Crystals without periodicity are commonly found, but they are less known than periodic crystals. They share many properties with each other, but the behaviour of electrons and phonons in aperiodic crystals has a richer structure.

In particular, there is a typical dynamic behaviour associated to the fact that these materials may be seen as periodic structures in a higher-dimensional space. The additional dimensions make it possible to find extra hydrodynamic modes under certain conditions. These modes have a low frequency. The question will be discussed whether these low frequency modes remain when the amplitudes become large.

Under certain conditions, to be discussed here, low frequency or low friction modes are still present. These waves are a type of solitary waves. Their properties will be discussed for a number of classes of aperiodic crystals. It makes it possible to obtain unlubricated almost frictionless motion.