The Frenkel-Kontorova Model: Concepts, Methods, and Applications
By O. Braun, Yuri Kivshar. 2004
548 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/e755b0eb57b688bf68665865a4749ee4f650fb5c
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Citations in the corpus
- 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.”
- The role of aperiodic order in science and technology (2006, background): “In the ideal case, when two workpieces with incommensurate lattices are brought in contact, the minimal force required to achieve sliding (known as the static frictional force) vanishes, provided the two substrates are stiff enough [139].”
- Novel effects of strains in graphene and other two dimensional materials (2015, background): “The Frenkel-Kontorova model addresses the first issue, namely to study the ground state of a system where a substrate potential and the elastic energy of a 1D or 2D lattice compete.[13, 14, 34, 51] It exhibits three possible ground state phases, depending on the relative periodicities of the lattice”
- 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): “When the potential is switched on but the perturbation is small, thatis, below the critical perturbation strength, the system is in the so calledsli ing phaseand the chain can oscillate in the lattice and the ion positions follow a Kolmogorov-Arnol’d-Moser curve [Braun & Kivshar 2004].”
- Macroscale superlubricity enabled by graphene nanoscroll formation (2015, background): “Superlubricity has been demonstrated for highly oriented pyrolytic graphite (HOPG) surfaces ( 8 ), as well as for multiwalled carbon nanotubes (MWCNTs), when the conditions for incommen-surate contacts are met in a dry environment ( 9 ).”