## Speaker:

Gautam Iyer

## Institution:

CMU

## Time:

Monday, June 3, 2019 - 4:00pm to 5:00pm

## Host:

## Location:

RH 306

We study the effective behavior of a Brownian motion in both

one and two dimensional comb like domains. This problem arises in a

variety of physical situations such as transport in tissues, and linear

porous media. We show convergence to a limiting process when both

the spacing between the teeth, and the probability of entering a tooth

vanish at the same rate. This limiting process exhibits an anomalous

diffusive behavior, and can be described as a Brownian motion

time-changed by the local time of an independent sticky Brownian motion.

At the PDE level, this leads to equations that have fractional time

derivatives and are similar to the Bassett differential equation.