Self-avoiding random walks on a lattice

Supervisor: Dr Daniel Read

Email: d.j.read@leeds.ac.uk

Phone: +44 (0)113 3435124

Office: 8.19j

Polymers are long chain molecules made by joining together many (thousands or more) similar chemical units. The simplest model for the shape of a polymer is a random walk, in which each step along the chain chooses a direction independently of all the others. Isolated chains in a good solvent execute "self-avoiding random walks", which is a random walk that does not cross itself. This self-avoidance leads to different scaling of the size of the chain as a function of the number of chamical units in the chain.

One of the simplest ways of modelling the shapes of a polymer molecule is to simulate a random walk on a regular lattice (i.e. each unit is placed at a lattice point rather than at some continuous position in space). Both simple random walks and self-avoiding walks can be simulated in this way. The aim of this project is to write and use some simple computer code to simulate self-avoiding random walks on a lattice. How far we get will depend on prior programming experience (which will be taken into account!).

Books

Rubinstein, M.; Colby, R.H.: Polymer Physics Oxford Univ. Press, 2003

Vanderzande, C.: Lattice models of polymers Cambridge Univ. Press, 1998

Home page

Branched polymers in all shapes and sizes