8 papers · 1 filter
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…
The discrete dislocation dynamics of multiple dislocation loops
Stefania Patrizi, Mary Vaughan
We consider a nonlocal reaction-diffusion equation that physically arises from the classical Peierls-Nabarro model for dislocations in crystalline structures. Our initial configura…
A convergence result for the derivation of front propagation in nonlocal phase field models
Stefania Patrizi, Mary Vaughan
We prove that the mean curvature of a smooth surface in , , arises as the limit of a sequence of functions that are intrinsically related to the difference b…
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…