Theodore Kolokolnikov

Non-locality with respect to nonlocal interactions and nonlocal equations is a common theme in many recent pure and applied mathematical works. It has attracted attention from all branches of mathematics, including applied math, math biology...

Aggregation is an ubiquitous natural phenomenon that pervades both the animal world and many inanimate physical systems. In the animal kingdom, group formation is observed across all levels from bacterial colonies and insect swarms to complex...

Aggregation is an ubiquitous natural phenomenon that pervades both the animal world and many inanimate physical systems. In the animal kingdom, group formation is observed across all levels from bacterial colonies and insect swarms to complex...

We study pattern formation in a model of cyanobacteria motion recently proposed by Galante, Wisen Bhaya and Levy. By taking a continuum limit of their model, we derive a novel fourth-order nonlinear parabolic PDE. Using this PDE, we derive the...

Agent-based models are widely used in numerous applications. They have an advantage of being easy to formulate and to implement on a computer. On the other hand, to get any mathematical insight (motivated by, but going beyond computer simulations)...