Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session E40: Leo Kadanoff Session I |
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Sponsoring Units: GSNP GPC Chair: Sidney Nagel, University of Chicago Room: 343 |
Tuesday, March 15, 2016 8:00AM - 8:12AM |
E40.00001: Droplet formation and neck rupture in granular streams and dense suspensions Heinrich Jaeger When a pendant drop of liquid breaks off, the final stages of neck formation before the singular event of separation are well described by a power law with an exponent that characterizes the liquid. Specifically, a linear decrease of the neck width with time to breakup implies a highly viscous liquid, while sublinear behavior with exponent 2/3 signals the inviscid limit. It therefore has come as a complete surprise that droplet neck formation in dry granular streams as well as concentrated suspensions, both systems with high apparent viscosity, exhibits the same scaling as the inviscid case. I will discuss some of the experimental evidence for this behavior and attempt an explanation that explicitly considers an aspect unique to the presence of the particles: the feedback between the ability of a (nearly) jammed state to deform and the Gaussian curvature introduced by the neck [Preview Abstract] |
Tuesday, March 15, 2016 8:12AM - 8:24AM |
E40.00002: Particle Laden Flows from Theory to Experiment Andrea Bertozzi Leo Kadanoff inspired a generation of collaboration across the boundaries of applied mathematics, theoretical physics, engineering, an experimental physics. His influence is seen in laboratories, classrooms, PhD theses, and even undergraduate research across the world. In this talk I review a body of research at UCLA spanning the past ten years in which we have worked to understand the basic physics of particle laden flow by comparing experiments with mathematical models. The project was inspired by some initial experiments and models developed by A. Hosoi's group at MIT. We derive and analyze systems of conservation laws with rich behavior that includes multiple shocks, rarefactions, and singular shocks - and study these along side laboratory experiments. Our work includes both basic physics problems and industrial applications such as spiral separators used in the mining industry. [Preview Abstract] |
Tuesday, March 15, 2016 8:24AM - 8:36AM |
E40.00003: Surface tension models for particle laden thin films Jeffrey Wong, Li Wang, Andrea Bertozzi We study viscous slurries on an incline, for which particles migrate in a fluid due to a combination of gravity-induced settling and shear-induced migration. The lubrication model for the bulk of the fluid is a hyperbolic system of conservation laws for the film height and particle concentration which exhibits in interesting behavior, including singular shock solutions corresponding to accumulation of particles at the front. The addition of surface tension to the model produces a a capillary ridge that is affected by the particle accumulation and in two dimensions leads to fingering instabilities. We compare this model to experimental results. [Preview Abstract] |
Tuesday, March 15, 2016 8:36AM - 8:48AM |
E40.00004: Plastic flow of polycrystalline materials James Langer Leo Kadanoff had a long interest in fluid flows, especially fingering instabilities. This interest was one example of his insatiable curiosity about simple, fundamentally important, and often multidisciplinary phenomena. Here is an example of another class of such phenomena that I had hoped to show him this year. The experts in polycrystalline solid mechanics have insisted for decades that their central problem -- dislocation-mediated strain hardening -- is intrinsically unsolvable. I think they're wrong. My colleagues and I have made progress recently in theories of both amorphous and polycrystalline plasticity by introducing an effective disorder temperature as a dynamical variable in our equations of motion. In this way, we have been able to describe how the densities of flow defects or dislocations evolve in response to external forcing, and thus to develop theories that promise to become as predictive, and full of surprises, as the laws of fluid flow. [Preview Abstract] |
Tuesday, March 15, 2016 8:48AM - 9:00AM |
E40.00005: Scaling theory of the jamming transition Andrea Liu, Carl Goodrich, James Sethna, Sidney Nagel The concept of jamming was first introduced at the University of Chicago by Sid Nagel and Tom Witten. By now we know that there is a zero-temperature critical jamming transition that marks the onset of rigidity in packings of soft repulsive spheres. In contrast to the perfect fcc crystal state, which is the maximally stable state for such systems, the jammed state is only marginally stable mechanically, and thus represents an opposite extreme to the perfect crystal. This marginal stability gives rise to power law scalings and diverging length scales at the transition. Here I will discuss recent developments that put the jamming transition in the same place that the Ising transition was when Leo Kadanoff introduced the ideas of coarse-graining and rescaling into critical phenomena. [Preview Abstract] |
Tuesday, March 15, 2016 9:00AM - 9:12AM |
E40.00006: Thermal Boundary Layer Equation for Turbulent Rayleigh-B\'{e}nard Convection Emily SC Ching, Olga Shishkina, Susanne Horn, Sebastian Wagner Turbulent Rayleigh-B\'{e}nard convection, consisting of a fluid confined between two horizontal plates, heated from below and cooled from above, is a paradigm system for studying turbulent thermal convection, which is ubiquitous in nature. In turbulent Rayleigh-B\'{e}nard convection, there are viscous boundary layers near all rigid walls and two thermal boundary layers, one above the bottom plate and one below the top plate. The classical Prandtl-Blasius-Pohlhausen theory has often been used to describe the mean velocity and temperature boundary layer profiles but systematic deviations are known to exist. These deviations are due to turbulent fluctuations. In this talk, we report a new thermal boundary layer equation for turbulent Rayleigh-B\'{e}nard convection derived for Prandtl number (Pr) greater than 1, which takes into account the effects of turbulent fluctuations by using the idea of an eddy thermal diffusivity. Solving this equation, we have obtained two analytical mean temperature profiles for Pr $\sim 1$ and Pr $\gg 1$. These two theoretical predictions are shown to be in excellent agreement with the results of our direct numerical simulations for Pr=4.38 (water) and Pr=2547.9 (glycerol). [Preview Abstract] |
Tuesday, March 15, 2016 9:12AM - 9:24AM |
E40.00007: Leo Kadanoff's legacy for turbulent thermal convection Detlef Lohse Rayleigh-Benard (RB) convection — the buoyancy-driven flow of a fluid heated from below and cooled from above — is a classical problem in fluid dynamics. It played a crucial role in the development of stability theory in hydrodynamics (Rayleigh, Chandrasekhar) and had been paradigmatic in pattern formation and in the study of spatial-temporal chaos (Ahlers, Libchaber, and many other). It was Leo Kadanoff and his associates in Chicago who, in the 1980s and 1990s, propagated the RB system as paradigmatic for the {\it physics} of fully developed turbulence and contributed tremendously to today’s understanding of thermally driven turbulence. He and his experimental coworkers (Libchaber et al.) revealed the importance of the thermal plumes and the large-scale wind, and elucidated the interplay between thermal boundary layers and bulk. His scaling analysis laid the basis for our present understanding of turbulent convection, which I will review in this talk, highlighting Leo’s trailblazing contributions. [Preview Abstract] |
Tuesday, March 15, 2016 9:24AM - 9:36AM |
E40.00008: Control and large deformations of marginal disordered structures Arvind Murugan, Matthew Pinson, Elizabeth Chen Designed deformations, such as origami patterns, provide a way to make easily controlled mechanical metamaterials with tailored responses to external forces. We focus on an often overlooked regime of origami - non-linear deformations of large disordered origami patterns with no symmetries. We find that practical questions of control in origami have counterintuitive answers, because of intimate connections to spin glasses and neural networks. For example, 1 degree of freedom origami structures are actually difficult to control about the flat state with a single actuator; the actuator is thrown off by an exponential number of `red herring' zero modes for small deformations, all but one of which disappear at larger deformations. Conversely, structures with multiple programmed motions are much easier to control than expected - in fact, they are as easy to control as a dedicated single-motion structure if the number of programmed motions is below a threshold (`memory capacity'). [Preview Abstract] |
Tuesday, March 15, 2016 9:36AM - 9:48AM |
E40.00009: Planarity of Force Tilings in Jammed Packings of Disks Kabir Ramola, Bulbul Chakraborty We propose a new order parameter for load induced jamming transitions in disk packings based on the planarity of force tilings. Contact forces between disks in mechanical equilibrium can be arranged in a dual space to form a network (tiling) represented by a set of vertices and edges $\mathcal{G} = (V,E)$. A Delaunay triangulation of these vertices then forms a related network $\mathcal{G}_D = (V,E_D)$. We define a planarity order parameter $\psi$ as the overlap of these two graphs $\psi = \langle \mathcal{G}_D| \mathcal{G} \rangle$. We use this parameter to characterize jamming transitions in two dimensional granular systems. We find clear signatures of the existence of non-planar and planar phases as a function of external load. We study this behaviour using simulation data of frictionless soft disks and experimental data of frictional disk packings. [Preview Abstract] |
Tuesday, March 15, 2016 9:48AM - 10:00AM |
E40.00010: Consolidation by lubrication at sedimentary jamming fronts Douglas Durian, Carlos Ortiz, Ted Brzinski We formulate a nonlinear partial differential equation to describe changes in packing fraction for sedimenting particles at low Reynolds number. It is based on two key fluid-mediated forces. One is the viscous interaction of a particle with the surrounding suspension, which causes the settling speed to decrease with increasing packing fraction according to a hindered settling function; we constrain its form by a comprehensive data compilation. The other ingredient is a lubrication force that resists change in separation between neighboring particles; it diverges at contact and hence captures the accumulation of a close-packed sediment. These forces, plus gravity and mass conservation, lead to a new "sedimentation equation" that we propose for the evolution of packing fraction versus position and time. Asymptotic and numerical solutions are presented, and compared with experiment, for the shape of the stationary jamming front between sediment and suspension that moves upwards at constant shape and speed. [Preview Abstract] |
Tuesday, March 15, 2016 10:00AM - 10:12AM |
E40.00011: What are the microscopic origins of shear jamming? Bob Behringer, Dong Wang, Jie Ren, Jonathan Bares, Bulbul Chakraborty, Lenka Kovalcinova, Lou Kondic Granular materials can jam by shear: shear strain applied to a stress-free state in a packing fraction range $\phi_S < \phi <\phi_J$, leads to mechanically stable (jammed) anisotropic states (Bi et al. Nature, 2011). $\phi_J$ is the lowest $\phi$ for which an isotropic state is jammed, and shear jamming ceases below $\phi_S$. The process of shear jamming involves the formation of strong force networks that are initially highly anistropic `force chains', then become become more isotropic with increasing shear. The mechanisms that lead to shear jamming are also presumably similar to those that lead to Reynolds dilatancy. What microscopic processes can account for shear jamming? Force chains, roughly linear sequences of particles experiencing average or above forces are not stable by themselves. Hence, force chain particles must form additional `non-chain' contacts. Here, we propose micro-scale structures and their response to shear that serve as a basis to understand the formation of stable force networks and shear jamming. We identify these structures in experimental and numerical data, and track their response to shear. [Preview Abstract] |
Tuesday, March 15, 2016 10:12AM - 10:24AM |
E40.00012: Itokawa: a case for ballistic segregation Troy Shinbrot, Tapan Sabawula, Theo Siu, Miguel Vivar Lazo, Pinaki Chakraborty Recent photographs of the asteroid Itokawa have revealed strong separation between regions populated almost entirely by small pebbles and other regions consisting only of larger boulders. This size separation has been attributed to the Brazil Nut Effect (BNE), however we point out here that the BNE depends on conditions such as isotropic gravity, parallel sidewalls and periodic vertical shaking that are wholly absent on asteroids. On the other hand, surface areas of boulders and pebbles appear to be comparable on Itokawa, and in this situation it follows that the asteroid must have suffered many orders of magnitude more collisions with pebbles than with boulders. We observe that a pebble will tend to bounce off of a boulder but will sink into a sea of similar pebbles, and so we predict that seas of pebbles must grow on such asteroids. We carry out experiments and simulations to evaluate this and related predictions, and we demonstrate that this new mechanism of segregation based on simple counting of grains can produce the strong separation of sizes reported. [Preview Abstract] |
Tuesday, March 15, 2016 10:24AM - 10:36AM |
E40.00013: A trans-phase granular continuum relation and its use in simulation Ken Kamrin, Sachith Dunatunga, Hesam Askari The ability to model a large granular system as a continuum would offer tremendous benefits in computation time compared to discrete particle methods. However, two infamous problems arise in the pursuit of this vision: (i) the constitutive relation for granular materials is still unclear and hotly debated, and (ii) a model and corresponding numerical method must wear ``many hats'' as, in general circumstances, it must be able to capture and accurately represent the material as it crosses through its collisional, dense-flowing, and solid-like states. Here we present a minimal trans-phase model, merging an elastic response beneath a fictional yield criterion, a mu(I) rheology for liquid-like flow above the static yield criterion, and a disconnection rule to model separation of the grains into a low-temperature gas. We simulate our model with a meshless method (in high strain/mixing cases) and the finite-element method. It is able to match experimental data in many geometries, including collapsing columns, impact on granular beds, draining silos, and granular drag problems. [Preview Abstract] |
Tuesday, March 15, 2016 10:36AM - 10:48AM |
E40.00014: A Hierarchy of Dynamic Equilibria and a View of a Fly's Equilibrium Reflex Z. Jane Wang Understanding structures within a structure is a topic that has fascinated Leo throughout his life, and we are now benefiting from his fundamental insights when we think about living organisms. A living organism is far from statistical equilibrium and it does not have a single critical parameter. Nevertheless, each organism has a hierarchical structure within itself. Recently, asking how often a fly must sense its orientation in order to balance in air has led us to suggest one of the fly's 17 steering muscles, the first basalar muscle, is responsible for maintaining flight stability. Here I suggest that the chain of events associated with flight equilibrium reflex can be viewed as a succession of local linear transformation about a set of dynamic equilibria[1]. Each of the functionally different parts, the sensors, motor neurons, muscles, wing-hinges, flapping wings, and the thorax, operates near its own dynamic equilibrium, often close to the boundary between stability and instability. Locomotion rises as an organism responds to a small perturbation from these equilibria. [1] ZJ Wang, Ann. Rev. Cond. Matter Physics, Vol 7, 2016 [Preview Abstract] |
Tuesday, March 15, 2016 10:48AM - 11:00AM |
E40.00015: The life of vortex knots and the flow of helicity William Irvine What happens if you take a vortex loop - akin to a smoke ring in air - and tie it into a knot or a link? The knottiness (Helicity) of a fluid is a conserved quantity in many idealized situations (such as Euler fluids) offering the potential for fundamental insights into fluid flow. In real fluids, progress has been hindered by lack of accessible experimental systems. I will tell of how to make a vortex knot and link in water, in the wave function of a superfluid (on a computer) and of what happens thence, with an emphasis on universal aspects of the dynamics and the flow of helicity. [Preview Abstract] |
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