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Article overview
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Inferring the plasticity of epithelial tissues from their geometry | | Marko Popovic
; Valentin Druelle
; Natalie A. Dye
; Frank Jülicher
; Matthieu Wyart
; | | Date: |
12 Feb 2020 | | Abstract: | Inferring flow properties from geometry alone is of practical importance in a
range of systems, including biological tissues and particulate materials. In
the latter case, a key and hard-to-measure quantity controlling plasticity is
the density $P(x)$ of weak spots, where $x$ is the additional stress required
for local failure. In the thermodynamic limit $P(x)$ is singular at $x= 0$ in
the entire solid phase below the yield stress $Sigma_c$, and marks the
presence of avalanches of plastic events that become smaller only for stresses
$Sigma>Sigma_c$. We first show that the vertex model of epithelial tissues
has a similar phenomenology: in the absence of noise, it presents a yield
stress $Sigma_c$ above which a stationary flow rate $dotgamma>0$ is
sustainable. The avalanches size $S$ and their duration $ au$ diverge as $S
sim dot{gamma}^{-a}$ and $ au sim dot{gamma}^{-c}$ respectively, with $a
approx1/4$ and $c approx 2/3$. Yet, we argue quite generally and test in that
model that for energy functionals that depend on topology, the stability $x$ of
weak spots (called T1 transitions in that context) is proportional to the
length $L$ of the bond that vanishes in this event. This implies that for this
class of models $P(x)$ is readily measurable from geometry alone. We find that
$P(L)$ exhibits a power law in the developing fruit fly wing with exponents
similar to that of the vertex model in its solid phase. It raises the
possibility that collective and non-linear effects are important during
development, and suggests a new route to study outstanding questions associated
with the yielding transition. | | Source: | arXiv, 2002.5133 | | Services: | Forum | Review | PDF | Favorites | |
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