Recently the authors proposed a model and related analysis on waves in long-range metamaterials. Nonlocal elasticity can be produced by several interacting forces acting between particles at long distance, as Coulomb or magnetic-static forces. The chance of introducing this long-distance forces has a disruptive effect in the elastic dynamics. In fact, classical elasticity is based only upon closest particles interaction in which short range-elastic forces act.
Nonlocal long -range effects are at the base of new phenomena investigated by the authors. In one dimensional systems, this permits the chance of modifying the phase and group velocity of the waveguide, even producing waves transporting energy backwards. In the two-dimensional case a richer scenario is opened. This paper investigates the chance of transporting the energy over a two-dimensional domain through vibrations that can follow a given path. The relationship between the path and the connection template is investigated.
This paper investigates new phenomena in elastic wave propagation in metamaterials, characterised
by long-range interactions. The kind of waves borne in this context unveil wave-stopping,
negative group velocity, instability and hypersonic or superluminal effects, both for instantaneous
and for nonlocal retarded actions. Closed form results are presented and a universal propagation
map synthesizes the expected properties of these materials. Perspectives in physics, engineering and
social dynamics are discussed.
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