Georgia Institute of Technology College of Sciences

In this seminar we will show that the nonlinear mechanics of solids with distributed dislocations can be formulated as a nonlinear elasticity problem provided that the material manifold – where the body is stress-free − is chosen appropriately. Choosing a Weitzenböck manifold (a manifold with a flat and metric-compatible affine connection that has torsion) with torsion tensor identified with the given dislocation density tensor the body would be stress-free in the material manifold by construction. For classical nonlinear elastic solids in order to calculate stresses one needs to know the changes of the relative distances, i.e. a metric in the material manifold is needed. For distributed dislocations this metric is the metric compatible with the Weitzenböck connection. We will present exact solutions for the residual stress field of several distributed dislocation problems in incompressible nonlinear elastic solids using Cartan's method of moving frames. We will also discuss zero-stress dislocation distributions in nonlinear dislocation mechanics.

A discussion of the paper "Understanding the Errors of SHAPE-Directed RNA Structure Modeling" by Kladwang et al (2011).

Consider a series of n single-server queues each with unlimited waiting space and FIFO discipline. At first the system is empty, then m customers are placed in the first queue. The service times of all the customers at all the queues are iid. We are interested in the exit time of the last customer from the last server and that's when queues meet random matrices and GUEs. If the number of customers is a small fractional power of the number of servers, and as such customers stay within a tube, that's when queues encounter Tracy and Widom. This talk will be self contained and accessible to graduate students.

In large part, the waves that we observe in the open ocean are created by wind blowing over the water. The precise nature of this process occurs has been intensely studied, but is still not understood very well at a mathematically rigorous level. In this talk, we side-step that issue, somewhat, and consider the steady problem. That is, we prove the existence of small-amplitude traveling waves in a two phase air-water system that can be viewed as the eventual product of wind generation. This is joint work with Oliver Buhler and Jalal Shatah.