[PAST EVENT] Mathematics Colloquium - Oleksandr Misiats, VCU

November 17, 2023
2pm - 3pm
Jones Hall, Room 302
200 Ukrop Way
Williamsburg, VA 23185Map this location
Access & Features
  • Free food
  • Open to the public
Jones Hall

Title: Patterns in Shape Memory Alloys: Variational Perspective.

In this talk I will describe a class of minimization problems arising in modelling shape memory alloys. I will start with a shape memory material illustration, followed with a simple one dimensional model. Its extensions in 2D and 3D will help us understand the energetic mechanism behind the formation of multiscale patterns in physical experiments. By means of sharp upper and lower bounds, we show that certain experimentally observed structures provide optimal energy scaling law. Despite the fact that the problem is highly nonconvex due to the presence of phase constraints and the singular perturbation, in my talk, I will describe a relaxation method which allows the use of the convex duality technique for the purpose of obtaining a sharp lower bound.


Vladimir Bolotnikov