Apr

29

2016

Stress tensors calculated from numerical modeling of biological or physical problems are often, in practice, analyzed through scalar representations of these tensors, i.e., visually displayed as max and min stress values over the problem regions. Even though the stress tensor invariants and principal directions are equally well known, they are less often investigated.

May

02

2016

May

02

2016

Coming soon. This is a joint Colloquium with the Department of Physics at Oregon State University, jointly hosted by Vrushali Bokil and Juan Restrepo from Mathematics, and DavideLazzati and Heidi Schellman from the Department of Physics.

May

03

2016

May

03

2016

We introduce a class of stochastic processes that we call hierarchical branching processes. By construction, the processes satisfy the Tokunaga, and hence Horton, self-similarity constraints. Taking the limit of averaged stochastic dynamics, we obtain the deterministic system of differential equations that describe the temporal dynamics of a Tokunaga branching system. In particular, we study the averaged tree width function to establish a phase transition in the Tokunaga dynamics that separates fading and explosive branching.