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 give two characterizations, one for the class of generalized Young measures generated
by\, A\, A-free measures and one for the class generated by B B-gradient measures B u B u …

The emergence of long range order at low temperatures in atomistic systems with
continuous symmetry is a fundamental, yet poorly understood phenomenon in physics. To …

This paper focuses on the connections between four stochastic and deterministic models for
the motion of straight screw dislocations. Starting from a description of screw dislocation …

It is shown that in core-radius cutoff regularized simplified elasticity (where the elastic energy
depends quadratically on the full displacement gradient rather than its symmetrized version) …

We consider an interacting particle system with singular interaction, describing the dynamics
of finite numbers of (charged) dislocations in one-dimensional space, including annihilation …

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 …

This paper is devoted to the construction of generalized multiscale Young measures, which
are the extension of Pedregal's multiscale Young measures Trans. Amer. Math. Soc., 358 …