Mark Bradley

Professor
B.S., University of Toronto, 1979; Ph.D., Stanford University, 1985.

Theory of Disordered Materials

Statistical mechanics gives us a nearly complete understanding of translationally-invariant systems of many particles in equilibrium. Structural disorder can strongly alter the behavior of a material, however, and presents a serious challenge to the theorist since translational symmetry can no longer be exploited. Percolation theory is the simplest, most generic model of a disordered material. We are studying the fractal geometry of the clusters in percolation using large-scale numerical simulations. We have also developed exact mappings of percolation onto other problems in statistical physics. These mappings are useful if the equivalent problem can be exactly solved. A second major challenge to theorists is to develop an understanding of the behavior of statistical systems driven far from equilibrium, and my group has an on-going effort in this area. We are currently studying the behavior of a system that is both structurally disordered and far from equilibrium. Our model describes the damage done to metal thin films by electromigration, an important cause of integrated circuit failure. In addition to performing simulations, we have made substantial progress analytically on our model. We are also studying granular materials. These are a special type of disordered material formed by packing many small, micron-sized particles into a container, and then fusing the particles together through the application of heat and pressure. There is an enormous variety of granular materials, ranging from ceramics to sandstones. For many years, packings of identical spheres have been studied as a model of granular materials. Real granular materials are composed of particles with a variety of shapes and sizes, however. We were the first to study the effects of grain shape on the structure of granular materials. Our simulations show that grain asphericity is extremely important, and that it leads to a new type of orientational order. We are currently simulating the convective flows that occur when a container full of particles is shaken up and down.