# Brownian motion and the diffusion equation

#### Brownian motion and the diffusion equation

- Event time: 1:00pm
- Event date: 19th February 2001
- Speaker: Matthias Fuchs (University of Edinburgh)
- Location: Room 2511, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB

### Event details

For long times, the mean squared displacement of a single colloidal particle increases linearly in time as expected for a random walk. According to a text-book problem, the correction to this behaviour for long times decays very slowly only and follows a power-law. As the diffusion equation can be used to argue the existence of this anomaly, called ''long time tail'', it appears fruitful to search some more of its solutions for similar long time anomalies. A simple example is given by Brownian particles.

References:[1] Landau Lifshitz, ''Hydrodynamics'', 24, problem 5

Btw: There will be one equation (and some solutions of it) in the talk: the diffusion equation. The solutions could be called modes, but they will not be coupled.

### About Condensed Matter lunchtime seminars

This is a weekly series of informal talks given primarily by members of the soft condensed matter and statistical mechanics groups, but is also open to members of other groups and external visitors. The aim of the series is to promote discussion and learning of various topics at a level suitable to the broad background of the group. Everyone is welcome to attend..