We numerically study the effect of adding quenched disorder in the form ofrandomly placed pinning sites on jamming transitions in systems that jam at awell defined point J in the clean limit. Quenched disorder decreases thejamming density and introduces a depinning threshold. The onset of a finitethreshold coincides with point J at the lowest pinning densities, but forhigher pinning densities there is always a finite threshold even well belowjamming. We find that proximity to point J strongly affects the transportcurves and noise fluctuations, and observe a change from plastic behavior belowjamming, where the system is highly heterogeneous, to elastic depinning abovejamming. Many of the general features we find are related to other systemscontaining quenched disorder, including the peak effect observed in vortexsystems.
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