Diffusion on an expanding interval
The diffusion equation is used to model transport of particles, heat etc. and is usually solved in some fixed geometry e.g. on an interval in 1d, or inside a sphere in 3d. What happens if the domain is not static but changes over time? In this talk I will discuss an example (genetic diversity in a microbial colony) which leads to a particular diffusion equation on an expanding domain with absorbing boundaries, and calculate the probability distribution conditioned on the particle not being absorbed.
This is a roughly weekly series of didactical blackboard talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..