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In contexts such as suspension feeding in marine ecologies there is an interplay between brownian motion of nonmotile particles and their advection by flows from swimming microorganisms. As a laboratory realization, we study passive tracers in suspensions of eukaryotic swimmers, the alga Chlamydomonas reinhardtii. While the cells behave ballistically over short intervals, the tracers behave diffusively, with a time-dependent but self-similar probability distribution function of displacements consisting of a gaussian core and robust exponential tails. We emphasize the role of flagellar beating in creating oscillatory flows that exceed brownian motion far from each swimmer.

All Together Now (Sometimes) Motile cilia and flagella protrude from the surface of many eukaryotic cells. Understanding how cilia and flagella operate is important for understanding ciliated cells in metazoans, the ecology and behavior of motile microorganisms, and the mechanisms of molecular motors and signal transduction. Using very-high-speed video microscopy, Polin et al. (p. 487 ; see the Perspective by Stocker and Durham ) discovered that the biflagellated cells of the single-cell alga Chlamydomonas rheinhartii switch between synchronous beating, which keeps the cells traveling forward, and asynchronous beating, which allows the organisms to make sharp turns. This random progression occurs in the dark and allows cells to diffuse, and it may underpin directional movement toward light in the same way that the run-and-tumble behavior of prokaryotes allows them to move up chemical gradients.

We present three movie clips showing tracer particle motion in oscillatory shear flows created using a Couette flow cell. The volume fraction φ of the sample shown in the movie clips is 0.30; the x (flow) direction is horizontal and the z (axial or

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Library of Congress Cataloging-in-Publication Data Abarbanel, H.D.1. Analysis of observed chaotic data / Henry D.1. Abarbanel. p. cm. -(Institute for nonlinear science) Includes bibliographical references and index.

The particle dynamics and shear forces of granular matter in a Couette geometry are determined experimentally. The normalized tangential velocity V (y) declines strongly with distance y from the moving wall, independent of the shear rate and of the shear dynamics. Local RMS velocity fluctuations δV (y) scale with the local velocity gradient to the power 0.4 ± 0.05. These results agree with a locally Newtonian, continuum model, where the granular medium is assumed to behave as a liquid with a local temperature δV (y) 2 and density dependent viscosity.An important property of granular matter is partial fluidization in response to shear stresses [1]. Stationary granular matter can sustain normal loads and shear stresses, but if a threshold shear stress is exceeded, part of the material starts to flow with properties that appear to differ from those of a Newtonian fluid. Unlike ordinary fluids, granular materials do not exhibit intrinsic thermal motion. Instead, the granular 'temperature', generally defined as the square of RMS velocity fluctuations δV 2 , is created by the flow itself. As a result, the mean flow and RMS fluctuations are related. This fundamental connection has been investigated experimentally [2], but remains poorly understood.The flow of sheared granular materials has been investigated in the steady state in several experiments by shearing material in a Couette cell between a stationary outer cylinder and a rotating inner cylinder [3][4][5]. All experiments indicate that the mean particle velocity parallel to the shear direction V (y) decreases faster than linearly away from the inner cylinder.The velocity profile in three dimensions was determined by Mueth et al. [5]. Measurements were carried out both in the interior of the material using X-ray and NMR techniques, and on the bottom surface of the Couette cell by optical imaging. These measurements showed that the velocity profile on the bottom surface and in the interior are the same. V (y) varies from nearly Gaussian for kidney shaped particles to roughly exponential for spherical particles. Layering of particles is suggested as the cause of this variation.In previous studies in a planar geometry [6], we have found that most of the flow is confined to 5 − 6 layers of particles close to the shear plane. The mean particle velocities during brief slips of the shearing plate decrease roughly exponentially with distance away from the moving plate, consistent with the findings in the Couette geometry.The aim of the present experiment is to understand the relationship between mean velocities, RMS fluctuations and shear forces of a steady state shear flow. We have developed a locally Newtonian, continuum model that describes the granular medium as a liquid with nonuniform temperature and density dependent viscosity. The interplay between mean flow and RMS velocity fluctuations can be understood quantitatively in this context, as we demonstrate.In order to accomplish fluidization independent of shear, we apply an upward airflow at a variable rate throug...

The development and interaction of solitary wave pulses is critical to understanding wavy film flows on an inclined (or vertical) surface. Sufficiently far downstream, the wave structure consists of a generally irregular sequence of solitary waves independent of the conditions at the inlet. The velocity of periodic solitary waves is found to depend on their frequency and amplitude. Larger pulses travel faster; this property, plus a strong inelasticity, causes larger pulses to absorb others during interactions, leaving a nearly flat interface behind. These wave interactions lead to the production of solitary wave trains from periodic small amplitude waves. The spacings between solitary waves can be irregular for several different reasons, including the amplification of ambient noise, and the interaction process itself. On the other hand, this irregularity is suppressed by the addition of periodic forcing.