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math.AP2019
Discrete-to-continuum limits of multi-body systems with bulk and surface long-range interactions
Annika Bach, Andrea Braides, Marco Cicalese
We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence. We consider energy densities that may depend on interact…
math.AP2019
Random finite-difference discretizations of the Ambrosio-Tortorelli functional with optimal mesh size
Annika Bach, Marco Cicalese, Matthias Ruf
We propose and analyze a finite-difference discretization of the Ambrosio-Tortorelli functional. It is known that if the discretization is made with respect to an underlying period…