6 papers
Slow Patterns in Multilayer Dislocation Evolution with Dynamic Boundary Conditions
Yuan Gao, Stefania Patrizi
In this paper, we study the slow patterns of multilayer dislocation dynamics modeled by a multiscale parabolic equation in the half-plane coupled with a dynamic boundary condition…
Asymptotic expansion of a nonlocal phase transition energy
Serena Dipierro, Stefania Patrizi, Enrico Valdinoci +1
We study the asymptotic behavior of the fractional Allen--Cahn energy functional in bounded domains with prescribed Dirichlet boundary conditions. When the fractional power $s \in…
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…
A fractional glance to the theory of edge dislocations
Serena Dipierro, Stefania Patrizi, Enrico Valdinoci
We revisit some recents results inspired by the Peierls-Nabarro model on edge dislocations for crystals which rely on the fractional Laplace representation of the corresponding equ…
From the Peierls-Nabarro model to the equation of motion of the dislocation continuum
Stefania Patrizi, Tharathep Sangsawang
We consider a semi-linear integro-differential equation in dimension one associated to the half Laplacian %This model describes the evolution of phase transitions associated to dis…
Derivation of Orowan's law from the Peierls-Nabarro model
Régis Monneau, Stefania Patrizi
In this paper we consider the time dependent Peierls-Nabarro model in dimension one. This model is a semi-linear integro-differential equation associated to the half Laplacian. Thi…