Eric Schwen | Searcharxiv

arXiv2022

Universal scaling for disordered viscoelastic matter near the onset of rigidity

The onset of rigidity in interacting liquids, as they undergo a transition to a disordered solid, is associated with a rearrangement of the low-frequency vibrational spectrum. In this letter, we derive scaling forms for the singular dynamical response of disordered viscoelastic networks near both jamming and rigidity percolation. Using effective-medium theory, we extract critical exponents, invariant scaling combinations and analytical formulas for universal scaling functions near these transitions. Our scaling forms describe the behavior in space and time near the various onsets of rigidity, for rigid and floppy phases and the crossover region, including diverging length and time scales at the transitions.

cond-mat.soft↗

arXiv2022

Universal scaling for disordered viscoelastic matter II: Collapses, global behavior and spatio-temporal properties

Disordered viscoelastic materials are ubiquitous and exhibit fascinating invariant scaling properties. In a companion article, we have presented comprehensive new results for the critical behavior of the dynamic susceptibility of disordered elastic systems near the onset of rigidity. Here we provide additional details of the derivation of the singular scaling forms of the longitudinal response near both jamming and rigidity percolation. We then discuss global aspects associated with these forms, and make scaling collapse plots for both undamped and overdamped dynamics in both the rigid and floppy phases. We also derive critical exponents, invariant scaling combinations and analytical formulas for universal scaling functions of several quantities such as transverse and density responses, elastic moduli, viscosities, and correlation functions. Finally, we discuss tentative experimental protocols to measure these behaviors in colloidal suspensions.

cond-mat.soft↗