Brown University
Department of Mathematics
Brown Distinguished Lectures
Brown University
Department of Mathematics
Brown Distinguished Lectures
Brown University
Division of Engineering
Joint Materials/Solid Mechanics Seminar Series
Abstract: Studies of metal plasticity often focus on relations for strength and work hardening. Efforts -- by many researchers -- have contributed to forging a connection between strength, dislocation density and the boundary value problem, in turn advancing notions of internal length scales. In such (mesoscale) models, attention is routinely lent to the strength of obstacles (e.g. forest dislocations, solute atoms, precipitates). Recent focus has turned to the topic of the mobile dislocation density. This task is complicated by the necessity to pose some notion of ensemble velocity and the magnitude of the mobile density.
This presentation will review several examples -- the results of extensive collaboration - where insight into the temporal evolution of the mobile density is essential to understanding the mechanisms of plastic deformation. The examples include application to metals, highlighting effects of the initial microstructure in development of the dislocation forest and spatio-temporal dynamics (the Portevin-LeChatelier effect). Attention will then turn to the creep of ice single crystals in torsion. Ice presents an excellent material for validation of models based on the dynamics of mobile dislocation density: the near viscous response, combined with highly anisotropic behavior, highlights interplay between the mobile dislocation density and development of internal stresses.
Center for Fluid Mechanics
And
The Fluids, Thermal and Chemical Processes Group
Of
The Division Of Engineering
Seminar Series
School of Chemical & Biomolecular Engineering, Georgia Institute of Technology Atlanta, Georgia | |
Abstract: Over the last decade, particle tracking microrheology has matured as a new tool for complex fluids research. The main advantages of microrheology over traditional macroscopic rheometry are: the required sample size is extremely small (< 1 microliter), local viscoelastic properties can be probed with high spatial resolution (~1 10 micrometer), and the sample is not disturbed by moving rheometer parts. I will present a few examples of recent work in my group that highlight how the technique can be exploited to acquire unique information about the dynamics of complex fluids.
First, I will discuss the development of a dialysis cell for studying microstructural rearrangements due to changes in solvent composition. With macroscopic rheometry, it is virtually impossible to change the solvent composition in a sample in a controlled manner during an experiment. By integrating microfluidics and microrheology, we have created a device that enables us to achieve rapid and reversible changes in solvent composition via diffusive mass transport. The microdialysis cell can be used for well-defined experiments with solvent-sensitive materials and I will present results for two such complex fluids: 1) alginate hydrogels, 2) biomimetic self-assembled block-copolypeptide hydrogels.
In another project, we have employed microrheology to monitor the progress of photopolymerization of UV curable acrylate resins and hydrogels. In this case, microrheology enables a detailed study of three-dimensional gelation profiles with a spatial and temporal resolution that is inaccessible to a rheometer. The results of our experiments clearly show the shortcomings of the models that are currently used to predict the outcome of photopolymerization reactions and provide a solid basis for the development and validation of more detailed microscopic photopolymerization models.
Dr. Victor Breedveld is an assistant professor in Chemical & Biomolecular Engineering at the Georgia Institute of Technology. His research focuses on the structure and rheology of complex fluids, with a particular interest in the development and use of novel experimental techniques to elucidate the microstructural dynamics of these materials. In 2006, he received the NSF-CAREER award.
Brown Analysis Seminar
Brown University,
Center for Computational Molecular Biology Seminar
Harvard University, Cambridge, MA | |
Abstract: New sequencing technologies are beginning to transform the very approaches that biologists employ. For geneticists interested in speciation or, as Charles Darwin termed, "that mystery of mysteries", the availability of genomic sequence from closely related species of sequenced model organisms holds great promise. Using 454 sequencing, we have generated a 1.5X coverage of the Drosophila mauritiana genome. D. mauritiana is a sibling species of the genetics workhorse, D. melanogaster, as well as the more closely related species, D. simulans and D. sechellia. The genomes of these species were used to both assemble the D. mauritiana genome and to shed light on its divergence at the molecular level. In addition to the comparative analyses, a number of challenges will be highlighted, including the short and error-prone nature of 454 reads relative to Sanger sequencing reads. We hold that such laboratory-scale genomics provide an emerging entry point to successfully answer outstanding biological questions.
Brown University,
Division of Applied Mathematics,
TRANSATLANTIC SEMINAR
Abstract: After introducing the concept of abstract Volterra Operators, a result about the spectral radius for the linear case is shown which can be used to prove an abstract Gronwall lemma. This lemma in turn is applied to obtain global existence results for nonlinear Volterra equations.
Department of Mathematics Colloquium
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