Principles for targetted energy transfer between localised vibrational states have been developed and tested numerically.
Discrete breathers have been proved to exist in hardening Fermi-Pasta-Ulam chains and related lattices.
Existence of a globally attracting sliding solution has been proved for overdamped inertial dynamics of tilted Frenkel-Kontorova chains.
Experimental work has been carried out on methyl rotations and proton transfer in molecular crystals.