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

Abstract

Disordered viscoelastic materials are ubiquitous and exhibit fascinating invariant scaling properties. In a companion article [1], 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.

Jamming and Unusual Charge Density Fluctuations of Strange Metals

“…Starting with scaling forms for the longitudinal susceptibility that were derived recently by some of us [17,37], we will write down a coarse-grained effective description for the long-wavelength and low-frequency bosonic excitations in a liquid at the brink of rigidity percolation (RP), a specific kind of continuous rigidity transition [38]; see Fig. 1(a).…”

“…Our starting point is based on a recently proposed scaling ansatz for the dynamical susceptibilities near classical jamming and RP [17,37]. There has been a dearth of solvable models in finite dimensions where universal features of the dynamical susceptibilities can be analyzed in a reliable fashion; we utilized the tractable effective medium theory [31] to compute these in Ref.…”

“…There has been a dearth of solvable models in finite dimensions where universal features of the dynamical susceptibilities can be analyzed in a reliable fashion; we utilized the tractable effective medium theory [31] to compute these in Ref. [17,37] and obtained their explicit analytical forms [40]. Given that the strange metals where the anomalous density fluctuations have been observed are quasi two-dimensional, we will model our system as a stack of weakly coupled twodimensional layers.…”