Lefschetz Center for Dynamical Systems Seminar
Brown University
Joint Materials/Solid Mechanics Seminar Series
Clark University, Worcester, Massachusetts | |
Granular Matter | |
Abstract: The presence of cohesive forces between particles can have a considerable influence on the stability, flow and segregation properties of granular matter. Although qualitative facts are well known and often exploited in industrial process, a detailed knowledge of the properties even in comparison with non-cohesive granular matter has not yet been attained. In this context, we discuss a series of experiments where cohesion forces are important due to either presence of small amounts of liquid or because particles are magnetized. High resolution digital imaging is used to measure the angle of repose and the extent of segregation of bi-disperse mixtures poured into a quasi-two dimensional silo. We will discuss the effect of particle size, volume fraction, viscosity and surface tension of the liquid. It can be noted that small particles preferentially clump in a bi-disperse mixture and this is observed to lead to subtle effects on the nature of the particle spatial-distribution at certain volume fractions of the liquid. In an attempt to understand the cohesion effects in a model system, we also study the clusters observed when magnetized steel beads are vibrated in a shallow container. We will discuss the formation of chains, rings and more compact clusters as the granular temperature is varied.
Center for Fluid Mechanics Seminar
Abstract: Even though parachutes have been in routine use for over 50 years, there is relatively little known about the flow field around the canopy. Even G.I. Taylor and Von Karman were interested in parachutes and published in this area. The subject can be divided into two regimes: that during the inflation of the canopy, and the other during terminal descent. Both regimes possess complex fluid dynamic phenomena and a better understanding of the key flow features would help with the modeling efforts.
A series of PIV experiments on small-scale parachute canopy models was conducted in a water tunnel to investigate in detail the flow field in the near wake during the inflation phase as well as the steady descent. The near wake is particularly important since the forces and moments experienced by the canopy are due primarily to the flow dynamics in the near wake. Temporal evolution of the vorticity field in the vicinity of the canopy and the integral measures of the wake will be discussed in this talk. It turns out that the rate of increase of fluid impulse in the wake is responsible for a major portion of the shock force experienced by the canopy during the inflation phase.
Brown Analysis Seminar
Applied Mathematics Colloquium
Scientific Computing Seminar
University of Washington Seattle, WA | |
Abstract: Due to its mathematical tractability, two-dimensional (2D) fluid equations are often used by mathematicians as a model for quasi-geostrophic (QG) turbulence in the atmosphere, using Charney's 1971 paper as justification. Superficially, 2D and QG turbulence both satisfy the twin conservation of energy and enstrophy, and are unlike 3D flows, which do not conserve enstrophy. Yet 2D turbulence differs from QG turbulence in fundamental ways, which are not generally known. Here we discuss ingredients missing in 2D turbulence formulations of large-scale atmospheric turbulence. We argue that there is no proof that energy cannot cascade downscale in QG turbulence. Indeed, observational evidence supports a downscale flux of both energy and enstrophy in the mesoscales. We then propose a solution to a puzzle in atmospheric energy spectrum, which remained unsolved in over 30 years.
PDE Seminar
Brown University Center for Statistical Sciences Seminar
The Arts and Sciences Professor of Statistics, Institute of Statistics and Decision Sciences, Duke University *Joint Seminar with Economics | |
Abstract: Often the goal of model selection is to choose a model for future prediction, and it is natural to measure the accuracy of a future prediction by squared error loss. Under the Bayesian approach, it is commonly perceived that the optimal predictive model is the model with highest posterior probability, but this is not necessarily the case. In this talk we show that, for selection from among normal linear models, the optimal predictive model is often the median probability model, which is defined as the model consisting of those variables which have overall posterior probability greater than or equal to 1/2 of being in a model. The median probability model often differs from the highest probability model. Examples include nonparametric regression and ANOVA. Crucial in defining the median probability model is the notion of variable inclusion probabilities, which are also key quantities in multiple comparisons and stochastic search.
Department of Mathematics Colloquium
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