7 papers
Bond failure in peridynamics: Nonequivalence of critical stretch and critical energy density criteria
Pablo Seleson, Pablo Raúl Stinga, Mary Vaughan
This paper rigorously analyzes bond failure in the peridynamic theory of solid mechanics, which is a fundamental component of fracture modeling. We compare analytically and numeric…
Weighted nonlocal area functionals without the triangle inequality
Serena Dipierro, Enrico Valdinoci, Mary Vaughan
We consider a weighted nonlocal area functional in which the coefficients do not satisfy the triangle inequality. In the context of three phase transitions, this means that one of…
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…
Continuous symmetrizations and uniqueness of solutions to nonlocal equations
Matias G. Delgadino, M. Vaughan
We show that nonlocal seminorms are strictly decreasing under the continuous Steiner rearrangement. This implies that all solutions to nonlocal equations which arise as critical po…