Anomalous sound attenuation in Voronoi liquid

Abstract

The physics of simple fluids in the hydrodynamic limit and notably the connection between the proper microscopic scales and the macroscopic hydrodynamical description are nowadays well understood. In particular, the three peak shape of the dynamical structure factor S(k,ω) is a universal feature, as well as the k-dependence of the peak position (∝k) and width ∝k, the latter accounting for the sound attenuation rate. In this paper, we present a theoretical model of monodisperse fluid, whose interactions are defined via the Voronoi tessellations of the configurations [called the Voronoi liquid and first studied in Ruscher et al., Europhys. Lett. 112, 66003 (2015)], which displays at low temperatures a marked violation of the universal features of S(k,ω) with a sound attenuation rate only ∝k. This anomalous behaviour, which apparently violates the basic symmetries of the liquid state, is traced back to the existence of a time scale which is both short enough for the viscoelastic features of the liquid to impact the relaxational dynamics and however long enough for the momentum diffusion to be substantially slower than the sound propagation on that characteristic time.

Voronoi glass-forming liquids: A structural study

“…This decomposition of the total force F i as a sum of pair terms F j→i verifies the properties expected from such a decomposition : one has F j→i parallel to r ij and F j→i = −F i→j by a simple verification (the term proportional to R 2 − R 2 i , absent in the monodisperse system [5], is required here to ensure the latter antisymmetry). In other words, this pair force decomposition complies with the so-called strong third Newton law (the law of action-reaction with F j→i parallel to r ij ).…”

“…In future work, we will study the dynamics of this model, with a particular emphasis on the glass transition scenario. We have shown in [5] that the dynamical properties of the Voronoi liquid could be quite different from that of ordinary liquids. It is interesting to see to what extent deviations with respect to the "usual" behaviour could also show up in the binary Voronoi liquid.…”

“…where z ij = r ij · e z − L z [(r ij · e z )/L z ] is the z component of the vector r ij compliant with the minimum image convention ([x] holds here for the integer nearest to x), and F i→j,z = F i→j · e z . We showed in a preceding work [5] that the decomposition of the force to a sum of partial forces obeying the strong third Newton law does not guarantee that (21) is a correct expression for the zz component of the stress tensor. Fortunately, this is however true here, as shown in Appendix B 2.…”

“…The (monodisperse) Voronoi liquid [4] has shown convincingly that this class of fluids, though perfectly thermodynamically stable bona fide fluids, is able to display strongly unusual traits, for instance a large mesoscopic range where the sound attenuation behaves anomalously. It has been shown in [5] that this regime does not violate the existing body of knowledge on liquid physics [6], but that the atypical definition of the Voronoi fluid induces atypical numerical values of the basic structural and thermodynamic observables, allowing the fluid to visit some "regions" of the parameter space which are never probed by more widespread models, and thus to reveal this anomalous regime.…”

Active glasses

“…They found that a glass-like regime with caging behavior and subdiffusive dynamics can be achieved if the rate of cell cycling is sufficiently low. Finally, a recent series of papers by Ruscher and co-workers [143][144][145] studied the glassy physics of the so-called Voronoi liquid, which is defined such that each Voronoi position tends to move towards the centroid of the Voronoi cell to which it belongs. Although this model was not motivated by biological experiments, it revealed a multitude of non-trivial glassy features; it will be interesting to explore if and how the Voronoi liquid can be linked to other Voronoi-based models of confluent living cells.…”