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

TL;DR

This paper explores the universal scaling laws and critical behaviors of disordered viscoelastic materials, providing analytical formulas, scaling collapses, and experimental suggestions for understanding their global and spatio-temporal properties.

Contribution

It offers new derivations of singular scaling forms, critical exponents, and universal functions for disordered viscoelastic matter near rigidity transitions, expanding on prior work.

Findings

Derived critical exponents and universal scaling functions.

Presented scaling collapse plots for different dynamics and phases.

Proposed experimental protocols for measuring scaling behaviors.

Abstract

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.