20 citations · 46 across the 9 of their papers we have counts for
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Continuity of the Peierls barrier and robustness of laminations
Blaz Mramor, Bob Rink
We study the Peierls barrier for a broad class of monotone variational problems. These problems arise naturally in solid state physics and from Hamiltonian twist maps. We start wit…
The laminations of a crystal near an anti-continuum limit
Vincent Knibbeler, Blaz Mramor, Bob Rink
The anti-continuum limit of a monotone variational recurrence relation consists of a lattice of uncoupled particles in a periodic background. This limit supports many trivial equil…
On the destruction of minimal foliations
Blaz Mramor, Bob Rink
Monotone variational recurrence relations such as the Frenkel-Kontorova lattice, arise in solid state physics, conservative lattice dynamics and as Hamiltonian twist maps. For such…
Ghost circles in lattice Aubry-Mather theory
Blaz Mramor, Bob Rink
Monotone lattice recurrence relations such as the Frenkel-Kontorova lattice, arise in Hamiltonian lattice mechanics as models for fe?rromagnetism and as discretization of elliptic…
A dichotomy theorem for minimizers of monotone recurrence relations
Blaz Mramor, Bob Rink
Variational monotone recurrence relations arise in solid state physics as generalizations of the Frenkel-Kontorova model for a ferromagnetic crystal. For such problems, Aubry-Mathe…