Wednesday, March 19, 2014 at 3:00 PM in SAS 4201
Daniel Balague, NC State Mathematics
Stability Analysis of Rings for 2nd Order Models in Swarming
In this work we consider second order models in swarming in which individuals interact pairwise with a power-law repulsive-attractive potential. We study the stability for flock and mill ring solutions and we show how the stability of these solutions is related to the stability of a first order model. In unstable situations it is also possible to observe formation of clusters and fat rings.
Wednesday, March 26, 2014 at 3:00 PM in SAS 4201
Jesus Rosado, UCLA
Effects of emotion in swarming dynamics
We will extend classic swarming models to describe the
influence of emotional contagion between the individuals of the group. Well study them at three different scales: microscopic, kinetic and macroscopic, and see how the study of the continuum limit helps us understand key features of the model.
Wednesday, April 9, 2014 at 3:00 AM in SAS 4201
Andrew Cooper, NC State
Singularities of the Mean Curvature Flow
The mean curvature flow of submanifolds is the downward gradient flow for the area functional. Though it is gradient, the flow is nonlinear, so finite-time singularities are expected. In this talk well introduce some basics of the mean curvature flow and give a characterization of what goes wrong to cause the singularity, by using the interplay between two different rescaling analyses. Well also show some examples where these two singularity models can give enough information to allow singularity resolution.
Wednesday, April 16, 2014 at 3:00 AM in SAS 4201
Matthias Eller, Georgetown University
The shape derivative of boundary value problems
In the context of shape optimization the shape derivative is of fundamental importance. If the region in space or space-time underlying the boundary value problem (BVP) is allowed to vary in direction of a given vector field, one can compute the derivative of the solution to the BVP in direction of this vector field. The shape derivative for a wide class of BVPs for linear partial differential equations can be characterized as a solution of another BVP with a non-traditional boundary condition. Scalar equations and systems of equations will be considered and issues of regularity will be discussed.
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