4 papers · 1 filter
A threshold for higher-order asymptotic development of genuinely nonlocal phase transition energies
Serena Dipierro, Enrico Valdinoci, Mary Vaughan
We study the higher-order asymptotic development of a nonlocal phase transition energy in bounded domains and with prescribed external boundary conditions. The energy under conside…
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…