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math.AP2022
Discrete Dislocations Dynamics with annihilation as the limit of the Peierls-Nabarro model in one dimension
Patrick van Meurs, Stefania Patrizi
Plasticity of metals is the emergent phenomenon of many crystal defects (dislocations) which interact and move on microscopic time and length scales. Two of the commonly used model…
math.AP2022
Derivation of the 1-D Groma-Balogh equations from the Peierls-Nabarro model
Stefania Patrizi, Tharathep Sangsawang
We consider a semi-linear integro-differential equation in dimension one associated to the half Laplacian whose solution represents the atom dislocation in a crystal. The equation…