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The last few years have seen dramatic advances in the growth, fabrication and characterization of low-dimensional materials, such as graphene on the one and, and a wide variety of nanostructures on the other, such as those formed from ultrathin films, wires, disks and other ‘dots’. The elements of the nanostructures may be formed either singly or in spatial arrays that can be periodic or otherwise (in one dimension or more) and may involve more than one type of material. Most studies of these artificially engineered materials have been driven by their potential for device applications that involve smaller and smaller physical dimensions and novel utilization of the nanostructuring. In particular, the dynamical properties of these materials are of fundamental interest for the devices that involve high-frequency operation and/or switching.
Phonons
Exchange-dominated magnetic excitations
Dipole-exchange magnetic excitations
Electronic and plasmonic excitations
Polaritons
Mixed excitations
Nonlinear dynamics for nonmagnetic excitations
Nonlinear dynamics for magnetic excitations
Appendix A. Some mathematical topics