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Anomalous segregation dynamics of self-propelled particles

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Anomalous segregation dynamics of self-propelled particles
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62
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A number of novel experimental and theoretical results have recently been obtained on active soft matter, demonstrating the various interesting universal and anomalous features of this kind of driven systems. Here we consider the adhesion difference-driven segregation of actively moving units, a fundamental but still poorly explored aspect of collective motility. In particular, we propose a model in which particles have a tendency to adhere through a mechanism which makes them both stay in touch and synchronize their direction of motion—but the interaction is limited to particles of the same kind. The calculations corresponding to the related differential equations can be made in parallel, thus a powerful GPU card allows large scale simulations. We find that in a very large system of particles, interacting without explicit alignment rule, three basic segregation regimes seem to exist as a function of time: (i) at the beginning the time dependence of the correlation length is analogous to that predicted by the Cahn–Hilliard theory, (ii) next rapid segregation occurs characterized with a separation of the different kinds of units being faster than any previously suggested speed, finally, (iii) the growth of the characteristic sizes in the system slows down due to a new regime in which self-confined, rotating, splitting and re-joining clusters appear. Our results can explain recent observations of segregating tissue cells in vitro.
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Transcript: English(auto-generated)
When two different types of epithelial cells were cultured in the experiments, the cells were reported to segregate in two clusters, growing faster than a simple diffusive process would have implied. The characteristic size of two clusters increased with time according to an approximate
power law with an exponent close to one. To explain the fast segregation observed in the experiments, we propose a self-propelled particle model with a local interaction rule. Large-scale simulations of more than 100,000 particles reveal three well-distinctable regimes,
the middle of which displays the above-mentioned fast segregation. For short times, segregation is dominated by the random movement of single cells and clusters grow according to the can-heliot dynamics. When the clusters reach a specific size, their movement becomes aligned and follow ballistic movements. At this point, the system enters the phase of fast segregation.
This regime ends when the clusters grow so large that particles constituting them become uncorrelated and start to flow inside the clusters. When this happens, segregation slows down and clusters converge to their final size. Also, if the volume coverage of the two cell types deviates from the even mixture ratio,
we observe the same alteration in the exponent that was found in the Brownian dynamics. These results suggest that mixture ratio may affect particle exponents in a universal way independent of the details of the underlying dynamics.