Inferring the flow properties of epithelial tissues from their geometry

摘要: Amorphous materials exhibit complex material proprteties with strongly nonlinear behaviors. Below a yield stress they behave as plastic solids, while start to above critical $\Sigma_c$. A key quantity controlling plasticity which is, however, hard measure is the density $P(x)$ of weak spots, where $x$ additional required for local failure. In thermodynamic limit $P(x)\sim x^\theta$ singular at $x= 0$ in solid phase below This singularity related presence system spannig avalanches events. Here we address question if spots and flow properties can be determined from geometry an amporphous structure alone. We show that vertex model cell packings tissues exhibits phenomenology amorphous systems. As approached above, strain rate vanishes size $S$ their duration $\tau$ diverge. then general, energy functional depend on topology, value proportional length $L$ bond event. For this class models therefore readily measurable Applying approach quantification packing developing wing epithelium fruit fly, find tissue $P(L)$ power law exponents similar those found numerically its phase. suggests non-linear emerge collective behaviors these govern developmental processes. Our based relation between topology energetics new route outstanding questions associated yielding transition.