Organizers: Eitan Tadmor
When: See schedule below
Where: CSIC 4122

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  • How Grain Boundaries Move

    Speaker: Prof. David Srolovitz (Department of Materials Science and Engineering, University of Pennsylvania) -

    When: Wed, September 6, 2017 - 2:00pm
    Where: CSIC 4122

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    Abstract: Grain boundaries are interfaces across which crystal orientation changes. Traditional analysis suggest that grain boundary migration is effectively motion by mean curvature. However, this view is not in accordance with what we now know as the structure of grain boundaries on an atomic level. Just as surfaces of crystals move and roughen through the dynamics of surface steps, grain boundary dynamics is controlled by the motion of line defects known as disconnections. Unlike surface steps, disconnections are sources of long range stress (i.e., they have both dislocation and step character). In this talk, I will present an approach for understanding the motion of grain boundaries via disconnection motion and the relationship between disconnections and the underlying crystal structure. Next, I will discuss the homogenization of this type of disconnection-driven motion to yield a crystal-structure specific grain boundary equation of motion. I will then show several atomistic and numerical examples of “tame" GB motion (i.e., in bicyrstals) and GB motion “in the wild” (within polycrystals). This is very much a work in progress so I will also outline approaches for generalizations to general interface controlled microstructure evolution.
  • Spreading in a kinetic reaction-transport equation for population dynamics

    Speaker: Dr. Nils Caillerie (Department of Mathematics and Statistics, Georgetown University) -

    When: Wed, September 20, 2017 - 2:00pm
    Where: CSIC 4122

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    Abstract: In this talk, we will focus on a kinetic equation modeling the spatial dynamics of a set of particles subject to intra-specific competition. This equation is motivated by the study of the propagation of biological populations, such as the Escherichia coli bacterium or the cane toad Rhinella marina, for which the classical diffusion approximation underestimates the actual range expansion of the species. We will use the optics geometrics approach as well as Hamilton-Jacobi equations to study spreading results for this equation. As we will see, the multi-dimensional case engenders technical difficulties, and possible over-representation of fast individuals at the edge of the front.