Universal scaling for disordered viscoelastic matter near the onset of rigidity
arXiv:2103.07474 · doi:10.1103/PhysRevE.106.L052601
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.
8 pages, 4 figures. To appear as a letter in Phys. Rev. E
References in corpus (7)
- Critical scaling in linear response of frictionless granular packings near jamming
- Exact theory of dense amorphous hard spheres in high dimension. I. The free energy
- Measuring nonlinear stresses generated by defects in 3D colloidal crystals
- Dynamical behavior of disordered spring networks
- Nonlocal elasticity near jamming
- Mean-Field Predictions of Scaling Prefactors Match Low-Dimensional Jammed Packings
- The mechanics of anisotropic spring networks