Department of Physics PapersCopyright (c) 2017 University of Pennsylvania All rights reserved.
https://repository.upenn.edu/physics_papers
Recent documents in Department of Physics Papersen-usSun, 15 Oct 2017 01:53:22 PDT3600Vanishing Elasticity for Wet Foams: Equivalence With Emulsions and Role of Polydispersity
https://repository.upenn.edu/physics_papers/643
https://repository.upenn.edu/physics_papers/643Fri, 13 Oct 2017 14:37:29 PDT
We present an experimental study of the rheology of polydisperse aqueous foams of different gas volume fractions φ. With oscillatory deformation at fixed frequency, we determine the behavior of the maximum stress as a function of the strain amplitude. At low strain, the maximum stress increases linearly, defining a shear modulus G.G. At progressively higher strains, the response eventually becomes nonlinear, defining the yield strain and the yield stress. While φ decreases toward φc=0.635±0.01,φc=0.635±0.01, GG goes to zero, and the yield stress decreases by many orders of magnitude with a quadratic behavior. The yield strain, which can be extrapolated to 0.18±0.020.18±0.02 at φ=1,φ=1, has a minimum value of 0.045±0.0100.045±0.010 at φc.φc. This behavior shows the occurrence of a melting transition located at φc,φc, which can be correlated to the random close packing of spheres. We compare these results to similar ones obtained previously for monodisperse and polydisperse emulsions. Our new experiments clarify the rheological similarities between emulsions and foams, as well as the role of polydispersity. We find that as long as polydispersity is moderate, it does not play a crucial role in the elastic response of foams and emulsions.
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A. Saint-James et al.Speckle-Visibility Spectroscopy: A Tool to Study Time-Varying Dynamics
https://repository.upenn.edu/physics_papers/642
https://repository.upenn.edu/physics_papers/642Fri, 13 Oct 2017 14:37:25 PDT
We describe a multispeckle dynamic light scattering technique capable of resolving the motion of scattering sites in cases that this motion changes systematically with time. The method is based on the visibility of the speckle pattern formed by the scattered light as detected by a single exposure of a digital camera. Whereas previous multispeckle methods rely on correlations between images, here the connection with scattering site dynamics is made more simply in terms of the variance of intensity among the pixels of the camerafor the specified exposure duration. The essence is that the speckle pattern is more visible, i.e., the variance of detected intensity levels is greater, when the dynamics of the scattering site motion is slow compared to the exposure time of the camera. The theory for analyzing the moments of the spatial intensity distribution in terms of the electric-field autocorrelation is presented. It is tested for two well-understood samples, a colloidal suspension of Brownian particles and a coarsening foam, where the dynamics can be treated as stationary and hence can be benchmarked by traditional methods. However, our speckle-visibility method is particularly appropriate for samples in which the dynamics vary with time, either slowly or rapidly, limited only by the exposure time fidelity of the camera. Potential applications range from soft-glassy materials, to granular avalanches, to flowmetry of living tissue.
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R. Bandyopadhyay et al.Spatially Heterogeneous Dynamics in a Granular System Near Jamming
https://repository.upenn.edu/physics_papers/641
https://repository.upenn.edu/physics_papers/641Fri, 13 Oct 2017 14:37:21 PDT
In supercooled liquids and dense colloidal suspensions, strings of correlated motion represent a dynamical correlation length that grows as the glass transition is approached. Here, we present a granular system driven close to the jamming transition that shares this hallmark dynamical feature. In analogy, it exhibits a dynamical length scale that grows as the jamming transition is approached.
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A. R. Abate et al.Coffee Rings and Coffee Disks: Physics on the Edge
https://repository.upenn.edu/physics_papers/640
https://repository.upenn.edu/physics_papers/640Fri, 13 Oct 2017 14:37:15 PDT
As many a coffee drinker knows, a drying drop of coffee typically leaves behind a ring-shaped stain of small grounds. Though the phenomenon is common, the mechanisms that drive it are rich with physics. As first elucidated by Robert Deegan and colleagues in 1997, the coffee ring results from radially outward fluid flows induced by so-called contact line pinning: The outer edge of a spilled coffee droplet grabs onto rough spots on the solid surface and becomes pinned in place. The evaporating drop thus retains its pinned diameter and flattens while it dries. That flattening, in turn, is accompanied by fluid flowing from the middle of the drop toward its edge to replenish evaporating water. Suspended particles—the coffee grounds—are carried to the edge of the drop by that flow. Once there, they pile up, one at a time, into a tightly jammed packing and produce the coffee ring. Deegan and company studied the ring growth empirically by following the individual frames in a video of plastic colloidal spheres suspended in an evaporating droplet.
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Peter J. Yunker et al.Wetting Phenomena of Binary Liquid Mixtures on Chemically Altered Substrates
https://repository.upenn.edu/physics_papers/639
https://repository.upenn.edu/physics_papers/639Fri, 13 Oct 2017 14:37:11 PDT
We report measurements of the state of wetting of two liquid mixtures at coexistence near their respective critical consolute temperatures. Borosilicate glass capillary tubes were reacted with hexamethyldisilazane to produce substrates of uniform and controlled silylation. Surfaces of low coverage exhibit a series of first-order partial to complete wetting transitions and obey a short-range force scaling relation. Surfaces of high coverage yield surprising results which may be understood as a consequence of long-range forces.
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Douglas J. Durian et al.Continued Exploration of the Wetting Phase Diagram
https://repository.upenn.edu/physics_papers/638
https://repository.upenn.edu/physics_papers/638Fri, 13 Oct 2017 14:37:08 PDT
Measurements are presented of the state of wetting of a binary liquid mixture on heavily silylated glass, which are believed to probe a new region of the wetting phase diagram. We find unusual temperature dependence and the first experimental evidence of a possible "partial drying" transition recently predicted by Ebner and Saam for the case of strong short-range substrate-liquid forces opposed by a weak long-range force.
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Douglas J. Durian et al.Temperature-Driven Motion of a Wetting Layer
https://repository.upenn.edu/physics_papers/637
https://repository.upenn.edu/physics_papers/637Fri, 13 Oct 2017 14:37:03 PDT
The wetting layer formed by a phase-separated binary liquid mixture in contact with a glass substrate is observed to have a large nonequilibrium response in thickness to small temperature perturbations. An independent theoretical and physical picture is developed, which also provides a direct means of measuring the forces responsible for wetting and their effect on the dynamics of diffusion-limited interfacial motion. As an example, the curvature and anharmonicity of the minimum in the effective interface potential are found.
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Douglas J. Durian et al.Capillary Behavior of Binary Liquid Mixtures Near Criticality: Rise and Kinetics
https://repository.upenn.edu/physics_papers/636
https://repository.upenn.edu/physics_papers/636Fri, 13 Oct 2017 14:37:00 PDT
In three different phase-separated binary liquid mixtures we have observed stationary capillary rises in which the meniscus curvature is inconsistent with the sign of the rise. This ‘‘inverted-meniscus’’ configuration occurs within approximately 50 mK of the mixture’s critical temperature and shows no sign of decay after much longer than the characteristic time for relaxation. We also report experiments showing that perturbation of the wetting layer inside the capillary tube can dramatically affect the capillary rise. This motivates three scenarios in which the behavior of the wetting layer foils an equilibrium capillary rise measurement of the contact angle and produces an inverted meniscus.
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Douglas J. Durian et al.Wetting Transitions in a Cylindrical Pore
https://repository.upenn.edu/physics_papers/635
https://repository.upenn.edu/physics_papers/635Fri, 13 Oct 2017 14:36:56 PDT
The wetting behavior of two-phase systems confined inside cylindrical pores is studied theoretically. The confined geometry gives rise to wetting configurations, or microstructures, which have no analog in the well-studied planar case. Many features observed in experiments on binary liquid mixtures in porous media, previously interpreted in terms of random fields, are shown to be consistent with wetting in a confined geometry with no randomness.
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Andrea J. Liu et al.Scaling Behavior in Shaving Cream
https://repository.upenn.edu/physics_papers/634
https://repository.upenn.edu/physics_papers/634Fri, 13 Oct 2017 14:36:52 PDT
The coarsening of a three-dimensional foam is studied with multiple light-scattering techniques. Scaling behavior is observed with the average bubble diameter growing in time as t^{z} where z=0.45±0.05. Changes in the packing conditions during coarsening give rise to a dynamical process that also exhibits temporal scaling. Neighboring bubbles undergo sudden structural rearrangement events at a rate per unit volume that decays as t^{−y }where y=2.0±0.2.
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Douglas J. Durian et al.Scaling of Transient Hydrodynamic Interactions in Concentrated Suspensions
https://repository.upenn.edu/physics_papers/633
https://repository.upenn.edu/physics_papers/633Fri, 13 Oct 2017 14:36:49 PDT
The mean-square displacement 〈Δr^{2}(τ)〉 of particles in concentrated suspensions is measured at times sufficiently short to observe the transient nature of hydrodynamic interactions. For all volume fractions φ, the velocity autocorrelation function decays as a power law R(τ)∼τ^{−3/2}. A remarkable scaling with φ is observed for the time-dependent self-diffusion coefficient D_{s}(τ)=〈Δr^{2}(τ)〉/6τ: If D_{s}(τ) is scaled by its asymptotic value and if time is scaled by a viscous time inversely proportional to the shear viscosity of the suspension, all the data fall onto a single master curve.
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J. X. Zhu et al.Viscous and Elastic Fingering Instabilities in Foam
https://repository.upenn.edu/physics_papers/632
https://repository.upenn.edu/physics_papers/632Fri, 13 Oct 2017 14:36:45 PDT
We investigate pattern formation in the immiscible displacement of foam from a confining geometry. The dominant length scales with the driving pressure gradient as for a Newtonian fluid, but depends surprisingly on the ratio of plate separation to bubble diameter. The pattern morphology exhibits a transition from a jagged, presumably elastic, character to a smooth, viscous character as the shear strain rate rises far above the natural internal relaxation time scale of the foam. These features may result from the two-dimensional nature of the flows and the unusual rheology of foams.
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S. S. Park et al.Influence of Boundary Reflection and Refraction on Diffusive Photon Transport
https://repository.upenn.edu/physics_papers/631
https://repository.upenn.edu/physics_papers/631Fri, 13 Oct 2017 14:36:41 PDT
We report computer simulations which test the accuracy of the diffusion theories used in the analysis of multiple light scattering data. Explicitly including scattering anisotropy and boundary reflections, we find that the predicted probability for transmission through a slab is accurate to 1% if the slab thickness is greater than about 5 transport mean free paths. For strictly isotropic scattering and no boundary reflections, the exact diffusion theory prediction is accurate to this level for all thicknesses. In addition, we predict how the angular distribution of transmitted photons is affected by boundary reflectivity, both with and without refraction. Simulations show that, to a similar extent, corrections to diffusion theory from a more general transport theory are not needed here, either. Our results suggest an experimental means of measuring the so-called extrapolation length ratio which characterizes boundary effects, and thus have important implications for the analysis of static transmission and diffusing-wave spectroscopy data.
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Douglas J. DurianAccuracy of Diffusing-Wave Spectroscopy Theories
https://repository.upenn.edu/physics_papers/630
https://repository.upenn.edu/physics_papers/630Fri, 13 Oct 2017 14:36:38 PDT
Random walk computer simulations are reported for the electric field autocorrelation of photons transmitted through multiple-scattering slabs. The results are used as a benchmark for judging the accuracy of competing theories of diffusing-wave spectroscopy (DWS), and also for distinguishing between errors introduced from the approximation of diffusive photon transport and from the continuum approximation that the total square wave-vector transfer of a transmitted photon is proportional to its path length in the material. An important conclusion is that these errors partially cancel, giving accuracies on the order of a few percent for typical experimental situations. Detailed comparisons are made as a function of optical thickness, boundary reflectivity, as well as scattering anisotropy; guidelines are generated for optimizing the analysis of actual DWS data in terms of the dynamics of individual scattering sites.
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Douglas J. DurianNonlinear Bubble Dynamics in a Slowly Driven Foam
https://repository.upenn.edu/physics_papers/629
https://repository.upenn.edu/physics_papers/629Fri, 13 Oct 2017 14:36:34 PDT
Sudden topological rearrangement of neighboring bubbles in a foam occur during coarsening, and can also be induced by applied forces. Diffusing-wave spectroscopy measurements are presented of such dynamics before, during, and after an imposed shear strain. The rate of rearrangements is proportional to the strain rate, and the shape of the correlation functions shows that they are spatially and temporally uncorrelated. Macroscopic deformation is thus accomplished by a nonlinear microscopic process reminiscent of dynamics in the propagation of earthquake faults or the flow of granular media.
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A. D. Gopal et al.Foam Mechanics at the Bubble Scale
https://repository.upenn.edu/physics_papers/628
https://repository.upenn.edu/physics_papers/628Fri, 13 Oct 2017 14:36:30 PDT
By focusing on entire bubbles rather than films or vertices, a simple model is proposed for the deformation and flow of foam in which dimensionality, polydispersity, and liquid content can easily be varied. Simulation results are presented for the linear elastic properties as a function of bubble volume fraction, showing a melting transition where the static shear modulus vanishes and the relaxation time scale peaks. Results are also presented for shear stress versus strain rate, showing intermittent flow via avalanchelike topological rearrangements and Bingham-plastic behavior.
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Douglas J. DurianAngular Distribution of Diffusely Transmitted Light
https://repository.upenn.edu/physics_papers/627
https://repository.upenn.edu/physics_papers/627Fri, 13 Oct 2017 14:36:25 PDT
The angular dependence of light diffusely transmitted through an opaque medium is shown to depend directly on the reflective nature of the sample boundary, independent of scattering anisotropy. Experimental data are presented for glass frits and for liquid samples, such as colloidal suspensions and aqueous foams, contained in glass cells and placed in either air, water, or glycerin baths. Results compare well with a simple theoretical prediction based on the diffusion approximation and also with random walk simulations. The importance of this work is not only in providing a simple quantitative explanation of a complex transport problem, but in establishing the proper treatment of boundary conditions for diffusion theory analyses of multiple light scattering experiments.
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M. U. Vera et al.Bubble-Scale Model of Foam Mechanics: Melting, Nonlinear Behavior, and Avalanches
https://repository.upenn.edu/physics_papers/626
https://repository.upenn.edu/physics_papers/626Fri, 13 Oct 2017 14:36:20 PDT
By focusing on entire gas bubbles, rather than soap films or vertices, a microscopic model was recently developed for the macroscopic deformation and flow of foam in which dimensionality, energy storage, and dissipation mechanisms, polydispersity, and the gas-liquid ratio all can be varied easily [D. J. Durian, Phys. Rev. Lett. 75, 4780 (1995)]. Here, a more complete account of the model is presented, along with results for linear rheological properties as a function of the latter two important physical parameters. It is shown that the elastic character vanishes with increasing liquid content in a manner that is consistent with rigidity percolation and that is almost independent of polydispersity. As the melting transition is approached, the bubble motion becomes increasingly nonaffine and the relaxation time scale appears to diverge. Results are also presented for nonlinear behavior at large applied stress, and for the sudden avalanchelike rearrangements of bubbles from one tightly packed configuration to another at small applied strain rates. The distribution of released energy is a power law for small events, but exhibits an exponential cutoff independent of system size. This is in accord with multiple light scattering experiments, but not with other simulations predicting self-organized criticality.
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Douglas J. DurianParticle Motions in a Gas-Fluidized Bed of Sand
https://repository.upenn.edu/physics_papers/625
https://repository.upenn.edu/physics_papers/625Fri, 13 Oct 2017 14:36:15 PDT
We report measurements by diffusing-wave spectroscopy of particle motions in a gas-fluidized bed. The homogenous state of the bed known as the uniformly fluidized state is actually a weak solid in which particles are at rest. The only truly fluid state is an inhomogenous mixture of gas bubbles and of liquid regions in which microscopic particle dynamics are shown to be collisional. The motion of macroscopic bubbles is the source of particle motions in the bed. Measurements of mean free paths, collision rates, and velocity fluctuations (the “granular temperature”) show that dissipation occurs nonuniformly in the medium.
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Narayanan Menon et al.Diffusing-Light Spectroscopies Beyond the Diffusion Limit: The Role of Ballistic Transport and Anisotropic Scattering
https://repository.upenn.edu/physics_papers/624
https://repository.upenn.edu/physics_papers/624Fri, 13 Oct 2017 14:36:08 PDT
Diffuse transmission and diffusing-wave spectroscopy (DWS) can be used to probe the structure and dynamics of opaque materials such as colloids, foams, and sand. A crucial step is to model photon transport as a diffusion process. This approach is acceptable for optically thick samples, far into the limit of strong multiple scattering; however, it becomes increasingly inaccurate for thinner samples for several reasons. Here, we correct for two of these defects. By modeling photon propagation by a telegrapher equation with suitable boundary conditions, we can account for the ballistic transport of photons at finite speed between successive scattering events. By introducing a discontinuity in the photon concentration at the source point, and then averaging over a range of penetration depths, we can account for the fact that photons usually scatter anisotropically into the forward direction, rather than being completely randomized at each event. The accuracy of our approach is tested by comparison both with random walk computer simulations and with experiments on specially designed suspensions of polystyrene spheres. We find that our predictions extend the utility of diffuse transmission to slabs of all thicknesses and of DWS to slabs down to about two transport mean free paths.
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P. A. Lemieux et al.Statistics of Shear-Induced Rearrangements in a Two-Dimensional Model Foam
https://repository.upenn.edu/physics_papers/623
https://repository.upenn.edu/physics_papers/623Fri, 13 Oct 2017 14:36:01 PDT
Under steady shear, a foam relaxes stress through intermittent rearrangements of bubbles accompanied by sudden drops in the stored elastic energy. We use a simple model of foam that incorporates both elasticity and dissipation to study the statistics of bubble rearrangements in terms of energy drops, the number of nearest neighbor changes, and the rate of neighbor-switching (T1) events. We do this for a two-dimensional system as a function of system size, shear rate, dissipation mechanism, and gas area fraction. We find that for dry foams, there is a well-defined quasistatic limit at low shear rates where localized rearrangements occur at a constant rate per unit strain, independent of both system size and dissipation mechanism. These results are in good qualitative agreement with experiments on two-dimensional and three-dimensional foams. In contrast, we find for progessively wetter foams that the event size distribution broadens into a power law that is cut off only by system size. This is consistent with criticality at the melting transition.
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Shubha Tewari et al.Instabilities in a Liquid-Fluidized Bed of Gas Bubbles
https://repository.upenn.edu/physics_papers/622
https://repository.upenn.edu/physics_papers/622Fri, 13 Oct 2017 14:35:55 PDT
Gas bubbles in an aqueous foam can be unjammed, or fluidized, by introducing a forced flow of the continuous liquid phase at a sufficiently high rate. We observe that the resulting bubble dynamics are spatially inhomogeneous, exhibiting a sequence of instabilities vs increasing flow rate. First irregular swirls appear, then a single convective roll, and finally a series of stratified convection rolls each with a different average bubble size.
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M. U. Vera et al.From Avalanches to Fluid Flow: A Continuous Picture of Grain Dynamics Down a Heap
https://repository.upenn.edu/physics_papers/621
https://repository.upenn.edu/physics_papers/621Fri, 13 Oct 2017 14:35:51 PDT
Surface flows are excited by steadily adding spherical glass beads to the top of a heap. To simultaneously characterize the fast single-grain dynamics and the much slower collective intermittency of the flow, we extend photon-correlation spectroscopy via fourth-order temporal correlations in the scattered light intensity. We find that microscopic grain dynamics during an avalanche are similar to those in the continuous flow just above the transition. We also find that there is a minimum jamming time, even arbitrarily close to the transition.
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P. A. Lemieux et al.Hysteresis and Packing in Gas-Fluidized Beds
https://repository.upenn.edu/physics_papers/620
https://repository.upenn.edu/physics_papers/620Fri, 13 Oct 2017 14:35:46 PDT
The packing fraction and the pressure drop across gas-fluidized beds of granular media exhibit hysteresis as the gas-flow rate is cycled up and down across the fluidization transition. Presumably this is due to contact forces and transfer of stress to the surrounding walls, and hence should vary nontrivially with the aspect ratio of the sample. Here we present systematic measurements of the variation of hysteresis with particle size and aspect ratio of the sample. Remarkably, the hysteresis scales in a trivial way with these parameters, showing no evidence of long-range effects of the wall. Our measurements also show that the packing fraction becomes 0.590±0.004, independent of particle size and container shape, when the fluidizing flow of gas flow is slowly removed.
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R. Ojha et al.Enhanced Drainage and Coarsening in Aqueous Foams
https://repository.upenn.edu/physics_papers/619
https://repository.upenn.edu/physics_papers/619Fri, 13 Oct 2017 14:35:42 PDT
Experiments are presented elucidating how the evolution of foam microstructure by gas diffusion from high to low pressure bubbles can significantly speed up the rate of gravitational drainage, and vice versa. This includes detailed data on the liquid-fraction dependence of the coarsening rate, and on the liquid-fraction and the bubble-size profiles across a sample. These results can be described by a “coarsening equation” for the increase of bubble growth rate for drier foams. Spatial variation of the average bubble size and liquid fraction can also affect the growth and drainage rates.
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M. U. Vera et al.Effective Temperatures of a Driven System Near Jamming
https://repository.upenn.edu/physics_papers/618
https://repository.upenn.edu/physics_papers/618Fri, 13 Oct 2017 14:35:38 PDT
Fluctuations in a model of a sheared, zero-temperature foam are studied numerically. Five different quantities that independently reduce to the true temperature in an equilibrium thermal system are calculated. One of the quantities is calculated up to an unknown coefficient. The other four quantities have the same value and all five have the same shear-rate dependence. These results imply that statistical mechanics is useful for the system even though it is far from thermal equilibrium.
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Ian K. Ono et al.Low-Speed Impact Craters in Loose Granular Media
https://repository.upenn.edu/physics_papers/617
https://repository.upenn.edu/physics_papers/617Fri, 13 Oct 2017 14:35:34 PDT
We report on craters formed by balls dropped into dry, noncohesive, granular media. By explicit variation of ball density ρ_{b}, diameter D_{b}, and drop height H, the crater diameter is confirmed to scale as the 1/4 power of the energy of the ball at impact: D_{c}∼(ρ_{b}D^{3}_{b}H)^{1/4}. Against expectation, a different scaling law is discovered for the crater depth: d ∼ (ρ^{3/2}_{b}D^{2}_{b}H)^{1/3}. The scaling with properties of the medium is also established. The crater depth has significance for granular mechanics in that it relates to the stopping force on the ball.
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J. S. Uehara et al.Speckle Visibility Spectroscopy and Variable Granular Fluidization
https://repository.upenn.edu/physics_papers/616
https://repository.upenn.edu/physics_papers/616Fri, 13 Oct 2017 14:35:29 PDT
We introduce a dynamic light scattering technique capable of resolving motion that changes systematically, and rapidly, with time. It is based on the visibility of a speckle pattern for a given exposure duration. Applying this to a vibrated layer of glass beads, we measure the granular temperature and its variation with phase in the oscillation cycle. We observe several transitions involving jammed states, where the grains are at rest during some portion of the cycle. We also observe a two-step decay of the temperature on approach to jamming.
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P. K. Dixon et al.Relaxing in Foam
https://repository.upenn.edu/physics_papers/615
https://repository.upenn.edu/physics_papers/615Fri, 13 Oct 2017 14:35:26 PDT
We report how aqueous foams lose their elasticity along two trajectories in the jamming phase diagram. With time, bubbles unjam due to coarsening. Rheology is measured over nearly six (five) decades in frequency (time); surprisingly, it is linear and well behaved at low frequencies. With shear, bubbles also unjam. Rheology is measured by a novel method in which a step strain is superposed on an otherwise steady flow; transient elasticity vanishes at the same strain rate at which successive bubble rearrangements merge together. Thus we connect the macroscopic rheology with the underlying microscopic bubble dynamics.
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A. D. Gopal et al.Projectile-Shape Dependence of Impact Craters in Loose Granular Media
https://repository.upenn.edu/physics_papers/614
https://repository.upenn.edu/physics_papers/614Fri, 13 Oct 2017 14:35:22 PDT
We report on the penetration of cylindrical projectiles dropped from rest into a dry, noncohesive granular medium. The cylinder length, diameter, density, and tip shape are all explicitly varied. For deep penetrations, as compared to the cylinder diameter, the data collapse onto a single scaling law that varies as the 1/3 power of the total drop distance, the 1/2 power of cylinder length, and the 1/6 power of cylinder diameter. For shallow penetrations, the projectile shape plays a crucial role with sharper objects penetrating deeper.
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K. A. NewhallDynamics of Normal and Superfluid Fogs Using Diffusing-Wave Spectroscopy
https://repository.upenn.edu/physics_papers/613
https://repository.upenn.edu/physics_papers/613Fri, 13 Oct 2017 14:35:18 PDT
The dynamics of normal and superfluid fogs are studied using the technique of diffusing-wave spectroscopy. For a water fog generated with a 1.75 MH_{z} piezoelectric driver below the liquid surface, the 7 μm diameter droplets are found to have diffusive dynamics for correlation times long compared to the viscous time. For a fog of 10 μm diameter superfluid helium droplets in helium vapor at 1.5 K the motion appears to be ballistic for correlation times short compared to the viscous time. The velocity correlations between the helium droplets are found to depend on the initial velocity with which the droplets are injected from the helium surface into the fog.
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Heetae Kim et al.Penetration Depth for Shallow Impact Cratering
https://repository.upenn.edu/physics_papers/612
https://repository.upenn.edu/physics_papers/612Fri, 13 Oct 2017 14:35:15 PDT
We present data for the penetration of a variety of spheres, dropped from rest, into a loose noncohesive granular medium. We improve upon earlier work [J. S. Uehara et al., Phys. Rev. Lett. 90, 194301 (2003)] in three regards. First, we explore the behavior vs sphere diameter and density more systematically, by holding one of these parameters constant while varying the other. Second, we prepare the granular medium more reproducibly and, third, we measure the penetration depth more accurately. The new data support the previous conclusion that the penetration depth is proportional to the 1 ∕ 2 power of sphere density, the 2 ∕ 3 power of sphere diameter, and the 1 ∕ 3 power of total drop distance.
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M. A. Ambroso et al.Statistical Characterization of the Forces on Spheres in an Upflow of Air
https://repository.upenn.edu/physics_papers/611
https://repository.upenn.edu/physics_papers/611Fri, 13 Oct 2017 14:35:10 PDT
The dynamics of a sphere fluidized in a nearly levitating upflow of air were previously found to be identical to those of a Brownian particle in a two-dimensional harmonic trap, consistent with a Langevin equation [Ojha et al., Nature (London) 427, 521 (2004)]. The random forcing, the drag, and the trapping potential represent different aspects of the interaction of the sphere with the air flow. In this paper we vary the experimental conditions for a single sphere, and report on how the force terms in the Langevin equation scale with air flow speed, sphere radius, sphere density, and system size. We also report on the effective interaction potential between two spheres in an upflow of air.
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R. Ojha et al.Partition of Energy for Air-Fluidized Grains
https://repository.upenn.edu/physics_papers/610
https://repository.upenn.edu/physics_papers/610Fri, 13 Oct 2017 14:35:07 PDT
The dynamics of one and two identical spheres rolling in a nearly levitating upflow of air obey the Langevin equation and the fluctuation-dissipation relation [Ojha et al. Nature (London) 427, 521 (2004); Phys. Rev. E 71, 016313 (2005)]. To probe the range of validity of this statistical mechanical description, we perturb the original experiments in four ways. First, we break the circular symmetry of the confining potential by using a stadium-shaped trap, and find that the velocity distributions remain circularly symmetric. Second, we fluidize multiple spheres of different density, and find that all have the same effective temperature. Third, we fluidize two spheres of different size, and find that the thermal analogy progressively fails according to the size ratio. Fourth, we fluidize individual grains of aspherical shape, and find that the applicability of statistical mechanics depends on whether or not the grain chatters along its length, in the direction of airflow.
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A. R. Abate et al.Dynamics of Shallow Impact Cratering
https://repository.upenn.edu/physics_papers/609
https://repository.upenn.edu/physics_papers/609Fri, 13 Oct 2017 14:35:02 PDT
We present data for the time dependence of wooden spheres penetrating into a loose noncohesive packing of glass beads. The stopping time is a factor of 3 longer than the time d ∕ v_{0} needed to travel the total penetration distance d at the impact speed v_{0}. The acceleration decreases monotonically throughout the impact. These kinematics are modeled by a position- and velocity-dependent stopping force that is constrained to reproduce prior observations for the scaling of the penetration depth with the total drop distance.
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M. A. Ambroso et al.Abrasion of Flat Rotating Shapes
https://repository.upenn.edu/physics_papers/608
https://repository.upenn.edu/physics_papers/608Fri, 13 Oct 2017 14:34:57 PDT
We report on the erosion of flat linoleum “pebbles” under steady rotation in a slurry of abrasive grit. To quantify shape as a function of time, we develop a general method in which the pebble is photographed from multiple angles with respect to the grid of pixels with a digital camera. This reduces digitization noise and allows the local curvature of the contour to be computed with a controllable degree of uncertainty. Several shape descriptors are then employed to follow the evolution of different initial shapes toward a circle, where abrasion halts. The results are in good quantitative agreement with a simple model, where we propose that points along the contour move radially inward in proportion to the product of the radius and the derivative of radius with respect to angle.
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A. E. Roth et al.Propagating Waves in a Monolayer of Gas-Fluidized Rods
https://repository.upenn.edu/physics_papers/607
https://repository.upenn.edu/physics_papers/607Fri, 13 Oct 2017 14:34:52 PDT
We report on an observation of propagating compression waves in a quasi-two-dimensional monolayer of apolar granular rods fluidized by an upflow of air. The collective wave speed is an order of magnitude faster than the speed of the particles. This gives rise to anomalously large number fluctuations, ΔN~N^{0.72±0.04}, which are greater than ordinary number fluctuations of N^{1/2}. We characterize the waves by calculating the spatiotemporal power spectrum of the density. The position of observed peaks, as a function of frequency ω and wave vector k, yields a linear dispersion relationship in the long-time, long-wavelength limit and a wave speed c=ω/k. Repeating this analysis for systems at different densities and air speeds, we observe a linear increase in the wave speed with increasing packing fraction with almost no dependence on the air flow. We also observe that the parallel and perpendicular root-mean-square speeds of the rods are identical when waves are present, but become different at low packing fractions where there are no waves. Based on this apparent exclusivity, we map out the phase behavior for the existence of waves vs speed anisotropy as a function of density and fluidizing air flow.
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Linda J. DanielsEffect of Hydrogel Particle Additives on Water-Accessible Pore Structure of Sandy Soils: A Custom Pressure Plate Apparatus and Capillary Bundle Model
https://repository.upenn.edu/physics_papers/606
https://repository.upenn.edu/physics_papers/606Fri, 13 Oct 2017 14:34:48 PDT
To probe the effects of hydrogel particle additives on the water-accessible pore structure of sandy soils, we introduce a custom pressure plate method in which the volume of water expelled from a wet granular packing is measured as a function of applied pressure. Using a capillary bundle model, we show that the differential change in retained water per pressure increment is directly related to the cumulative cross-sectional area distribution f (r) of the water-accessible pores with radii less than r. This is validated by measurements of water expelled from a model sandy soil composed of 2-mm-diameter glass beads. In particular, it is found that the expelled water is dramatically dependent on sample height and that analysis using the capillary bundle model gives the same pore size distribution for all samples. The distribution is found to be approximately log normal, and the total cross-sectional area fraction of the accessible pore space is found to be f_{0} = 0.34. We then report on how the pore distribution and total water-accessible area fraction are affected by superabsorbent hydrogel particle additives, uniformly mixed into a fixed-height sample at varying concentrations. Under both fixed volume and free swelling conditions, the total area fraction of water-accessible pore space in a packing decreases exponentially as the gel concentration increases. The size distribution of the pores is significantly modified by the swollen hydrogel particles, such that large pores are clogged while small pores are formed.
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Y. Wei et al.Drag Force Scaling for Penetration Into Granular Media
https://repository.upenn.edu/physics_papers/605
https://repository.upenn.edu/physics_papers/605Fri, 13 Oct 2017 14:34:43 PDT
Impact dynamics is measured for spherical and cylindrical projectiles of many different densities dropped onto a variety non-cohesive granular media. The results are analyzed in terms of the material-dependent scaling of the inertial and frictional drag contributions to the total stopping force. The inertial drag force scales similar to that in fluids, except that it depends on the internal friction coefficient. The frictional drag force scales as the square-root of the density of granular medium and projectile, and hence cannot be explained by the combination of granular hydrostatic pressure and Coulomb friction law. The combined results provide an explanation for the previously observed penetration depth scaling.
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Hiroaki Katsuragi et al.Depth-Dependent Resistance of Granular Media to Vertical Penetration
https://repository.upenn.edu/physics_papers/604
https://repository.upenn.edu/physics_papers/604Fri, 13 Oct 2017 14:34:39 PDT
We measure the quasistatic friction force acting on intruders moving downwards into a granular medium. By utilizing different intruder geometries, we demonstrate that the force acts locally normal to the intruder surface. By altering the hydrostatic loading of grain contacts by a sub-fluidizing airflow through the bed, we demonstrate that the relevant frictional contacts are loaded by gravity rather than by the motion of the intruder itself. Lastly, by measuring the final penetration depth versus airspeed and using an earlier result for inertial drag, we demonstrate that the same quasistatic friction force acts during impact. Altogether this force is set by a friction coefficient, hydrostatic pressure, projectile size and shape, and a dimensionless proportionality constant. The latter is the same in nearly all experiments, and is surprisingly greater than one.
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Theodore A. Brzinski III et al.Importance of Boundary Reflections in the Theory of Diffusive Light Scattering
https://repository.upenn.edu/physics_papers/603
https://repository.upenn.edu/physics_papers/603Fri, 13 Oct 2017 14:34:34 PDT
This PDF file contains the letter “Letter: Importance of boundary reflections in the theory of diffusive light scattering [see 33(12)3849-3852(Dec1994)]” for OE Vol. 34 Issue 11
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Douglas J. DurianBubble Kinetics in a Steady-State Column of Aqueous Foam
https://repository.upenn.edu/physics_papers/602
https://repository.upenn.edu/physics_papers/602Fri, 13 Oct 2017 14:34:30 PDT
We measure the liquid content, the bubble speeds, and the distribution of bubble sizes, in a vertical column of aqueous foam maintained in steady state by continuous bubbling of gas into a surfactant solution. Nearly round bubbles accumulate at the solution/foam interface, and subsequently rise with constant speed. Upon moving up the column, they become larger due to gas diffusion and more polyhedral due to drainage. The size distribution is monodisperse near the bottom and polydisperse near the top, but there is an unexpected range of intermediate heights where it is bidisperse with small bubbles decorating the junctions between larger bubbles. We explain the evolution in both bidisperse and polydisperse regimes, using Laplace pressure differences and taking the liquid fraction profile as a given.
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K. Feitosa et al.Photon Channelling in Foams
https://repository.upenn.edu/physics_papers/601
https://repository.upenn.edu/physics_papers/601Fri, 13 Oct 2017 14:34:25 PDT
We report on the absorption of diffuse photons in aqueous foams by a dye added to the continuous liquid phase. For very wet and for dry foams, the absorption of the diffuse photons equals the absorption length of the liquid divided by the liquid volume fraction. This indicates that the diffuse photons propagate by a random walk, sampling each phase in proportion to its volume. Foams of intermediate wetness, by contrast, absorb photons more strongly than expected. A 2D computer simulation, modeling photons scattering in a foam crystal, also shows enhanced absorption. This encourages us to consider novel transport effects, such as the total internal reflection of photons inside the Plateau borders.
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A. S. Gittings et al.Reply to Comment by S. J. Cox and D. Weaire on "Free Drainage of Aqueous Foams: Container Shape Effects on Capillarity and Vertical Gradients"
https://repository.upenn.edu/physics_papers/600
https://repository.upenn.edu/physics_papers/600Fri, 13 Oct 2017 14:34:20 PDT
Cox and Weaire [1] rightly emphasize that our solution of the drainage equation for the “Eiffel Tower” geometry does not treat the boundary conditions. There should be a no- flow condition at the top, and, after leakage begins, the liquid fraction should be pegged to ε_{c} ≈ 0.36 at the bottom. They then show how approximating the no-flow conditions at the top can improve agreement with numerical solution. But as argued in [2], we maintain that the neglect of capillarity coming from boundary conditions at the bottom dominates, and that this cannot explain our measurements. At short times, capillarity can delay the onset of leakage, and at long times it can counter gravity and retain liquid in the foam indefinitely; in either case, leakage is slower than our approximate solution, contrary to experiment. Therefore, we speculated that the discrepancy arose from neglect of coarsening, whereby the average bubble size increases via gas diffusion from smaller to larger bubbles. This is an important puzzle because, while the drainage equation successfully predicts forced-drainage experiments, it fails dramatically for free-drainage experiments
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A. Saint-Jalmes et al.Free Drainage of Aqueous Foams: Container Shape Effects on Capillarity and Vertical Gradients
https://repository.upenn.edu/physics_papers/599
https://repository.upenn.edu/physics_papers/599Fri, 13 Oct 2017 14:34:16 PDT
The standard drainage equation applies only to foam columns of constant cross-sectional area. Here, we generalize to include the effects of arbitrary container shape and develop an exact solution for an exponential, "Eiffel Tower", sample. This geometry largely eliminates vertical wetness gradients, and hence capillary effects, and should permit a clean test of dissipation mechanisms. Agreement with experiment is not achieved at late times, however, highlighting the importance of both boundary conditions and coarsening.
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A. Saint-Jalmes et al.Effect of Interstitial Fluid on the Fraction of Flow Microstates That Precede Clogging in Granular Hoppers
https://repository.upenn.edu/physics_papers/598
https://repository.upenn.edu/physics_papers/598Fri, 13 Oct 2017 14:34:11 PDT
We report on the nature of flow events for the gravity-driven discharge of glass beads through a hole that is small enough that the hopper is susceptible to clogging. In particular, we measure the average and standard deviation of the distribution of discharged masses as a function of both hole and grain sizes. We do so in air, which is usual, but also with the system entirely submerged under water. This damps the grain dynamics and could be expected to dramatically affect the distribution of the flow events, which are described in prior work as avalanche-like. Though the flow is slower and the events last longer, we find that the average discharge mass is only slightly reduced for submerged grains. Furthermore, we find that the shape of the distribution remains exponential, implying that clogging is still a Poisson process even for immersed grains. Per Thomas and Durian [Phys. Rev. Lett. 114, 178001 (2015)], this allows for an interpretation of the average discharge mass in terms of the fraction of flow microstates that precede, i.e., that effectively cause, a stable clog to form. Since this fraction is barely altered by water, we conclude that the crucial microscopic variables are the grain positions; grain momenta play only a secondary role in destabilizing weak incipient arches. These insights should aid ongoing efforts to understand the susceptibility of granular hoppers to clogging.
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Juha Koivisto et al.Rheology of Sediment Transported by a Laminar Flow
https://repository.upenn.edu/physics_papers/597
https://repository.upenn.edu/physics_papers/597Fri, 13 Oct 2017 14:34:07 PDT
Understanding the dynamics of fluid-driven sediment transport remains challenging, as it occurs at the interface between a granular material and a fluid flow. Boyer, Guazzelli, and Pouliquen [Phys. Rev. Lett.107, 188301 (2011)] proposed a local rheology unifying dense dry-granular and viscous-suspension flows, but it has been validated only for neutrally buoyant particles in a confined and homogeneous system. Here we generalize the Boyer, Guazzelli, and Pouliquen model to account for the weight of a particle by addition of a pressure P_{0} and test the ability of this model to describe sediment transport in an idealized laboratory river. We subject a bed of settling plastic particles to a laminar-shear flow from above, and use refractive-index-matching to track particles' motion and determine local rheology—from the fluid-granular interface to deep in the granular bed. Data from all experiments collapse onto a single curve of friction μ as a function of the viscous number I_{v} over the range 3 × 10^{−5}≤ I_{v }≤ 2, validating the local rheology model. For I_{v }< 3 × 10^{−5}, however, data do not collapse. Instead of undergoing a jamming transition with μ → μ_{s} as expected, particles transition to a creeping regime where we observe a continuous decay of the friction coefficient μ ≤ μ_{s} as I_{v} decreases. The rheology of this creep regime cannot be described by the local model, and more work is needed to determine whether a nonlocal rheology model can be modified to account for our findings.
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Morgane Houssais et al.Intermittency and Velocity Fluctuations in Hopper Flows Prone to Clogging
https://repository.upenn.edu/physics_papers/596
https://repository.upenn.edu/physics_papers/596Fri, 13 Oct 2017 14:34:02 PDT
We study experimentally the dynamics of granular media in a discharging hopper. In such flows, there often appears to be a critical outlet size D_{c} such that the flow never clogs for D > D_{c}. We report on the time-averaged velocity distributions, as well as temporal intermittency in the ensemble-averaged velocity of grains in a viewing window, for both D < D_{c} and D > D_{c}, near and far from the outlet. We characterize the velocity distributions by the standard deviation and the skewness of the distribution of vertical velocities. We propose a measure for intermittency based on the two-sample Kolmogorov-Smirnov D_{KS} statistic for the velocity distributions as a function of time. We find that there is no discontinuity or kink in these various measures as a function of hole size. This result supports the proposition that there is no well-defined D_{c} and that clogging is always possible. Furthermore, the intermittency time scale of the flow is set by the speed of the grains at the hopper exit. This latter finding is consistent with a model of clogging as the independent sampling for stable configurations at the exit with a rate set by the exiting grain speed [C. C. Thomas and D. J. Durian, Phys. Rev. Lett. 114, 178001 (2015)].
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C. C. Thomas et al.Divergence of Voronoi Cell Anisotropy Vector: A Threshold-Free Characterization of Local Structure in Amorphous Materials
https://repository.upenn.edu/physics_papers/595
https://repository.upenn.edu/physics_papers/595Fri, 13 Oct 2017 14:33:58 PDT
Characterizing structural inhomogeneity is an essential step in understanding the mechanical response of amorphous materials. We introduce a threshold-free measure based on the field of vectors pointing from the center of each particle to the centroid of the Voronoi cell in which the particle resides. These vectors tend to point in toward regions of high free volume and away from regions of low free volume, reminiscent of sinks and sources in a vector field. We compute the local divergence of these vectors, where positive values correspond to overpacked regions and negative values identify underpacked regions within the material. Distributions of this divergence are nearly Gaussian with zero mean, allowing for structural characterization using only the moments of the distribution. We explore how the standard deviation and skewness vary with the packing fraction for simulations of bidisperse systems and find a kink in these moments that coincides with the jamming transition.
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Jennifer M. Rieser et al.Fraction of Clogging Configurations Sampled by Granular Hopper Flow
https://repository.upenn.edu/physics_papers/594
https://repository.upenn.edu/physics_papers/594Fri, 13 Oct 2017 14:33:53 PDT
We measure the fraction F of flowing grain configurations that precede a clog, based on the average mass discharged between clogging events for various aperture geometries. By tilting the hopper, we demonstrate that F is a function of the hole area projected in the direction of the exiting grain velocity. By varying the length of slits, we demonstrate that grains clog in the same manner as if they were flowing out of a set of smaller independent circular openings. The collapsed data for F can be fit to a decay that is exponential in hole width raised to the power of the system dimensionality. This is consistent with a simple model in which individual grains near the hole have a large but constant probability to precede a clog. Such a picture implies that there is no sharp clogging transition, and that all hoppers have a nonzero probability to clog.
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C. C. Thomas et al.Deformation-Driven Diffusion and Plastic Flow in Amorphous Granular Pillars
https://repository.upenn.edu/physics_papers/593
https://repository.upenn.edu/physics_papers/593Fri, 13 Oct 2017 14:33:49 PDT
We report a combined experimental and simulation study of deformation-induced diffusion in compacted quasi-two-dimensional amorphous granular pillars, in which thermal fluctuations play a negligible role. The pillars, consisting of bidisperse cylindrical acetal plastic particles standing upright on a substrate, are deformed uniaxially and quasistatically by a rigid bar moving at a constant speed. The plastic flow and particle rearrangements in the pillars are characterized by computing the best-fit affine transformation strain and nonaffine displacement associated with each particle between two stages of deformation. The nonaffine displacement exhibits exponential crossover from ballistic to diffusive behavior with respect to the cumulative deviatoric strain, indicating that in athermal granular packings, the cumulative deviatoric strain plays the role of time in thermal systems and drives effective particle diffusion. We further study the size-dependent deformation of the granular pillars by simulation, and find that different-sized pillars follow self-similar shape evolution during deformation. In addition, the yield stress of the pillars increases linearly with pillar size. Formation of transient shear lines in the pillars during deformation becomes more evident as pillar size increases. The width of these elementary shear bands is about twice the diameter of a particle, and does not vary with pillar size.
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Wenbin Li et al.Identifying Structural Flow Defects in Disordered Solids Using Machine-Learning Methods
https://repository.upenn.edu/physics_papers/592
https://repository.upenn.edu/physics_papers/592Fri, 13 Oct 2017 14:33:43 PDT
We use machine-learning methods on local structure to identify flow defects—or particles susceptible to rearrangement—in jammed and glassy systems. We apply this method successfully to two very different systems: a two-dimensional experimental realization of a granular pillar under compression and a Lennard-Jones glass in both two and three dimensions above and below its glass transition temperature. We also identify characteristics of flow defects that differentiate them from the rest of the sample. Our results show it is possible to discern subtle structural features responsible for heterogeneous dynamics observed across a broad range of disordered materials.
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E. D. Cubuk et al.Penetration Depth Scaling for Impact Into Wet Granular Packings
https://repository.upenn.edu/physics_papers/591
https://repository.upenn.edu/physics_papers/591Fri, 13 Oct 2017 14:33:39 PDT
We present experimental measurements of penetration depths for the impact of spheres into wetted granular media. We observe that the penetration depth in the liquid saturated case scales with projectile density, size, and drop height in a fashion consistent with the scaling observed in the dry case, but with smaller penetrations. Neither viscous drag nor density effects can explain the enhancement to the stopping force. The penetration depth exhibits a complicated dependence on liquid fraction, accompanied by a change in the drop-height dependence, that must be the consequence of accompanying changes in the conformation of the liquid phase in the interstices.
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Theodore A. Brzinski III et al.Kinetics of Gravity-Driven Water Channels Under Steady Rainfall
https://repository.upenn.edu/physics_papers/590
https://repository.upenn.edu/physics_papers/590Fri, 13 Oct 2017 14:33:34 PDT
We investigate the formation of fingered flow in dry granular media under simulated rainfall using a quasi-two-dimensional experimental setup composed of a random close packing of monodisperse glass beads. Using controlled experiments, we analyze the finger instabilities that develop from the wetting front as a function of fundamental granular (particle size) and fluid properties (rainfall, viscosity). These finger instabilities act as precursors for water channels, which serve as outlets for water drainage. We look into the characteristics of the homogeneous wetting front and channel size as well as estimate relevant time scales involved in the instability formation and the velocity of the channel fingertip. We compare our experimental results with that of the well-known prediction developed by Parlange and Hill [D. E. Hill and J. Y. Parlange, Soil Sci. Soc. Am. Proc. 36, 697 (1972)]. This model is based on linear stability analysis of the growth of perturbations arising at the interface between two immiscible fluids. Results show that, in terms of morphology, experiments agree with the proposed model. However, in terms of kinetics we nevertheless account for another term that describes the homogenization of the wetting front. This result shows that the manner we introduce the fluid to a porous medium can also influence the formation of finger instabilities. The results also help us to calculate the ideal flow rate needed for homogeneous distribution of water in the soil and minimization of runoff, given the grain size, fluid density, and fluid viscosity. This could have applications in optimizing use of irrigation water.
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Cesare M. Cejas et al.Morphology of Rain Water Channeling in Systematically Varied Model Sandy Soils
https://repository.upenn.edu/physics_papers/589
https://repository.upenn.edu/physics_papers/589Fri, 13 Oct 2017 14:33:30 PDT
We visualize the formation of fingered flow in dry model sandy soils under different rain conditions using a quasi-2D experimental setup and systematically determine the impact of the soil grain diameter and surface wetting properties on the water channeling phenomenon. The model sandy soils we use are random closely packed glass beads with varied diameters and surface treatments. For hydrophilic sandy soils, our experiments show that rain water infiltrates a shallow top layer of soil and creates a horizontal water wetting front that grows downward homogeneously until instabilities occur to form fingered flows. For hydrophobic sandy soils, in contrast, we observe that rain water ponds on the top of the soil surface until the hydraulic pressure is strong enough to overcome the capillary repellency of soil and create narrow water channels that penetrate the soil packing. Varying the raindrop impinging speed has little influence on water channel formation. However, varying the rain rate causes significant changes in the water infiltration depth, water channel width, and water channel separation. At a fixed rain condition, we combine the effects of the grain diameter and surface hydrophobicity into a single parameter and determine its influence on the water infiltration depth, water channel width, and water channel separation. We also demonstrate the efficiency of several soil water improvement methods that relate to the rain water channeling phenomenon, including prewetting sandy soils at different levels before rainfall, modifying soil surface flatness, and applying superabsorbent hydrogel particles as soil modifiers.
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Yuli Wei et al.Structure and Coarsening at the Surface of a Dry Three-Dimensional Aqueous Foam
https://repository.upenn.edu/physics_papers/588
https://repository.upenn.edu/physics_papers/588Fri, 13 Oct 2017 14:33:26 PDT
We utilize total-internal reflection to isolate the two-dimensional surface foam formed at the planar boundary of a three-dimensional sample. The resulting images of surface Plateau borders are consistent with Plateau's laws for a truly two-dimensional foam. Samples are allowed to coarsen into a self-similar scaling state where statistical distributions appear independent of time, except for an overall scale factor. There we find that statistical measures of side number distributions, size-topology correlations, and bubble shapes are all very similar to those for two-dimensional foams. However, the size number distribution is slightly broader, and the shapes are slightly more elongated. A more obvious difference is that T2 processes now include the creation of surface bubbles, due to rearrangement in the bulk, and von Neumann's law is dramatically violated for individual bubbles. But nevertheless, our most striking finding is that von Neumann's law appears to holds on average, namely, the average rate of area change for surface bubbles appears to be proportional to the number of sides minus six, but with individual bubbles showing a wide distribution of deviations from this average behavior.
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R. E. Roth et al.Granular Discharge Rate for Submerged Hoppers
https://repository.upenn.edu/physics_papers/587
https://repository.upenn.edu/physics_papers/587Fri, 13 Oct 2017 14:33:21 PDT
The discharge of spherical grains from a hole in the bottom of a right circular cylinder is measured with the entire system underwater. We find that the discharge rate depends on filling height, in contrast to the well-known case of dry non-cohesive grains. It is further surprising that the rate increases up to about twenty five percent, as the hopper empties and the granular pressure head decreases. For deep filling, where the discharge rate is constant, we measure the behavior as a function of both grain and hole diameters. The discharge rate scale is set by the product of hole area and the terminal falling speed of isolated grains. But there is a small-hole cutoff of about two and half grain diameters, which is larger than the analogous cutoff in the Beverloo equation for dry grains.
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T. J. Wilson et al.A Model for the Two-Phase Behavior of Fluids in Dilute Porous Media
https://repository.upenn.edu/physics_papers/586
https://repository.upenn.edu/physics_papers/586Fri, 13 Oct 2017 14:33:17 PDT
Experiments show that the coexistence region of a vapor-liquid system or binary liquid mixture is dramatically narrowed when the fluid is confined in a dilute porous medium such as a silica aerogel. We propose a simple model of the gel as a periodic array of cylindrical strands, and study the phase behavior of an Ising system confined in this geometry. Our results suggest that the coexistence region should widen out at lower temperatures, and that the narrowness observed near the critical point may be a fluctuation-induced effect.
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James P. Donley et al.Spin Waves in the Dilute Heisenberg Ferromagnet
https://repository.upenn.edu/physics_papers/585
https://repository.upenn.edu/physics_papers/585Fri, 13 Oct 2017 14:33:14 PDT
The energy of long wave length spin waves in dilute Heisenberg ferromagnets is calculated. It is shown that spin waves can exist only within an infinite cluster of magnetic spins and that such spin waves are mechanically stable. Heuristic arguments based on dimensionality of the infinite cluster imply that there is no thermal instability of the type discussed by Mermin and Wagner. Thus, the critical concentration for ferromagnetism is essentially equal to percolation concentration.
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A. Brooks Harris et al.Randomly Dilute Two Dimensional Ising Models
https://repository.upenn.edu/physics_papers/584
https://repository.upenn.edu/physics_papers/584Fri, 13 Oct 2017 14:33:11 PDT
Calculations of the specific heat and magnetization of quenched, site‐diluted, N×N square and triangular Ising lattices have been carried out by a Monte Carlo method. For spin concentrations x of 0.8 and 0.9, lattices of size N=64 did not give sharp transitions. For a triangular lattice with N=128 and x=0.904, we found a well‐defined peak in the specific heat and an abrupt change in the magnetization at T=0.865 T_{c}(1). Linear interpolation gives s≡d/dx[T_{c}(x)/T_{c}(1)]_{x=1}=1.40±0.05, in excellent agreement with the high temperature series calculations of Rushbrooke et al. For the square lattice we calculate s=1.5±0.1. We also determined site magnetization as a function of the number of ’’live’’ nearest neighbors.
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R. Fisch et al.Static Properties of Dilute Ferri‐ and Antiferromagnets
https://repository.upenn.edu/physics_papers/583
https://repository.upenn.edu/physics_papers/583Fri, 13 Oct 2017 14:33:08 PDT
We report microscopic calculation of the static magnetic and spin‐wave properties of dilute antiferromagnetis (e.g. KMn_{1−x} Zn _{x}F_{3}) and of dilute ferromagnetic garnets. The results are valid at low temperatures but are not restricted to low concentration of dilutents.
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Scott Kirkpatrick et al.Spin‐Waves in Dilute Antiferromagnets
https://repository.upenn.edu/physics_papers/582
https://repository.upenn.edu/physics_papers/582Fri, 13 Oct 2017 14:33:04 PDT
The effect of dilution on spin waves in isotropic Heisenberg antiferromagnets is studied. The model includes only nearest‐neighbor interactions for a bcc lattice and spin‐wave interactions are neglected, i.e. the results are correct in the limit s→∞. The dynamical susceptibility X (?,ω) and inelastic neutron cross section are obtained for arrays 8192 sites randomly occupied by a concentration c of magnetic ions. For a given array the calculation is done by inverting the dynamical matrix and thus is essentially exact. Our results are as follows. For large k we find that Ising‐like resonances corresponding to different numbers of occupied neighboring sites become increasingly prominent as c is decreased. The envelope of these resonances agrees with previous results using the coherent potential approximation where fluctuations in environment are suppressed. For small k we find a single spinwave resonance broadened by the random dilution. The application of these results to Mn_{c} Zn _{1−c}F_{2} is discussed.
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W. K. Holcomb et al.Effect of Randomness on Critical Behavior of Spin Models
https://repository.upenn.edu/physics_papers/581
https://repository.upenn.edu/physics_papers/581Fri, 13 Oct 2017 14:33:01 PDT
Renormalization group methods are used to analyze the critical behavior of random Ising models. The Wilson‐Fischer ε‐expansion for the recursion relations for n‐component continuous spin models are developed for randomly inhomogeneous systems. In addition to the usual variables for a homogeneous system there appears a variable which in essence describes local fluctuations in T_{ c }. From the structure and stability of the fixed points we conclude that critical exponents are unaffected by randomness for n≳4 but are renormalized by randomness for 1<n
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Thomas C. Lubensky et al.Series Study of Random Animals in General Dimensions
https://repository.upenn.edu/physics_papers/580
https://repository.upenn.edu/physics_papers/580Fri, 13 Oct 2017 14:32:58 PDT
We construct general-dimension series for the random animal problem up to 15th order. These represent an improvement of five terms in four dimensions and above and one term in three dimensions. These series are analyzed, together with existing series in two dimensions, and series for the related Yang-Lee edge problem, to obtain accurate estimates of critical parameters, in particular, the correction to scaling exponent. There appears to be excellent agreement between the two models for both dominant and correction exponents.
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Joan Adler et al.Symmetry of Magnetic Structures: The Case of CeAl<sub>2</sub>
https://repository.upenn.edu/physics_papers/579
https://repository.upenn.edu/physics_papers/579Fri, 13 Oct 2017 14:32:55 PDT
This article presents a group-theoretical investigation of an incommensurate magnetic structure in the case where the crystal structure is centrosymmetric while the structure vector k is not conserved by inversion. A first method starts with the conventional group-theoretical treatment taking into account the transformations which conserve k and then combines the solutions to obtain a centrosymmetric and real magnetization. A second method includes inversion in the group-theoretical treatment, for instance by introducing the complex conjugation operator and corepresentations. The general theory is applied to CeAl_{2} with the scope of improving the knowledge of its magnetic structure.
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J. Schweizer et al.