Universal scaling for disordered viscoelastic matter near the onset of rigidity

TL;DR

This paper derives universal scaling laws for the dynamical response of disordered viscoelastic materials near the transition to rigidity, revealing critical exponents and invariant scaling functions applicable to jamming and percolation transitions.

Contribution

It introduces a unified scaling framework for the vibrational and dynamical properties of disordered viscoelastic networks near rigidity transitions, using effective-medium theory.

Findings

Derived critical exponents for rigidity transitions

Identified invariant scaling combinations and formulas

Described diverging length and time scales at transitions

Abstract

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.