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We introduce and theoretically investigate a minimal particle-based model for a new class of active matter where particles exhibit directional, volume-conserving division in confinement while interacting sterically, mimicking cells in early embryogenesis. We find that complex motion, synchronized within division cycles, displays strong collective effects and becomes self-similar in the long-time limit. Introducing the method of normalized retraced trajectories, we show that the transgenerational motion caused by cell division can be mapped to a time-inhomogenous random walk with an exponentially decreasing length scale. Analytical predictions for this stochastic process allow us to extract effective parameters, indicating unusual effects of crowding and absence of jamming. Robustness of our findings against desynchronized divisions, cell size dispersity, and variations in confinement hints at universal behavior. Our results establish an understanding of complex dynamics exhibited by isovolumentric division over long timescales, paving the way for new bioengineering strategies and perspectives on living matter., Comment: 9 pages, 3 figures

Growth is a known driver of cellular dynamics in a range of dense aggregates from bacterial colonies to developing tissues to tumors. Hence, universal physical principles underlying these dynamics are of great interdisciplinary interest. Here, we study the emergent dynamics arising from the interplay of growth, steric repulsion and motility in a minimal agent-based model of exponentially growing three-dimensional spheroids. Our results show that, without cell motility, deterministic motion caused by overall volume expansion dominates the dynamics of individual cells in the radial direction, while growth and division lead to cellular-scale diffusive motion in the tangential direction, whose magnitude is largely independent of expansion velocity. Despite this small-scale diffusion, we show that cell lineages are subject to confinement in their local environment, quenching weak cell motility. At higher motility, we find a transient regime of tangential superdiffusivity, which is accompanied by global mixing of cells. A quantitative analysis reveals a diverging mixing time scale at the transition, reminiscent of glassy dynamics. Our study highlights the complex interaction of local cell division and motility with global expansion, mediated exclusively by mechanics. The observations may serve as a baseline for the identification of phenomena caused by additional biological mechanisms in experiments on tissue spheroids, which have become a popular model system in biophysics and other fields. The mixing dynamics might also be relevant for competition or tumor progression., Comment: 9 pages, 4 figures, 8 supplementary figures, 5 supplementary videos

The Braess paradox can be observed in road networks used by selfish users. It describes the counterintuitive situation in which adding a new, per se faster, origin-destination connection to a road network results in increased travel times for all network users. We study the network as originally proposed by Braess but introduce microscopic particle dynamics based on the totally asymmetric exclusion processes. In contrast to our previous work [10.1103/PhysRevE.94.062312], where routes were chosen randomly according to turning rates, here we study the case of drivers with fixed route choices. We find that travel time reduction due to the new road only happens at really low densities and Braess' paradox dominates the largest part of the phase diagram. Furthermore, the domain wall phase observed in [10.1103/PhysRevE.94.062312] vanishes. In the present model gridlock states are observed in a large part of phase space. We conclude that the construcion of a new road can often be very critical and should be considered carefully., Comment: 25 pages, 16 figures

We study the Braess paradox in the transport network as originally proposed by Braess with totally asymmetric exclusion processes (TASEPs) on the edges. The Braess paradox describes the counterintuitive situation in which adding an edge to a road network leads to a user optimum with higher travel times for all network users. Travel times on the TASEPs are nonlinear in the density, and jammed states can occur due to the microscopic exclusion principle, leading to a more realistic description of trafficlike transport on the network than in previously studied linear macroscopic mathematical models. Furthermore, the stochastic dynamics allows us to explore the effects of fluctuations on network performance. We observe that for low densities, the added edge leads to lower travel times. For slightly higher densities, the Braess paradox occurs in its classical sense. At intermediate densities, strong fluctuations in the travel times dominate the system's behavior due to links that are in a domain-wall state. At high densities, the added link leads to lower travel times. We present a phase diagram that predicts the system's state depending on the global density and crucial path-length ratios., Comment: 14 pages, 17 figures