Homogenization of the Peierls-Nabarro model for dislocation dynamics and the Orowan's law

Details Homogenization of the Peierls-Nabarro model for dislocation dynamics and the Orowan's law Homogenization of the Peierls-Nabarro model for dislocation dynamics and the Orowan's law

2010-07-17

arxiv.org/abs/1007.2915v1

Mathematics

Analysis of PDEs

43 pages

Scientific paper

This paper is concerned with a result of homogenization of an integro-differential equation describing dislocation dynamics. Our model involves both an anisotropic L\'{e}vy operator of order 1 and a potential depending periodically on $u/\ep$. The limit equation is a non-local Hamilton-Jacobi equation, which is an effective plastic law for densities of dislocations moving in a single slip plane. In dimension 1, we are able to characterize the Hamiltonian of the limit equation close to the origin, recovering a property known in physics as the Orowan's law.

Affiliated with

Also associated with

No associations

Rating

Homogenization of the Peierls-Nabarro model for dislocation dynamics and the Orowan's law does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Homogenization of the Peierls-Nabarro model for dislocation dynamics and the Orowan's law, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homogenization of the Peierls-Nabarro model for dislocation dynamics and the Orowan's law will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-658935