Gaussian Velocity Research Articles

ALMA-IMF. XIII. N2H+ kinematic analysis of the intermediate protocluster G353.41

The ALMA-IMF Large Program provides multi-tracer observations of 15 Galactic massive protoclusters at a matched sensitivity and spatial resolution. We focus on the dense gas kinematics of the G353.41 protocluster traced by N$_2$H$^+$ (1$-$0), with a spatial resolution of sim \,0.02 pc. G353.41, at a distance of sim 2\,kpc, is embedded in a larger-scale ($ filament and has a mass of odot within $1.3 pc$^2$. We extracted the N$_2$H$^+$ (1$-$0) isolated line component and decomposed it by fitting up to three Gaussian velocity components. This allows us to identify velocity structures that are either muddled or impossible to identify in the traditional position-velocity diagram. We identify multiple velocity gradients on large (sim 1\,pc) and small scales (sim 0.2\,pc). We find good agreement between the N$_2$H$^+$ velocities and the previously reported DCN core velocities, suggesting that cores are kinematically coupled with the dense gas in which they form. We have measured nine converging ``V-shaped'' velocity gradients (VGs) ($ $) that are well resolved (sizes $ mostly located in filaments, which are sometimes associated with cores near their point of convergence. We interpret these V-shapes as inflowing gas feeding the regions near cores (the immediate sites of star formation). We estimated the timescales associated with V-shapes as $, and we interpret them as inflow timescales. The average inflow timescale is $ kyr, or about twice the free-fall time of cores in the same area ($ but substantially shorter than protostar lifetime estimates ($ Myr). We derived mass accretion rates in the range of $(0.35-8.77)\ $ M$_ odot $ yr$^ $. This feeding might lead to further filament collapse and the formation of new cores. We suggest that the protocluster is collapsing on large scales, but the velocity signature of collapse is slow compared to pure free-fall. Thus, these data are consistent with a comparatively slow global protocluster contraction under gravity, and faster core formation within, suggesting the formation of multiple generations of stars over the protocluster's lifetime.

Adaptive merging migration

Velocity errors and data noise are inevitable for seismic imaging of field data sets in current production; therefore, it is desirable to improve the seismic images as part of the migration process to mitigate the influence of such errors and noise. To address this, we develop a new method of adaptive merging migration (AMM). Our method can produce migrated sections of equal quality to conventional migration methods given a correct velocity model and noise-free data. In addition, it can ameliorate the seismic image quality when applied with erroneous migration velocity models or noisy seismic data. AMM uses an efficient recursive Radon transform to generate multiple p-component images, representing migrated sections associated with different local plane slopes. It then adaptively merges the subsections from those p-component images that are less distorted by velocity errors or noise into the whole image. Such merging is implemented by computing adaptive weights followed by a selective stacking. We use three synthetic velocity models and one field data set to evaluate the AMM performance on isolated Gaussian velocity errors, inaccurate smoothed velocities, velocity errors around high-contrast and short-wavelength interfaces, and noisy seismic data. Numerical tests conducted on synthetic and field data sets validate that AMM can effectively improve the seismic image quality in the presence of different types of velocity errors and data noise.

2.5D Magnetohydrodynamic Simulation of the Formation and Evolution of Plasmoids in Coronal Current Sheets

In the present paper, using MPI-AMRVAC, we perform a 2.5D numerical magnetohydrodynamic simulation of the dynamics and associated thermodynamical evolution of an initially force-free Harris current sheet subjected to an external velocity perturbation under the condition of uniform resistivity. The amplitude of the magnetic field is taken to be 10 G, typical of the solar corona. We impose a Gaussian velocity pulse across this current sheet that mimics the interaction of fast magnetoacoustic waves with a current sheet in the corona. This leads to a variety of dynamics and plasma processes in the current sheet, which is initially quasi-static. The initial pulse interacts with the current sheet and splits into a pair of counterpropagating wavefronts, which form a rarefied region that leads to an inflow and a thinning of the current sheet. The thinning results in Petschek-type magnetic reconnection followed by a tearing instability and plasmoid formation. The reconnection outflows containing outward-moving plasmoids have accelerated motions with velocities ranging from 105 to 303 km s−1. The average temperature and density of the plasmoids are found to be 8 MK and twice the background density of the solar corona, respectively. These estimates of the velocity, temperature, and density of the plasmoids are similar to values reported from various solar coronal observations. Therefore, we infer that the external triggering of a quasi-static current sheet by a single-velocity pulse is capable of initiating magnetic reconnection and plasmoid formation in the absence of a localized enhancement of resistivity in the solar corona.

Detection of atomic vortex beam using the near-field diffraction method

We theoretically introduce the method for detecting the atomic vortex (AV) of a helium atomic beam. The AV detection is based on near-field diffraction. The simulations relied on the Feynman path integral. The Gaussian beam and velocity distribution of helium atoms are taken into account. Gravitational field is also included in this study. This research can be useful in the field of matter-wave optics.

Gaussian and Gaussian-pulsed-like Fermi velocity graphene structures

Gaussian and Gaussian-related structures are quite attractive due to its versatility to modulate the electronic transport, including its possibility as electron filters. Here, we show that these non-conventional profiles are not the exception when dealing with Fermi velocity barriers in monolayer graphene. In particular, we show that Gaussian Fermi velocity graphene barriers (G-FVGBs) and Gaussian-pulsed-like Fermi velocity graphene superlattices (GPL-FVGSLs) can serve as electron band-pass filters and oscillating conductance structures. We reach this conclusion by theoretically studying the transmission and transport properties of the mentioned structures. The study is based on the continuum model, the transfer matrix method and the Landauer–Büttiker formalism. We find nearly flat transmission bands or pass bands for G-FVGBs modulable through the system parameters. The pass bands improve as the maximum ratio of Fermi velocities () increases, however its omnidirectional range is reduced. These characteristics result in a decaying conductance (integrated transmission) with . The integrated transmission remains practically unaltered with the size of the system due to the saturation of the electron pass band filtering. In the case of GPL-FVGSLs the GPL profile results in regions of high transmission probability that can merge as flat transmission minibands if the pulse fraction and the superlattice parameters are appropriately tuned. The GPL profile also results in conductance (integrated transmission) oscillations that can be multiplied or reduced in number by adjusting the pulse fraction as well as the superlattice parameters.

Design and Fabrication of Robotic arm for Multiple Degrees of Freedom Control

This paper details the design, construction, and evaluation of a highly flexible, high-precision robotic arm primarily used in prosthetic and rehabilitation engineering applications. The robotic arm was designed using 3D printing and SolidWorks and features a modular design that simplifies the manufacturing process and improves scalability. The arm has three degrees of freedom and is realized by a well-designed circuit program integrating ESP32 and STM32 microcontrollers. The structural integrity and functionality of the arm were verified through finite element analysis and kinematic simulation. The study also presents a novel path-planning algorithm for the robot arm, which is based on linear position and Gaussian velocity models and is effective in generating smooth, continuous, and physically constrained paths. This work provides an open-source solution that offers a cost-effective and robust platform for diverse robotics applications.

MP70-04 URETERAL PERISTALSIS LONGITUDINAL MOTION MINIMIZES REFLUX

You have accessJournal of UrologyCME1 Apr 2023MP70-04 URETERAL PERISTALSIS LONGITUDINAL MOTION MINIMIZES REFLUX Kourosh Kalayeh, Haotian Xie, J. Brian Fowlkes, William W. Schultz, and Bryan S. Sack Kourosh KalayehKourosh Kalayeh More articles by this author , Haotian XieHaotian Xie More articles by this author , J. Brian FowlkesJ. Brian Fowlkes More articles by this author , William W. SchultzWilliam W. Schultz More articles by this author , and Bryan S. SackBryan S. Sack More articles by this author View All Author Informationhttps://doi.org/10.1097/JU.0000000000003338.04AboutPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareFacebookLinked InTwitterEmail Abstract INTRODUCTION AND OBJECTIVE: Lack of sufficient ureteral peristalsis is theorized as one of the mechanisms contributing to ureteral dilation in vesicoureteral reflux (VUR) and non-obstructing megaureters. To help understand the phathophysiologic mechanism for these disorders, we first need to understand the dynamics of normal ureteral peristalsis, which results in near complete clearance of urine from the ureter (i.e., non-dilated). We hypothesize that the clinically observed ureteral wall longitudinal motion is crucial to prevent and/or limit peristaltic reflux (i.e., retrograde flow of urine during an episode of peristalsis). METHODS: To examine this hypothesis, based on the lubrication theory in fluid mechanics, we modeled ureteral peristalsis mathematically as an infinite train of sinusoidal waves and analyzed the antegrade and retrograde flows in the ureter. In doing so, we accounted for ureteral wall longitudinal motion by imposing a periodic Gaussian longitudinal velocity on the wall, Figure 1 (a) and (b), inspired by videos of ureteral operations. RESULTS: Effects of wall longitudinal motion on peristaltic reflux and performance are shown in Figure 1 (c) & (d), and Figure 2 (a) & (b), respectively. The results are shown as an example for a typical clinical case with discharge rate of 1.62 mL/min and peristaltic amplitude of 80 % of lumen diameter. As shown, by considering wall longitudinal motion, the range of urine flow rates resulting in peristaltic reflux drops substantially. The minimum required flow rate to prevent peristaltic reflux drops by 50% when including the wall longitudinal motion effect, Figure 2 (a). Similarly, the required flow rate to limit the reflux volume fraction below a critical value of 2% (chosen as an example, based on clinical expertise) drops by 70%, Figure 2 (b). CONCLUSIONS: This computational model is the first to include longitudinal wall motion, which aligns with our hypothesis that it is important for minimizing peristaltic reflux. This supports the clinical observation of normal ureters having high emptying ability and helps direct further investigations to understand ureteral disorders. Source of Funding: This research has been partially supported by grants from the Michigan Institute for Clinical and Health Research (MICHR), and the Departments of Urology and Radiology at the University of Michigan © 2023 by American Urological Association Education and Research, Inc.FiguresReferencesRelatedDetails Volume 209Issue Supplement 4April 2023Page: e1004 Advertisement Copyright & Permissions© 2023 by American Urological Association Education and Research, Inc.MetricsAuthor Information Kourosh Kalayeh More articles by this author Haotian Xie More articles by this author J. Brian Fowlkes More articles by this author William W. Schultz More articles by this author Bryan S. Sack More articles by this author Expand All Advertisement PDF downloadLoading ...

TriPField: A 3D Potential Field Model and Its Applications to Local Path Planning of Autonomous Vehicles

Potential fields have been integrated with local path-planning algorithms for autonomous vehicles (AVs) to tackle challenging scenarios with dense and dynamic obstacles. Most existing potential fields are isotropic without considering the traffic agent’s geometric shape and could cause failures due to local minima. We propose a three-dimensional potential field (TriPField) model to overcome this drawback by integrating an ellipsoid potential field with a Gaussian velocity field (GVF). Specifically, we model the surrounding vehicles as ellipsoids in corresponding ellipsoidal coordinates, where the formulated Laplace equation is solved with boundary conditions. Meanwhile, we develop a nonparametric GVF to capture the multi-vehicle interactions and then plan the AV’s velocity profiles, reducing the path search space and improving computing efficiency. Finally, a local path-planning framework with our TriPField is developed by integrating model predictive control to consider the constraints of vehicle kinematics. Our proposed approach is verified in three typical scenarios, i.e., active lane change, on-ramp merging, and car following. Experimental results show that our TriPField-based planner obtains a shorter, smoother local path with a slight jerk during control, especially in the scenarios with dense traffic flow, compared with traditional potential field-based planners. Our proposed TriPField-based planner can perform emergent obstacle avoidance for AVs with a high success rate even when the surrounding vehicles behave abnormally.

Anomalous scaling in kinematic magnetohydrodynamic turbulence: Two-loop anomalous dimensions of leading composite operators.

Using the field theoretic formulation of the kinematic magnetohydrodynamic turbulence, the explicit expressions for the anomalous dimensions of leading composite operators, which govern the inertial-range scaling properties of correlation functions of the weak magnetic field passively advected by the electrically conductive turbulent environment driven by the Navier-Stokes velocity field, are derived and analyzed in the second order of the corresponding perturbation expansion (in the two-loop approximation). Their properties are compared to the properties of the same anomalous dimensions obtained in the framework of the Kazantsev-Kraichnan model of the kinematic magnetohydrodynamics with the Gaussian statistics of the turbulent velocity field as well as to the analogous anomalous dimensions of the leading composite operators in the problem of the passive scalar advection by the Gaussian (the Kraichnan model) and non-Gaussian (driven by the Navier-Stokes equation) turbulent velocity field. It is shown that, regardless of the Gaussian or non-Gaussian statistics of the turbulent velocity field, the two-loop corrections to the leading anomalous dimensions are much more important in the case of the problem of the passive advection of the vector (magnetic) field than in the case of the problem of the passive advection of scalar fields. At the same time, it is also shown that, in phenomenologically the most interesting case with three spatial dimensions, higher velocity correlations of the turbulent environment given by the Navier-Stokes velocity field play a rather limited role in the anomalous scaling of passive scalar as well as passive vector quantities, i.e., that the two-loop corrections to the corresponding leading anomalous dimensions are rather close to those obtained in the framework of the Gaussian models, especially as for the problem of scalar field advection. On the other hand, the role of the non-Gaussian statistics of the turbulent velocity field becomes dominant for higher spatial dimensions in the case of the kinematic magnetohydrodynamic turbulence but remains negligible in the problem of the passive scalar advection.

Predicting radial profiles for jets with arbitrary buoyancy

The present study investigates the profiles of statistically axisymmetric turbulent jets with arbitrary buoyancy. Analytical expressions for the shape of the radial velocity, Reynolds stress and radial scalar flux profiles are derived from the governing equations by assuming self-similar Gaussian mean velocity and scalar profiles. Previously these have only been derived for the special cases of pure jets and plumes, whereas the present study generalises them to arbitrary buoyancies. These are then used to derive analytical expressions for the turbulent Schmidt/Prandtl numbers, which, along with the mean profiles, are shown to give predictions in agreement with existing literature.

Iterative Reweighted Least-Squares Gaussian Beam Migration and Velocity Inversion in the Image Domain Based on Point Spread Functions

Amplitude-preserving migration is very important for reservoir characterization, which can faithfully provide information on the strength of the reflectors. However, conventional migration algorithms do not compensate for variable illumination effects and can hardly obtain true amplitudes of medium parameter. Least squares migration (LSM) is an effective method to address this issue. Unfortunately, there is a key problem with LSM methods: most LSM methods only consider illumination compensation but not consider the accuracy of migration velocity model. The accuracy of the migration velocity model directly affects the quality of migrated images. Moreover, changes in velocity are more indicative of reservoir properties than reflectivity. Therefore, it is necessary to incorporate velocity estimation into migration imaging to realize joint inversions. Based on these facts, we present an iterative re-weighted LSM method by approximating the local Hessian using point spread functions. Then, we related the LSM results to the scattering potential, simultaneously achieving velocity update with illumination compensation. Based on the gradually changing characteristics of rock properties, we adopted a sparse derivative constraint rather than requiring the result to be sparse. Consequently, this processing caused the results to contain broader bandwidths, giving the image a more continuous and textured appearance. Next, we evaluated the proposed method using the Marmousi2 model. The results had higher resolution and a more reliable amplitude than the initial migration images. Hence, we efficaciously completed the velocity model update, with our method achieving encouraging results under both relatively accurate migration velocity and highly smoothed migration velocity model tests.

Emergent dynamics of light-induced active colloids probed by XPCS

Self-propelled particulate systems manifest certain collective behavior of living matter, which have been the subject of intense research over the past decades. One of the elegant methods for realizing such active motions is by means of custom synthesized Janus particles suspended in a catalytic medium that can be triggered upon illumination by ultraviolet light. In this work, the evolution of the particle dynamics from passive diffusive to active ballistic behavior upon light illumination was probed by multispeckle x-ray photon correlation spectroscopy (XPCS). This technique enables not only studying the emergence of active motions in three dimensions (3D) but also deciphering different contributions to the overall dynamics. Using a combination of homodyne and heterodyne analysis, the ensemble averaged mean velocity, velocity fluctuations and diffusion coefficient of particles were determined in the thermodynamic limit. Results revealed a gradual transition from diffusive to ballistic dynamics with systematic increase of the catalytic activity. At the intermediate region, the dynamics is dominated by Gaussian velocity fluctuations and an enhanced relaxation rate with a weaker wave vector dependence similar to superdiffusive behavior. For the highest activity, the dynamics became purely ballistic with Lorentzian-like distribution of velocity fluctuations. Presented results demonstrate that different aspects of active dynamics can be investigated in 3D over a broad range of Péclet numbers and other control parameters by means of multispeckle XPCS.

Comparative study of the single and double specularity coefficients on two-fluid modeling of a pseudo-2D gas–solid fluidized bed

The specularity coefficient is an unmeasurable parameter in the most popular wall boundary model during the two-fluid modeling of dense gas–solid flows. Using multiphaseEulerFoam solver, the influence of different specularity coefficient setting strategies on the gas–solid flow inside a pseudo-2D fluidized bed has been explored. It is found that the single specularity coefficient plays a regulatory role in the quantitative prediction. Increasing the specularity coefficient would cause a fluidization transition from freely bubbling to slugging, and the bed characteristics such as pressure drop and bed expansion present monotonic nonlinear changes. The double specularity coefficients approach is shown to significantly improve the predictive accuracy through verifying with the measured particle velocities, bubble diameter and rise velocity. In addition, the lognormal bubble size distribution and Gaussian bubble rise velocity distribution are observed. The specularity coefficient for walls in thickness direction is crucial and its different effects are unignorable. Overall, the present study provides a practical strategy of double specularity coefficients for the solid wall boundary conditions during two-fluid modeling.

Kinematic Structure of the Large Magellanic Cloud Globular Cluster System from Gaia eDR3 and Hubble Space Telescope Proper Motions

We have determined bulk proper motions (PMs) for 31 LMC GCs from Gaia eDR3 and Hubble Space Telescope data using multiple independent analysis techniques. Combined with literature values for distances, line-of-sight velocities, and existing bulk PMs, we extract full 6D phase-space information for 32 clusters, allowing us to examine the kinematics of the LMC GC system in detail. Except for two GCs (NGC 2159 and NGC 2210) whose high velocities suggest they are not long-term members of the LMC system, the data are consistent with a flattened configuration that rotates like the stellar disk. The one-dimensional velocity dispersions are on the order of 30 km s−1, similar to that of old stellar populations in the LMC disk. Similarly to the case for Milky Way disk clusters, the velocity anisotropy is such that the dispersion is smallest in the azimuthal direction; however, alternative anisotropies cannot be ruled out, due to distance uncertainties. The data are consistent with a single multidimensional Gaussian velocity distribution. Given the non-collisional nature of the LMC disk, this suggests that most, if not all, of the LMC GCs are formed by a single formation mechanism in the stellar disk, despite a significant spread in age and metallicity. Any accreted halo GC population is absent or far smaller in the LMC compared to the Milky Way.

High Schmidt-number turbulent advection and giant concentration fluctuations

We consider the effects of thermal noise on the Batchelor-Kraichnan theory of high Schmidt-number mixing in the viscous dissipation range of turbulent flows at sub-Kolmogorov scales. Starting with the nonlinear Landau-Lifshitz fluctuating hydrodynamic equations for a binary fluid mixture at low Mach numbers, we justify linearization around the deterministic Navier-Stokes solution in the dissipation range. For the latter solution we adopt the standard Kraichnan model, a Gaussian random velocity with spatially constant strain but white noise in time. Then, following prior work of Donev, Fai, and Vanden-Eijnden [J. Stat. Mech.: Theory Exp. (2014) P04004], we derive asymptotic high Schmidt limiting equations for the concentration field, in which the thermal velocity fluctuations are exactly represented by a Gaussian random velocity that is likewise white in time. We obtain the exact solution for concentration spectrum in this high Schmidt limiting model, showing that the Batchelor prediction in the viscous-convective range is unaltered. Thermal noise dramatically renormalizes the bare diffusivity in this range, but the effect is the same as in laminar flow and thus hidden phenomenologically. However, in the viscous-diffusive range at scales below the Batchelor length (typically micron scales) the predictions based on deterministic Navier-Stokes equations are drastically altered by thermal noise. Whereas the classical theories predict rapidly decaying spectra in the viscous-diffusive range, either Gaussian or exponential, we obtain a ${k}^{\ensuremath{-}2}$ power-law spectrum over a couple of decades starting just below the Batchelor length. This spectrum corresponds to nonequilibrium giant concentration fluctuations, which are due to the imposed concentration variations being advected by thermal velocity fluctuations and which are experimentally well observed in quiescent fluids. At higher wave numbers, the concentration spectrum instead goes to a ${k}^{2}$ equipartition spectrum due to equilibrium molecular fluctuations. We work out detailed predictions for water-glycerol and water-fluorescein mixtures. Finally, we discuss broad implications for turbulent flows and applications of our methods to experimentally accessible laminar flows.

The Role of Fault Rock Fabric in the Dynamics of Laboratory Faults

AbstractFault stability is inherently linked to the frictional and healing properties of fault rocks and associated fabrics. Their complex interaction controls how the stored elastic energy is dissipated, that is, through creep or seismic motion. In this work, we focus on the relevance of fault fabrics in controlling the reactivation and slip behavior of dolomite‐anhydrite analog faults. We designed a set of laboratory experiments where we first develop fault rocks characterized by different grain size reduction and localization at normal stresses of σN = 15, 35, 60, and 100 MPa and second, we reload and reactivate these fault rocks at the frictional stability transition, achieved at σN = 35 MPa by reducing the machine stiffness. If normal stress is lowered this way, reactivation occurs with relatively large stress drops and large peak‐slip velocities. Subsequent unstable behavior produces slow stick‐slip events with low stress drop and with either asymmetric or Gaussian slip velocity function depending on the inherited fault fabric. If normal stress is raised, deformation is accommodated within angular cataclasites promoting stable slip. The integration of microstructural data (showing brittle reworking of preexisting textures) with mechanical data (documenting restrengthening and dilation upon reactivation) suggests that frictional and chemically assisted healing, which is common in natural faults during the interseismic phase, can be a relevant process in developing large instabilities. We also conclude that fault rock heterogeneity (fault fabric) modulates the slip velocity function and thus the dynamics of repeating stick‐slip cycles.

Experimental study of turbulent bubbly jet. Part 1. Simultaneous measurement of three-dimensional velocity fields of bubbles and water

This study proposes a method for simultaneous measurements of time-resolved three-dimensional velocity fields of the dispersed and continuous phases of a turbulent bubbly jet at a low void fraction using Lagrangian particle tracking (LPT) velocimetry with the Shake-The-Box algorithm. Four high-speed cameras are used to acquire time series of images that include both bubbles and fluid tracer particles. Bubbles are firstly tracked using intensity differences between tracer particles and bubbles, then the bubble images are removed from the camera images and all tracer particles are tracked using the residual images. Subsequently, FlowFit interpolation is applied to the LPT results obtained by phase separation to investigate flow characteristics of a bubbly jet. The bubbly jet was divided into two regions along the vertical direction: jet-like and plume-like regions. Streamwise vortex structures of continuous phase were generated mainly by the rising bubbles. The Gaussian and top-hat velocity profiles matched well with the ensemble-averaged fluid and bubble velocities, respectively. The measured slip velocity in the radial direction was not constant but linearly increased. The classical assumption of self-similarity with Gaussian profiles for fluid velocity and bubble concentration is experimentally verified. The fluid volume flux and entrainment coefficient are obtained as a function of the slip velocity, void fraction, plume and bubble width based on three-dimensional measurements. We found that the classical integral theory agrees well with experiments in the plume region.

Non-Gaussian Generalization of the Kazantsev–Kraichnan Model for a Turbulent Dynamo

Abstract We consider a natural generalization of the Kazantsev–Kraichnan model for a small-scale turbulent dynamo. This generalization takes into account the statistical time asymmetry of a turbulent flow and thus allows one to describe velocity fields with energy cascade. For three-dimensional velocity fields, a generalized Kazantsev equation is derived, and the evolution of the second-order magnetic field correlator is investigated for large but finite magnetic Prandtl numbers. It is shown that as Pr m → ∞, the growth increment tends to the limit known from the T-exponential (Lagrangian deformation) method. Magnetic field generation is shown to be weaker than that in the Gaussian velocity field for any direction of the energy cascade and essentially depends on the Prandtl number.

A quenched local limit theorem for stochastic flows

We consider a particle undergoing Brownian motion in Euclidean space of any dimension, forced by a Gaussian random velocity field that is white in time and smooth in space. We show that conditional on the velocity field, the quenched density of the particle after a long time can be approximated pointwise by the product of a deterministic Gaussian density and a spacetime-stationary random field U. If the velocity field is additionally assumed to be incompressible, then U≡1 almost surely and we obtain a local central limit theorem.

Subdiffusion model for granular discharge in a submerged silo.

Silo discharge has been extensively studied for decades although questions remain regarding the nature of the velocity field, particularly for submerged systems. In this work, fluid-driven granular drainage was performed in a quasi-two-dimensional silo with grains submerged in fluid. While the observed Gaussian velocity profiles were generally consistent with current diffusion models, the diffusion length was found to significantly decrease with height in contrast to the increases previously seen in dry silos. We propose a phenomenological anomalous diffusion model for the spreading of the flow upwards in the cell, with the fluid-driven flows we study here falling in the category of subdiffusive behavior. As the viscous characteristics of the system were amplified, the diffusion length increased and the shape of the flowing zone in the silo changed, deviating further from the parabolic form predicted by traditional normal diffusion models, in effect becoming more subdiffusive as quantified by a decreasing diffusion exponent.