Lattice Models of Phase Transitions in Crystalline Solids

Vainchtein's research program seeks to advance the understanding of the dynamics of phase transitions in crystalline solids from the perspective of mesoscopic and microscopic frameworks. It focuses on a series of prototypical lattice models of increasing complexity with the ultimate goal of developing a quasicontinuum theory that captures the essential features of phase nucleation, interface kinetics, and the associated energy dissipation. The mathematical problems can often be reduced to quasilinear advance-delay differential-difference equations with bi-stable nonlinearity.

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