Breadcrumb
Percolation in elastic media
Supervisor: Isaac Chenchiah
Theme: Materials Science
(With Tanniemola Liverpool)
Percolation theory is concerned with the behaviour of connected clusters in a graph. When the behaviour in question is a mechanical property (such as stiffness or elastic energy density) the theory also provides a model for a variety of physical and biological systems, such as polymer gels and growing soft tissue. In this context, the problem changes from being purely probabilistic to being both combinatorial and mechanical. It becomes particularly interesting when the mechanical elements which comprise the material are small and thus subject to thermal fluctuations.
Then, developing a theoretical description of these materials requires mastering a subtle interplay between probability, statistical mechanics and elasticity. As a result, not much is understood about how the macroscopic properties of such materials depend on the microscopic configurations---this will be the subject of this project.
References:
Kesten, H., What is ... percolation?, Notices of the American Mathematical Society, 53(5), 572–573 (May 2006)
Wyart, M., Nagel, S. R., and Witten, T. A.: Geometric origin of excess low-frequency vibrational modes in weakly-connected amorphous solids, Europhys. Lett., 72(3), 486-492 (2005).