28 citations · 41 across the 12 of their papers we have counts for
16 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…
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…
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…
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…
Heteroclinic connections for nonlocal equations
Serena Dipierro, Stefania Patrizi, Enrico Valdinoci
We construct heteroclinic orbits for a strongly nonlocal integro-differential equation. Since the energy associated to the equation is infinite in such strongly nonlocal regime, th…
Homogenization and Orowan's law for anisotropic fractional operators of any order
Stefania Patrizi, Enrico Valdinoci
We consider an anisotropic Lévy operator of any order and we consider the homogenization properties of an evolution equation. The scaling properties and…
Long-time behavior for crystal dislocation dynamics
Stefania Patrizi, Enrico Valdinoci
We describe the asymptotic states for the solutions of a nonlocal equation of evolutionary type, which have the physical meaning of the atom dislocation function in a periodic crys…
Chaotic orbits for systems of nonlocal equations
Serena Dipierro, Stefania Patrizi, Enrico Valdinoci
We consider a system of nonlocal equations driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed…
Relaxation times for atom dislocations in crystals
Stefania Patrizi, Enrico Valdinoci
We study the relaxation times for a parabolic differential equation whose solution represents the atom dislocation in a crystal. The equation that we consider comprises the classic…
Crystal dislocations with different orientations and collisions
Stefania Patrizi, Enrico Valdinoci
We study a parabolic differential equation whose solution represents the atom dislocation in a crystal for a general type of Peierls-Nabarro model with possibly long range interact…
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…
Homogenization of the Peierls-Nabarro model for dislocation dynamics
Régis Monneau, Stefania Patrizi
This paper is concerned with a result of homogenization of an integro-differential equation describing dislocation dynamics. Our model involves both an anisotropic Lévy operator of…