The Frenkel-Kontorova Model

By O. Braun, Yuri Kivshar. 2004

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Statistical physics of fracture, friction, and earthquakes (2011, background): “This transition is called the breaking of analyticity transition or the Aubry transition (Peyrard and Aubry, 1983) (for extensive details see Braun and Kivshar (2004)).”
Colloquium : Phononics: Manipulating heat flow with electronic analogs and beyond (2011, background): “…that mimic solid state systems the FK model has been shown to provide a suitable theoretical description for possible nonlinear phenomena such as the occurrence of commensurate-incommensurate phase transitions (Floria and Mazo, 1996), kink-like structures and alike (Braun and Kivshar, 1998, 2004).”
Quantum simulations with cold trapped ions (2009, methodology): “…density (at the centre of the ion chain), where the average occupation of a lattice site is ( √ 5 + 1)/2 and results in the golden Kolmogorov–Arnol’d–Moser (KAM) curve for the ion positions commonly used for the studies of the Aubry transition (Aubry and Le Daeron 1983, Braun and Kivshar 2004).”
Colloquium: Modeling friction: From nanoscale to mesoscale (2011, methodology): “The basic model describing the sliding of crystalline interfaces is the one-dimensional Frenkel-Kontorova (FK) model; see Braun and Kivshar (2004) and references therein.”