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Published 2016 | Submitted
Journal Article Open

Effective behavior of an interface propagating through a periodic elastic medium


We consider a moving interface that is coupled to an elliptic equation in a heterogeneous medium. The problem is motivated by the study of displacive solid-solid phase transformations. We show that a nearly flat interface is given by the graph of the function g which evolves according to the equation g_t(x)=−(−Δ)^(1/2)g(x)+φ(x,g(x))+F. This equation also arises in the study of dislocations and fracture. We show in the periodic setting that such interfaces exhibit a stick-slip behavior associated with pinning and depinning. Further, we present some numerical evidence that the effective velocity of the phase boundary scales as the square-root of the excess macroscopic force above the depinning transition.

Additional Information

© 2016 EMS Publishing House. This work draws from the doctoral thesis of Patrick Dondl at the California Institute of Technology. It is a pleasure to acknowledge discussions with Bogdan Craciun, Nicolas Dirr and Aaron Yip. We gratefully acknowledge the financial support of the National Science Foundation (ACI-0204932, DMS-0311788).

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August 20, 2023
October 20, 2023