Showing papers by "Sidney R. Nagel published in 1999"

Two fluid drop snap-off problem : experiments and theory

Abstract: We address the dynamics of a drop with viscosity $\ensuremath{\lambda}\ensuremath{\eta}$ breaking up inside another fluid of viscosity $\ensuremath{\eta}$. We track the time evolution of the drop near snap-off in the experiments and then compare with a scaling theory developed for $\ensuremath{\lambda}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$. The theory is in excellent agreement with both the experiments and the previous simulations of Lister and Stone. Finally, we also investigate the $\ensuremath{\lambda}$ dependence of the drop shape and breaking rate, and develop a simple theory for the latter.

Dynamic shear modulus of tricresyl phosphate and squalane

Abstract: We have measured the shear modulus and viscosity of two supercooled liquids: tricresyl phosphate and squalane. In both cases we find that the width of the peak in the imaginary part of the shear modulus narrows as the temperature is lowered toward the glass transition temperature. For tricresyl phosphate, we find no evidence for a decoupling of the viscosity and shear modulus relaxation times from the relaxation times determined by dielectric spectroscopy.

Convection in horizontally vibrated granular material

Abstract: We report observations of convective motion in a container filled with granular material when it is vibrated in the horizontal direction. We find that the roughness of the boundaries and the container dimensions play an important role in determining the shape and number of the convection cells. When the container bottom and lateral walls are rough, the system typically exhibits four counter-rotating rolls stacked in two pairs on top of each other; for very low filling height, it is possible to observe a single row of rolls arranged laterally along the bottom of the container. With smooth walls, on the other hand, we find that the system typically forms only a single pair of counter-rotating convection rolls that originate in the two upper corners of the vibrated material; when the filling height is increased to a level that depends on the container width, we observe a transition to the four-roll state.

Introduction to the focus issue on granular materials

Abstract: In a review paper [H. M. Jaeger, S. R. Nagel, and R. P. Behringer, "Granular solids, liquids and gases," Rev. Mod. Phys. 68, 1259-1273 (1996)] a few years ago, we wrote about granular material as a distinctive form of matter that exhibits behavior rather different from that of ordinary solids, liquids, or gases. We traced this distinction to three characteristic properties. First, the individual particles making up a granular material are typically large so that thermal energy is irrelevant compared to gravitational energy. Consequently, concepts from equilibrium statistical mechanics are often not applicable. Second, the interactions between particles are frictional and can be mobilized to different degrees depending on the preparation history, giving rise to memory effects, i.e., a static pile will remember how it was formed. Third, when particles collide they do so inelastically so that a "gas" of particles will slow down and come to rest in clumps. In the intervening years, the research on granular matter has progressed rapidly and this may be a good time to ask what we have learned since that article was written. In this spirit, the present special issue of the journal Chaos assembles a spectrum of papers discussing recent developments in the field. (c) 1999 American Institute of Physics.

Noise stabilization of self-organized memories.

Abstract: This paper concerns a nonlinear dynamical system with many degrees of freedom which organizes to store memories, in that a configuration-dependent quantity is driven to take on preselected values. In Ref. @1# it is shown that in the absence of noise, the system encodes many memories during a transient period, but in the limit of long times retains no more than two of them. Thus, the purely deterministic system ‘‘learns,’’ and then it ‘‘forgets.’’ We examine the effects of adding noise to this system and demonstrate that certain types of noise can stabilize multiple memories so that they are remembered permanently. This noise stabilization is possible because the memory formation mechanism is fundamentally local, whereas forgetting is governed by the large-scale behavior of the system. Thus, it is possible for certain types of stochastic noise to modify the behavior at long wavelengths without destroying the local nonlinear dynamics which give rise to memory creation. We argue that the type of noise that we have found to stabilize multiple memories is likely to be present in some experiments on charge-density wave ~CDW! conductors such as NbSe3. Thus, our results could explain the experimental observation of multiple apparently permanent memories encoded in individual samples reported in Ref. @1#. Our analytic investigations of the behavior of this system both with and without noise show that insight into the mechanisms underlying memory formation as well as noise stabilization can be obtained by averaging the dynamical equations over intermediate-time periods. We determine analytically the dependence of the memory values on the noise parameters in the limit when a certain parameter k tends to zero. The large-scale behavior of the system follows closely that of a linear diffusion equation; we present analytic bounds on the differences between the evolution of the nonlinear equations and that of the linearized system that are uniform in time and logarithmic in the system size. Some of the analytic results for the system without noise were asserted but not justified in Ref. @1#. The paper is organized as follows. Section II briefly reviews the deterministic version of the model. Sections III and IV present our numerical work demonstrating that noise can stabilize multiple memories. Section V presents our analytic work which enables us to understand why noise can keep memories from being forgotten and also presents an averaging procedure which allows us to obtain analytic insight into the transient memories present in the map without noise in a certain limit. Section VI discusses our main results and possible relevance to CDW experiments. Appendix A demonstrates the uniqueness of the limit obtained by the averaging procedure of Sec. V and also discusses explicitly this limit for the case of multiple memories. Appendix B compares the time evolution of the full nonlinear system with the time evolution of a linearized model and shows that the linearized equations reproduce accurately aspects of the evolution on large scales ~though not the memory formation itself!.

Klopsteg Memorial Lecture (August, 1998): Physics at the breakfast table—or waking up to physics

Abstract: There are many complex phenomena that are so familiar to us that we forget to ask whether or not they are understood. In this lecture, I will discuss several familiar cases of effects that are so ubiquitous that we hardly realize that they defy our normal intuition about why they happen. The examples of poorly understood classical physics that I will choose can all be viewed at a breakfast table. I will mention the long tendrils left behind by honey spooned from one dish to another, the anomalous flow behavior of granular material, and the annoying rings deposited by spilled coffee on a table after the liquid evaporates. These are all nonlinear hydrodynamic phenomena which not only are of technological importance but can also lead the inquisitive into new realms of physics.

Incipient failure in sandpile models

Abstract: Elastoplastic and constitutive equation theories are two approaches based on very different assumptions for creating a continuum theory for the stress distributions in a static sandpile. Both models produce the same surprising prediction that in a two-dimensional granular pile constructed at its angle of repose, the outside wedge will be on the verge of failure. We show how these predictions can be tested experimentally.