Here you can find my current CV (PDF file) and my math genealogy.
Research Interests: I am generally interested in mathematical modeling of nonlinear phenomena in materials. In particular, I study a class of "smart" materials called shape memory alloys. When these materials are subjected to cyclic mechanical loading, they undergo a solid-solid phase transition which leads to hysteresis. This feature has many important applications, such as damage and vibration control in composite structures. To better understand the origin of hysteresis and the associated dynamics of phase boundaries, I employ physically motivated nonlinear models. The resulting mathematical problems typically involve minimization of nonconvex functionals and nonlinear PDEs that change type. Thus nonstandard analytical and numerical techniques are required. The main goal is to develop a model capable of capturing the most significant experimental observations, such as size and features of hysteresis loops, evolution of microstructure and details of interface dynamics. Recently I have been studying discrete models of martensitic phase transitions, in an attempt to understand the origin of energy dissipation observed at the macrolevel from the underlying micromodel. Other topics of interest are brittle fracture and adhesion.
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