We consider an evolution equation arising in the Peierls–Nabarro model for crystal
dislocation. We study the evolution of such a dislocation function and show that, at a …

Numerical simulations of crystal defects are necessarily restricted to finite computational
domains, supplying artificial boundary conditions that emulate the effect of embedding the …

This paper deals with the limit cases for s-fractional heat flows in a cylindrical domain, with
homogeneous Dirichlet boundary conditions, as s→ 0+ and s→ 1−. We describe the …

We prove that the classical line-tension approximation for dislocations in crystals, that is, the
approximation that neglects interactions at a distance between dislocation segments and …

In this paper we derive a line tension model for dislocations in 3D starting from a
geometrically nonlinear elastic energy with quadratic growth. In the asymptotic analysis, as …

We propose a discrete lattice model of the energy of dislocations in three-dimensional
crystals which properly accounts for lattice symmetry and geometry, arbitrary harmonic …

In this paper, a strain-gradient plasticity model is derived from a mesoscopic model for
straight parallel edge dislocations in an infinite cylindrical crystal. The main difference to …

We study variational models for dislocations in three dimensions in the line-tension scaling.
We present a unified approach which allows to treat energies with subquadratic growth at …

We consider a one-dimensional discrete particle system of two species coupled through
nonlocal interactions driven by the Newtonian potential, with repulsive self-interaction and …

In this paper we rigorously investigate the emergence of defects on Nematic Shells with a
genus different from one. This phenomenon is related to a non-trivial interplay between the …