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The onset of rigidity in interacting liquids, as they undergo a transition toa disordered solid, is associated with a rearrangement of the low-frequencyvibrational spectrum. In this letter, we derive scaling forms for the singulardynamical response of disordered viscoelastic networks near both jamming andrigidity percolation. Using effective-medium theory, we extract criticalexponents, invariant scaling combinations and analytical formulas for universalscaling functions near these transitions. Our scaling forms describe thebehavior in space and time near the various onsets of rigidity, for rigid andfloppy phases and the crossover region, including diverging length and timescales at the transitions.

Universal scaling for disordered viscoelastic matter near the onset of rigidity