TY - JOUR
T1 - Dislocation Dynamics in Crystals
T2 - A Macroscopic Theory in a Fractional Laplace Setting
AU - Dipierro, Serena
AU - Palatucci, Giampiero
AU - Valdinoci, Enrico
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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 macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior repulsive potential.
AB - 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 macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior repulsive potential.
UR - http://www.scopus.com/inward/record.url?scp=84930262043&partnerID=8YFLogxK
U2 - 10.1007/s00220-014-2118-6
DO - 10.1007/s00220-014-2118-6
M3 - Article
AN - SCOPUS:84930262043
VL - 333
SP - 1061
EP - 1105
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 2
ER -