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Researcher profile

Marko Popović

Marko Popović contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
cond-mat.softBiological Physicscond-mat.dis-nn

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Published work

3 published item(s)

preprint2026arXiv

Cell divisions suppress dynamical correlations in solid tissues

Developing tissues often maintain mechanical coherence while continuously remodeling through cellular processes such as cell divisions and rearrangements. In this way, they are an example of amorphous solids. In passive amorphous solids, local rearrangements can trigger one another through long-ranged elastic interactions, leading to system-spanning avalanches near yielding. Whether similar collective dynamics should be expected in living tissues is unclear, because cell divisions generate stress and remodeling events independently of local mechanical stability. Here, we address this question using a two-dimensional elastoplastic model in which cell divisions are treated as active plastic events. We find that while cell divisions fluidize the tissue below the passive yield stress, but preserve the marginal stability in the quasistatic limit. However, they also strongly suppress the system-spanning avalanches of cell rearrangements, in constrast with the expected behavior in passive amorphous solids. Finally, we show that the avalanche supression originates from the energy balance in the system. Namely, the energy injected by cell divisions allows for shear flow below the yield stress, but also provides a finite budget for rearrangements. These results suggest that proliferating tissues display the structural hallmarks of marginal amorphous solids while exhibiting much shorter-ranged correlations in dynamics, compared to passive amorphous solids.

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preprint2020arXiv

Inferring the flow properties of epithelial tissues from their geometry

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

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preprint2020arXiv

Thermal origin of quasi-localised excitations in glasses

Key aspects of glasses are controlled by the presence of excitations in which a group of particles can rearrange. Surprisingly, recent observations indicate that their density is dramatically reduced and their size decreases as the temperature of the supercooled liquid is lowered. Some theories predict these excitations to cause a gap in the spectrum of quasi-localised modes of the Hessian that grows upon cooling, while others predict a pseudo-gap ${D_L(ω)} \sim ω^α$. To unify these views and observations, we generate glassy configurations of controlled gap magnitude $ω_c$ at temperature ${T=0}$, using so-called `breathing' particles, and study how such gapped states respond to thermal fluctuations. We find that \textit{(i)}~the gap always fills up at finite $T$ with ${D_L(ω) \approx A_4(T) \, ω^4}$ and ${A_4 \sim \exp(-E_a / T)}$ at low $T$, \textit{(ii)}~$E_a$ rapidly grows with $ω_c$, in reasonable agreement with a simple scaling prediction ${E_a\sim ω_c^4}$ and \textit{(iii)}~at larger $ω_c$ excitations involve fewer particles, as we rationalise, and eventually become string-like. We propose an interpretation of mean-field theories of the glass transition, in which the modes beyond the gap act as an excitation reservoir, from which a pseudo-gap distribution is populated with its magnitude rapidly decreasing at lower $T$. We discuss how this picture unifies the rarefaction as well as the decreasing size of excitations upon cooling, together with a string-like relaxation occurring near the glass transition.

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