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Register a new userSoftness, anomalous dynamics, and fractal-like energy landscape in model cell tissues
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Epithelial cell tissues have a slow relaxation dynamics resembling that of supercooled liquids. Yet, they also have distinguishing features. These include an extended short-time sub-diffusive transient, as observed in some experiments and recent studies of model systems, and a sub-Arrhenius dependence of the relaxation time on temperature, as reported in numerical studies. Here we demonstrate that the anomalous glassy dynamics of epithelial tissues originates from the emergence of a fractal-like energy landscape, particles becoming virtually free to diffuse in specific phase space directions up to a small distance. Furthermore, we clarify that the stiffness of the cells tunes this anomalous behaviour, tissues of stiff cells having conventional glassy relaxation dynamics.
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Using molecular dynamics computer simulations we investigate the aging dynamics of a gel. We start from a fractal structure generated by the DLCA-DEF algorithm, onto which we then impose an interaction potential consisting of a short-range attraction as well as a long-range repulsion. After relaxing the system at T=0, we let it evolve at a fixed finite temperature. Depending on the temperature T we find different scenarios for the aging behavior. For T>0.2 the fractal structure is unstable and breaks up into small clusters which relax to equilibrium. For T<0.2 the structure is stable and the dynamics slows down with increasing waiting time. At intermediate and low T the mean squared displacement scales as t^{2/3} and we discuss several mechanisms for this anomalous time dependence. For intermediate T, the self-intermediate scattering function is given by a compressed exponential at small wave-vectors and by a stretched exponential at large wave-vectors. In contrast, for low T it is a stretched exponential for all wave-vectors. This behavior can be traced back to a subtle interplay between elastic rearrangements, fluctuations of chain-like filaments, and heterogeneity.
Motivated by the mean field prediction of a Gardner phase transition between a normal glass and a marginally stable glass, we investigate the off-equilibrium dynamics of three-dimensional polydisperse hard spheres, used as a model for colloidal or granular glasses. Deep inside the glass phase, we find that a sharp crossover pressure $P_{rm G}$ separates two distinct dynamical regimes. For pressure $P < P_{rm G}$, the glass behaves as a normal solid, displaying fast dynamics that quickly equilibrates within the glass free energy basin. For $P>P_{rm G}$, instead, the dynamics becomes strongly anomalous, displaying very large equilibration time scales, aging, and a constantly increasing dynamical susceptibility. The crossover at $P_{rm G}$ is strongly reminiscent of the one observed in three-dimensional spin-glasses in an external field, suggesting that the two systems could be in the same universality class, consistently with theoretical expectations.
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