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Metamaterials characterized by long-range forces introduce a breakthrough in the elastic dynamics. In this study, long-range interactions among particles in an elastic continuum are considered as an effect, for example, of the inclusion of electrical or electromagnetic forces, linking two different worlds: elasticity and electromagnetism. Three universal regimes are revealed and demonstrated in general, depending on the range, intensity and repulsion or attraction nature of the long-range force. Furthermore, the dynamics of populations, traffic models, and social behavior share interesting aspects related to interaction range, extending the reach of this work.

This paper expands a recent proposal by the authors to rederive the Langevin equation for a test particle in a finite-size thermal bath using a perturbation approach that yields a cascade of Langevin-type equations. Such an approach produces a different viewpoint for the fluctuation-dissipation duality by expressing them on similar scales. General properties of energy sharing between the test particle and the bath are outlined, investigating the resonant and nonresonant conditions. © 2016 American Physical Society.

We investigate the interaction of a particle with a finite-size bath represented by a set of independent linear oscillators with frequencies that fall within a finite bandwidth. We discover that when the oscillators have particular frequency distributions, the finite-size bath behaves much as an infinite-size bath exhibiting dissipation properties and thus allowing irreversible energy absorption from a particle immersed in it. We also present a reinterpretation of the Langevin equation using a perturbation approach in which the small parameter represents the inverse of the number of oscillators in the bath, elucidating the relationship between finite-size and infinite-size bath responses. © 2011 American Physical Society.