Cambridge CB2 1PZ
I work with Dr Simon Guest to explore how the symmetries influence the periodic frameworks. The initial inspirations are the exceptions of Clerk Maxwell's rule for rigidity of frameworks. These exceptions are proved to be related to symmetries of their configurations. For crystalline structures, which usually have high order of symmetries, the finite motions are not yet understood. We developed a computational method based on linear algebra to track the finite motion of the frameworks.
Most of my tested frameworks are “locally isostatic” repetitive frameworks - those that, on average, have the same number of constraints as degrees of freedom. This is an area where the basic structural mechanics are not well understood, but are nonetheless of tremendous potential for understanding crystallographic structures such as zeolites, which are important industrial materials, and newer materials such as Metal Organic Frameworks. Understanding finite deformations of these structures is important to understand mysterious properties such as negative thermal expansion coefficients.
Rigidity of frameworks, Symmetry, Motion of crystal frameworks, Exceptions of Maxwell's rule