Lefschetz Center for Dynamical Systems Seminar
Abstract: Two-dimensional turbulence is characterized by the ceaseless creation of filamentary structures and intense gradients of vorticity and passive scalars. This is the manifestation of the tracer cascade down to small scales and it can be explained in terms of ``chaotic advection'' (Aref 1984): the advection by vortices is responsible of chaotic Lagrangian trajectories of particles which tends to stretch and fold the tracer field. A natural way to study this cascade is to examine the dynamics of the tracer gradient. Earlier results on this topic have shown that the velocity gradient tensor can help to characterize the cascade properties in the physical space (Okubo 1970, Weiss 1981). Recently, it has been shown (Basdevant and Philipovitch 1994, Hua and Klein 1998) that the cascade properties are also determined by the acceleration gradient tensor in two-dimensional turbulence. Here we examine the tracer gradient dynamics taking into account the velocity and acceleration gradient tensors. We show that this dynamics can be explained in terms of the dynamics of the orientation of the tracer gradient with respect to strain axes. We stress the importance of two mechanisms: the competition between strain rate and ``effective'' rotation (i.e. rotation due to both vorticity and strain axes rotation), and the time evolution of the strain rate. Because of these mechanisms the tracer gradients tend to align with directions related to the velocity and acceleration gradient tensors. These results are confirmed by numerical simulations of two-dimensional turbulence and some interpretations are discussed.
Brown University Solid Mechanics Seminar Series
Carnegie-Mellon University, Pittsburgh, Pennsylvania | |
Abstract: This talk discusses the kinematics of geometrically necessary dislocations (GNDs) in finite plasticity and develops a concomitant gradient theory that accounts for GNDs within a thermomechanical framework. The theory is based on classical macroforces; microforces for each slip system consistent with a microforce balance; a mechanical version of the second law that includes, via the microforces, work performed during slip; a rate-dependent constitutive theory that includes dependences on a tensorial measure of geometrically necessary dislocations. The microforce balances are equivalent to nonlocal (pde) yield conditions for the individual slip systems. To make contact with classical dislocation theory, the microstresses are shown to represent counterparts of the Peach-Koehler force on a single dislocation.
Brown University, Division of Biology and Medicine, Center for Statistical Sciences Seminar
*Reception following seminar at 167 Angell Street, 2nd floor conference room. |
Abstract: Many late-onset diseases are caused by what appears to be a combination of a genetic predisposition to disease and environmental factors. The use of existing cohort studies provides an opportunity to infer genetic predisposition to disease on a representative sample of a study population, now that many such studies are gathering genetic information on the participants. One feature to using existing cohorts is that subjects may be censored prior to genetic sampling, and this adds a layer of complexity to the analysis. We develop a statistical framework to infer parameters of a latent variables model for disease onset. The latent variables model describes the role of genetic and modifiable risk factors on the onset ages of multiple diseases, and accounts for the possibility that an individual was censored for reasons related or unrelated to the diseases in question. The framework also allows for missing genetic information, so that subjects censored prior to genetic testing and therefore missing such information may still be included in the analysis. The model is applied to data gathered in the Framingham Heart Study for measuring the effect of different ApoE genotypes on the occurrence of various cardiovascular events.
Stochastic Systems Seminar
Special PDE Seminar
*Please Note Special Day, Time, and Place This Week Only |
Brown Analysis Seminar
Scientific Computing Seminar
Lawrence Livermore National Laboratory | |
Abstract: Adaptive Mesh Refinement (AMR) schemes are generally considered promising because of the ability of the scheme to place grid points or computational degrees of freedom at the location in the flow where the largest truncation errors occur. For a given order, AMR schemes can reduce work. However, when compared to high order non-adaptive methods, traditional 2nd order AMR schemes are computationally more expensive. We give precise estimates of work and restrictions on the size of the small scale grid and show that the requirements on the AMR scheme to be cheaper than a high order scheme are unrealistic for most computational scenarios.
PDE Seminar
Department of Mathematics Colloquium
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