Diffusive wave dynamics beyond the continuum limit

Scientists have observed and studied diffusive waves in contexts as disparate population genetics cell signaling. Often, these are propagated by discrete entities or agents, such individual cells the case of For a broad class waves, we characterize transition between collective propagation -- which wave speed is well-described continuum theory agents. We show that this depends heavily on dimensionality system propagates disordered systems yield dynamics largely consistent with lattice systems. In some dimensionalities, intuition closely packed sources more accurately mimic can be grossly violated.