Mathematics Colloquia and Seminars

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Description

In this talk, we will discuss the mixing and enhanced dissipation phenomena of the transport-diffusion equations. Then we will discuss their applications in flocking and sampling. In a flock of birds, agents tend to align their velocities with those of their neighbors. However, if the range of interaction is local, the birds might eventually lose contact with each other, and the flock's long-time behavior is undetermined. We will show that in a suitable parameter regime, the transport effect in the nonlinear equation can enhance the communication between agents and lead to global flocking. Another application of the enhanced dissipation is about the sampling of a probability distribution. In a recent work by Christie, Feng, Iyer, and Novikov, the authors identify an efficient sampling algorithm that exhibits fast convergence. We will consider a related model and derive some convergence results.