PIRE - mathematics, mechanics, materials science

Science at the triple point between
mathematics, mechanics and materials science

Research Areas

Pattern formation from energy minimization

Energy-driven pattern formation is seen in many settings. Examples include microstructures created by coherent phase transitions; folding patterns seen in thin elastic sheets; and dislocation patterns seen in crystal plasticity. In these and other areas, we strive to understand why structures seen in nature are preferred by the relevant variational principles. One recurrent theme is the development of rigorous dimension-reduction techniques, using methods from Gamma-convergence. A second is the development of methods for bounding the minimum energy. Upper bounds is often easy, using the patterns seen in nature. Lower bounds are more difficult, and the search for an ansatz-free lower bound is often the heart of the matter.