal scale mixture distributions that not only leads to adaptively shrunken estimators of the conditional cross-covariance but also facilitates a thorough theoretical investigation of the shrinkage properties. Our approach scales up to large functional datasets collected on a fine grid. We show through simulations and real data analysis that the Bayesian functional graphical model can efficiently reconstruct the functionally-evolving graphical models by accounting for within-function correlations.

Graphical models are commonly used to discover associations within gene or protein networks for complex diseases such as cancer. Most existing methods estimate a single graph for a population, while in many cases, researchers are interested in characterizing the heterogeneity of individual networks across subjects with respect to subject-level covariates. Examples include assessments of how the network varies with patient-specific prognostic scores or comparisons of tumor and normal graphs while accounting for tumor purity as a continuous predictor. In this paper, we propose a novel edge regression model for undirected graphs, which estimates conditional dependencies as a function of subject-level covariates. Bayesian shrinkage algorithms are used to induce sparsity in the underlying graphical models. We assess our model performance through simulation studies focused on comparing tumor and normal graphs while adjusting for tumor purity and a case study assessing how blood protein networks in hepatocellular carcinoma patients vary with severity of disease, measured by HepatoScore, a novel biomarker signature measuring disease severity.

This paper describes an experimental study of filtration of a colloidal suspension using microfluidic devices. A suspension of micrometer-scale colloids flows through parallel slit-shaped pores at fixed pressure drop. Clogs and cakes are systematically observed at pore entrance, for variable applied pressure drop and ionic strength. Based on image analysis of the layer of colloids close to the device wall, global and local studies are performed to analyse in detail the near-wall layer microstructure. Whereas global porosity of this layer does not seem to be affected by ionic strength and applied pressure drop, a local study shows some heterogeneity: clogs are more porous at the vicinity of the pore than far away. An analysis of medium-range order using radial distribution function shows a slightly more organized state at high ionic strength. This is confirmed by a local analysis using two-dimension continuous wavelet decomposition: the typical size of crystals of colloids is larger for low ionic strength, and it increases with distance from the pores. We bring these results together in a phase diagram involving colloid-colloid repulsive interactions and fluid velocity., Comment: 13 pages, 16 figures

Functional quantile regression (FQR) is a useful alternative to mean regression for functional data as it provides a comprehensive understanding of how scalar predictors influence the conditional distribution of functional responses. In this article, we study the FQR model for densely sampled, high-dimensional functional data without relying on parametric error or independent stochastic process assumptions, with the focus on statistical inference under this challenging regime along with scalable implementation. This is achieved by a simple but powerful distributed strategy, in which we first perform separate quantile regression to compute $M$-estimators at each sampling location, and then carry out estimation and inference for the entire coefficient functions by properly exploiting the uncertainty quantification and dependence structure of $M$-estimators. We derive a uniform Bahadur representation and a strong Gaussian approximation result for the $M$-estimators on the discrete sampling grid, leading to dimension reduction and serving as the basis for inference. An interpolation-based estimator with minimax optimality is proposed, and large sample properties for point and simultaneous interval estimators are established. The obtained minimax optimal rate under the FQR model shows an interesting phase transition phenomenon that has been previously observed in functional mean regression. The proposed methods are illustrated via simulations and an application to a mass spectrometry proteomics dataset.

Quasi-2D experiments of a submerged sediment layer creeping downward were performed, varying the channel tilt and a porous flow under the respective thresholds for yielding. Logarithmic decay rates of the deformation are observed, with the rate increasing with both control parameters. A new dimensionless parameter, $P^*$, accounting for both mean porous flow and gravity force effects on particle motion, allows a collapse of all the deformation results on a single curve. Two distinct creep regimes are identified, and correspond to a systematic change of the void size distribution as $P^*$ increases.

Dense, stabilized, frictional particulate suspensions in a viscous liquid undergo increasingly strong continuous shear thickening (CST) as the solid packing fraction, $\phi$, increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for even higher packing fractions. Recent studies have related shear thickening to a transition from mostly lubricated to predominantly frictional contacts with the increase in stress. The rheology and networks of frictional forces from two and three-dimensional simulations of shear-thickening suspensions are studied. These are analyzed using measures of the topology of the network, including tools of persistent homology. We observe that at low stress the frictional interaction networks are predominantly quasi-linear along the compression axis. With an increase in stress, the force networks become more isotropic, forming loops in addition to chain-like structures. The topological measures of Betti numbers and total persistence provide a compact means of describing the mean properties of the frictional force networks and provide a key link between macroscopic rheology and the microscopic interactions. A total persistence measure describing the significance of loops in the force network structure, as a function of stress and packing fraction, shows behavior similar to that of relative viscosity and displays a scaling law near the jamming fraction for both dimensionalities simulated., Comment: 15 pages

The phenomenon of shear-induced jamming is a factor in the complex rheological behavior of dense suspensions. Such shear-jammed states are fragile, i.e., they are not stable against applied stresses that are incompatible with the stress imposed to create them. This peculiar flow-history dependence of the stress response is due to flow-induced microstructures. To examine jammed states realized under constant shear stress, we perform dynamic simulations of non-Brownian particles with frictional contact forces and hydrodynamic lubrication forces. We find clear signatures that distinguish these fragile states from the more conventional isotropic jammed states., Comment: Supplementary Material: https://youtu.be/v5LKX8bpP-w

Research in functional regression has made great strides in expanding to non-Gaussian functional outcomes, but exploration of ordinal functional outcomes remains limited. Motivated by a study of computer-use behavior in rhesus macaques (Macaca mulatta), we introduce the Ordinal Probit Functional Outcome Regression model (OPFOR). OPFOR models can be fit using one of several basis functions including penalized B-splines, wavelets, and O'Sullivan splines -- the last of which typically performs best. Simulation using a variety of underlying covariance patterns shows that the model performs reasonably well in estimation under multiple basis functions with near nominal coverage for joint credible intervals. Finally, in application, we use Bayesian model selection criteria adapted to functional outcome regression to best characterize the relation between several demographic factors of interest and the monkeys' computer use over the course of a year. In comparison with a standard ordinal longitudinal analysis, OPFOR outperforms a cumulative-link mixed-effects model in simulation and provides additional and more nuanced information on the nature of the monkeys' computer-use behavior.

Predicting rapid and slower soil evolution remains a scientific challenge. This process involves poorly understood aspects of disordered granular matter and dense suspension dynamics. This study presents a novel two-dimensional experiment on a small-scale chip structure; this allows the observation of the deformation at the particle scale of a large-grained sediment bed, under conditions where friction dominate over cohesive and thermal forces, and with an imposed fluid flow. Experiments are performed at conditions which span the particle resuspension criterion, and particle motion is detected and analyzed. The void size population and statistics of particle trajectories bring insight to the sediment dynamics near fluidization conditions. Specifically, particle rearrangement and net bed compaction are observed at flow rates significantly below the criterion for instability growth. Above a threshold, a large vertical channel through the bed forms. In the range of flow rates where channelization can occur, the coexistence of compacting and dilating bed scenarios is observed. The results of the study enhance our capacity for modeling of both slow dynamics and eventual rapid destabilization of sediment beds. Microfluidics channel soil-on-a-chip studies open avenues to new investigations including dissolution-precipitation, fine particles transport, or micro-organisms swimming and population growth, which may depend on mechanics of the porous media itself.

Radiomics involves the study of tumor images to identify quantitative markers explaining cancer heterogeneity. The predominant approach is to extract hundreds to thousands of image features, including histogram features comprised of summaries of the marginal distribution of pixel intensities, which leads to multiple testing problems and can miss out on insights not contained in the selected features. In this paper, we present methods to model the entire marginal distribution of pixel intensities via the quantile function as functional data, regressed on a set of demographic, clinical, and genetic predictors. We call this approach quantile functional regression, regressing subject-specific marginal distributions across repeated measurements on a set of covariates, allowing us to assess which covariates are associated with the distribution in a global sense, as well as to identify distributional features characterizing these differences, including mean, variance, skewness, and various upper and lower quantiles. To account for smoothness in the quantile functions, we introduce custom basis functions we call quantlets that are sparse, regularized, near-lossless, and empirically defined, adapting to the features of a given data set. We fit this model using a Bayesian framework that uses nonlinear shrinkage of quantlet coefficients to regularize the functional regression coefficients and provides fully Bayesian inference after fitting a Markov chain Monte Carlo. We demonstrate the benefit of the basis space modeling through simulation studies, and apply the method to Magnetic resonance imaging (MRI) based radiomic dataset from Glioblastoma Multiforme to relate imaging-based quantile functions to demographic, clinical, and genetic predictors, finding specific differences in tumor pixel intensity distribution between males and females and between tumors with and without DDIT3 mutations., Comment: 83 pages, 32 figures. arXiv admin note: substantial text overlap with arXiv:1711.00031

Simulations are used to study the steady shear rheology of dense suspensions of frictional particles exhibiting discontinuous shear thickening and shear jamming, in which finite-range cohesive interactions result in a yield stress. We develop a constitutive model that combines yielding behavior and shear thinning at low stress with the frictional shear thickening at high stresses, in good agreement with the simulation results. This work shows that there is a distinct difference between solids below the yield stress and in the shear-jammed state, as the two occur at widely separated stress levels, separated by a region of stress in which the material is flowable., Comment: 5 pages, 4 figures, +Supplemental Material

Highly concentrated or 'dense" particle suspensions can undergo a sharp increase in viscosity, or shear thickening, under applies stress. Understanding the fundamental features leading to such rheological changes in dense suspensions is crucial to optimize flow conditions or to design flow modifiers for slurry processing. While local changes to the particle environment under an applied shear can be related to changes in viscosity, there is a broader need to connect the shear thickening transition to the fundamental organization of particle-interaction forces which lead to long-range organization. In particular, at a high volume fraction of particles, recent evidence indicates frictional forces between contacting particles is of importance. Herein, the network of frictional contact forces is analyzed within simulated two-dimensional shear thickening suspensions. Two topological metrics are studied to characterize the response of the contact force network (CFN) under varying applied shear stress. The metrics, geodesic index and the void parameter, reflect complementary aspects of the CFN: one is the connectedness of the contact network and the second is the distribution of spatial areas devoid of particle-particle contacts. Considered in relation to the variation of the viscosity, the topological metrics show that the network grows homogeneously at large scales but with many local regions devoid of contacts, indicating clearly the role of stress chain growth in causing the large change in the rheological response at the shear thickening transition.

Mass spectrometry proteomics, characterized by spiky, spatially heterogeneous functional data, can be used to identify potential cancer biomarkers. Existing mass spectrometry analyses utilize mean regression to detect spectral regions that are differentially expressed across groups. However, given the inter-patient heterogeneity that is a key hallmark of cancer, many biomarkers are only present at aberrant levels for a subset of, not all, cancer samples. Differences in these biomarkers can easily be missed by mean regression, but might be more easily detected by quantile-based approaches. Thus, we propose a unified Bayesian framework to perform quantile regression on functional responses. Our approach utilizes an asymmetric Laplace working likelihood, represents the functional coefficients with basis representations which enable borrowing of strength from nearby locations, and places a global-local shrinkage prior on the basis coefficients to achieve adaptive regularization. Different types of basis transform and continuous shrinkage priors can be used in our framework. A scalable Gibbs sampler is developed to generate posterior samples that can be used to perform Bayesian estimation and inference while accounting for multiple testing. Our framework performs quantile regression and coefficient regularization in a unified manner, allowing them to inform each other and leading to improvement in performance over competing methods as demonstrated by simulation studies. We also introduce an adjustment procedure to the model to improve its frequentist properties of posterior inference. We apply our model to identify proteomic biomarkers of pancreatic cancer that are differentially expressed for a subset of cancer patients compared to the normal controls, which were missed by previous mean-regression based approaches. Supplementary materials for this article are available online.

We develop a statistical framework for the rheology of dense, non-Brownian suspensions, based on correlations in a space representing forces, which is dual to position space. Working with the ensemble of steady state configurations obtained from simulations of suspensions in two dimensions, we find that the anisotropy of the pair correlation function in force space changes with confining shear stress ($\sigma_{xy}$) and packing fraction ($\phi$). Using these microscopic correlations, we build a statistical theory for the macroscopic friction coefficient: the anisotropy of the stress tensor, $\mu = \sigma_{xy}/P$. We find that $\mu$ decreases (i) as $\phi$ is increased and (ii) as $\sigma_{xy}$ is increased. Using a new constitutive relation between $\mu$ and viscosity for dense suspensions that generalizes the rate-independent one, we show that our theory predicts a Discontinuous Shear Thickening (DST) flow diagram that is in good agreement with numerical simulations, and the qualitative features of $\mu$ that lead to the generic flow diagram of a DST fluid observed in experiments., Comment: 6 pages, 4 figures, +Supplemental Material

Glaucoma, a leading cause of blindness, is characterized by optic nerve damage related to intraocular pressure (IOP), but its full etiology is unknown. Researchers at UAB have devised a custom device to measure scleral strain continuously around the eye under fixed levels of IOP, which here is used to assess how strain varies around the posterior pole, with IOP, and across glaucoma risk factors such as age. The hypothesis is that scleral strain decreases with age, which could alter biomechanics of the optic nerve head and cause damage that could eventually lead to glaucoma. To evaluate this hypothesis, we adapted Bayesian Functional Mixed Models to model these complex data consisting of correlated functions on spherical scleral surface, with nonparametric age effects allowed to vary in magnitude and smoothness across the scleral surface, multi-level random effect functions to capture within-subject correlation, and functional growth curve terms to capture serial correlation across IOPs that can vary around the scleral surface. Our method yields fully Bayesian inference on the scleral surface or any aggregation or transformation thereof, and reveals interesting insights into the biomechanical etiology of glaucoma. The general modeling framework described is very flexible and applicable to many complex, high-dimensional functional data., Comment: paper accepted in Journal of the American Statistical Association, 2018 -- to appear

Blockage of pores by particles is found in many processes, including filtration and oil extraction. We present filtration experiments through a linear array of ten channels with one dimension which is sub-micron, through which a dilute dispersion of Brownian polystyrene spheres flows under the action of a fixed pressure drop. The growth rate of a clog formed by particles at a pore entrance systematically increases with the number of already saturated (entirely clogged) pores, indicating that there is an interaction or "cross-talk" between the pores. This observation is interpreted based on a phenomenological model, stating that a diffusive redistribution of particles occurs along the membrane, from clogged to free pores. This one-dimensional model could be extended to two-dimensional membranes.

At the same solid volume fraction, bidisperse and polydisperse suspensions display lower viscosities, and weaker normal stress response, compared to monodisperse suspensions. The reduction of viscosity associated with size distribution can be explained by an increase of the maximum flowable, or jamming, solid fraction ${\phi}_m$. In this work, dense suspensions are simulated under strong shearing, where thermal motion and repulsive forces are negligible, but we allow for particle contact with a mild frictional interaction with interparticle friction coefficient of ${\mu} = 0.2$. Aspects of bidisperse suspension rheology are first revisited to establish that the approach reproduces established trends; the study of bidisperse suspensions at size ratios of large to small particle radii of $\delta = 2$ to 4 shows that a minimum in the viscosity occurs for ${\zeta}$ slightly above 0.5, where $\zeta = {\phi}_l/{\phi}$ is the fraction of the total solid volume occupied by the large particles. The simple shear flows of polydisperse suspensions with truncated normal and log normal size distributions, and bidisperse suspensions which are statistically equivalent with these polydisperse cases up to third moment of the size distribution, are simulated and the rheologies are extracted. Prior work shows that such distributions with equivalent low-order moments have similar ${\phi}_m$, and the rheological behaviors of normal, log normal and bidisperse cases are shown to be in close agreement for a wide range of standard deviation in particle size, with standard correlations which are functionally dependent on ${\phi}/{\phi}_m$ providing excellent agreement with the rheology found in simulation. The close agreement of both viscosity and normal stress response between bi- and polydisperse suspensions demonstrates the controlling influence of the maximum packing fraction in noncolloidal suspensions

In this paper, we develop a quantile functional regression modeling framework that models the distribution of a set of common repeated observations from a subject through the quantile function, which is regressed on a set of covariates to determine how these factors affect various aspects of the underlying subject-specific distribution. To account for smoothness in the quantile functions, we introduce custom basis functions we call \textit{quantlets} that are sparse, regularized, near-lossless, and empirically defined, adapting to the features of a given data set and containing a Gaussian subspace so {non-Gaussianness} can be assessed. While these quantlets could be used within various functional regression frameworks, we build a Bayesian framework that uses nonlinear shrinkage of quantlet coefficients to regularize the functional regression coefficients and allows fully Bayesian inferences after fitting a Markov chain Monte Carlo. Specifically, we apply global tests to assess which covariates have any effect on the distribution at all, followed by local tests to identify at which specific quantiles the differences lie while adjusting for multiple testing, and to assess whether the covariate affects certain major aspects of the distribution, including location, scale, skewness, Gaussianness, or tails. If the difference lies in these commonly-used summaries, our approach can still detect them, but our systematic modeling strategy can also detect effects on other aspects of the distribution that might be missed if one restricted attention to pre-chosen summaries. We demonstrate the benefit of the basis space modeling through simulation studies, and illustrate the method using a biomedical imaging data set in which we relate the distribution of pixel intensities from a tumor image to various demographic, clinical, and genetic characteristics., Comment: 41 pages, 8 figures

Discrete particle simulations are used to study the shear rheology of dense, stabilized, frictional particulate suspensions in a viscous liquid, toward development of a constitutive model for steady shear flows at arbitrary stress. These suspensions undergo increasingly strong continuous shear thickening (CST) as solid volume fraction $\phi$ increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for a range of $\phi$. When studied at controlled stress, the DST behavior is associated with non-monotonic flow curves of the steady-state stress as a function of shear rate. Recent studies have related shear thickening to a transition between mostly lubricated to predominantly frictional contacts with the increase in stress. In this study, the behavior is simulated over a wide range of the dimensionless parameters $(\phi,\tilde{\sigma}$, and $\mu)$, with $\tilde{\sigma} = \sigma/\sigma_0$ the dimensionless shear stress and $\mu$ the coefficient of interparticle friction: the dimensional stress is $\sigma$, and $\sigma_0 \propto F_0/ a^2$, where $F_0$ is the magnitude of repulsive force at contact and $a$ is the particle radius. The data have been used to populate the model of the lubricated-to-frictional rheology of Wyart and Cates [Phys. Rev. Lett.{\bf 112}, 098302 (2014)], which is based on the concept of two viscosity divergences or \textquotedblleft jamming\textquotedblright\ points at volume fraction $\phi_{\rm J}^0 = \phi_{\rm rcp}$ (random close packing) for the low-stress lubricated state, and at $\phi_{\rm J} (\mu) < \phi_{\rm J}^0$ for any nonzero $\mu$ in the frictional state; a generalization provides the normal stress response as well as the shear stress. A flow state map of this material is developed based on the simulation results., Comment: 12 pages, 10 figures

Dense suspensions can exhibit an abrupt change in their viscosity in response to increasing shear rate. The origin of this discontinuous shear thickening (DST) has been ascribed to the transformation of lubricated contacts to frictional, particle-on-particle contacts. Recent research on the flowing and jamming behavior of dense suspensions has explored the intersection of ideas from granular physics and Stokesian fluid dynamics to better understand this transition from lubricated to frictional rheology. DST is reminiscent of classical phase transitions, and a key question is how interactions between the microscopic constituents give rise to a macroscopic transition. In this paper, we extend a formalism that has proven to be successful in understanding shear jamming of dry grains to dense suspensions. Quantitative analysis of the collective evolution of the contact-force network accompanying the DST transition demonstrates clear changes in the distribution of microscopic variables, and leads to the identification of an "order parameter" characterizing DST., Comment: 4 pages. We welcome comments and criticisms

The dynamics of two liquid droplets coalescing in their saturated vapor phase are investigated by Lattice Boltzmann numerical simulations. Attention is paid to the effect of the vapor phase on the formation and growth dynamics of the liquid bridge in the viscous regime. We observe that the onset of the coalescence occurs earlier and the expansion of the bridge initially proceeds faster when the coalescence takes place in a saturated vapor compared to the coalescence in a non-condensable gas. We argue that the initially faster evolution of the coalescence in the saturated vapor is caused by the vapor transport through condensation during the early stages of the coalescence.

There was an error in data reduction, resulting in incorrect values for the normal stress differences $N_1$ and $N_2$ shown in Figs. 7-10, and the corrected figures are shown here. In particular, the algebraic sign of $N_1$ is changed, as are the relative magnitudes of $N_1$ and $N_2$. The negative values of $N_1$ for these non-shear-thickening suspensions are larger in magnitude than those reported by other workers, but both $N_1$ and $N_2$ are in general agreement with the accelerated Stokesian Dynamics calculations of Sierou and Brady [1]., Comment: v2 includes corrigendum to published version

Accelerated Stokesian Dynamics (ASD) simulation and a microstructural theory are applied to study structure and the viscosity of hard-sphere Brownian suspensions in active microrheology (MR).We consider moderate to dense suspensions, from near to far from equilibrium conditions.The theory explicitly considers many-body hydrodynamic interactions (HIs) in active MR, and is compared with ASD.Two conditions of moving the probe with constant force (CF) and constant velocity (CV) are considered.The structure is quantified using the probability distribution of colloidal particles around the probe, g(r), which is computed as a solution to the pair Smoluchowski equation (SE) for 0.2<\phi<0.50, and a range of Peclet numbers (Pe), describing the ratio of external force on the probe to thermal forces.Results of ASD and theory demonstrate that a wake zone depleted of bath particles behind the moving probe forms at large Pe, while a boundary-layer accumulation develops upstream.The wake length saturates at Pe>>1 for CF while it continuously grows in CV.This contrast in behavior is related to the dispersion in the motion of the probe under CF conditions, while CV motion has no dispersion.This effect is incorporated in the theory as a force-induced hydrodynamic diffusion flux in the pair SE. We also demonstrate that, despite this difference of structure in CF and CV, g(r) near the probe is set by Pe, for both CF and CV resulting in similar values for their viscosity.Using the theory, the structural anisotropy and Brownian viscosity near equilibrium are shown to be quantitatively similar in both CF and CV motions, which is in contrast with the dilute theory which predict distortions and Brownian viscosities twice as large in CV, relative to CF.This difference arises due to the many-body interactions associated with the equilibrium structure in the moderate to dense regime.

Dynamic particle-scale numerical simulations are used to show that the shear thickening observed in dense colloidal, or Brownian, suspensions is of a similar nature to that observed in non-colloidal suspensions, i.e., a stress-induced transition from a flow of lubricated near-contacting particles to a flow of a frictionally contacting network of particles. Abrupt (or discontinuous) shear thickening is found to be a geometric rather than hydrodynamic phenomenon; it stems from the strong sensitivity of the jamming volume fraction to the nature of contact forces between suspended particles. The thickening obtained in a colloidal suspension of purely hard frictional spheres is qualitatively similar to experimental observations. However, the agreement cannot be made quantitative with only hydrodynamics, frictional contacts and Brownian forces. Therefore the role of a short-range repulsive potential mimicking the stabilization of actual suspensions on the thickening is studied. The effects of Brownian and repulsive forces on the onset stress can be combined in an additive manner. The simulations including Brownian and stabilizing forces show excellent agreement with experimental data for the viscosity $\eta$ and the second normal stress difference $N_2$., Comment: 7 pages, 7 figures. v2: improved text. Accepted in PNAS