Active particles in heterogeneous media display new physics: existence of optimal noise and absence of bands and long-range order

We present a detailed study of the large-scale collective properties of self-propelled particles (SPPs) moving in two-dimensional heterogeneous space. The impact of spatial heterogeneities on the ordered, collectively moving phase is investigated. We show that for strong enough spatial heterogeneity, the well-documented high-density, high-ordered propagating bands that emerge in homogeneous space disappear. Moreover, the ordered phase does not exhibit long-range order, as occurs in homogeneous systems, but rather quasi-long range order: i.e. the SPP system becomes disordered in the thermodynamical limit. For finite size systems, we find that there is an optimal noise value that maximizes order. Interestingly, the system becomes disordered in two limits, for high noise values as well as for vanishing noise. This remarkable finding strongly suggests the existence of two critical points, instead of only one, associated to the collective motion transition. Density fluctuations are consistent with these observations, being higher and anomalously strong at the optimal noise, and decreasing and crossing over to normal for high and low noise values. Collective properties are investigated in static as well as dynamic heterogeneous environments, and by changing the symmetry of the velocity alignment mechanism of the SPPs.Comment: 16 pages, 11 figures, 60 reference

Diffusion, subdiffusion, and trapping of active particles in heterogeneous media

We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles avoid. Obstacle avoidance is characterized by the particle turning speed $\gamma$. We show, through simulations and analytical calculations, that the mean square displacement of particles exhibits two regimes as function of the density of obstacles $\rho_o$ and $\gamma$. We find that at low values of $\gamma$, particle motion is diffusive and characterized by a diffusion coefficient that displays a minimum at an intermediate obstacle density $\rho_o$. We observe that in high obstacle density regions and for large $\gamma$ values, spontaneous trapping of active particles occurs. We show that such trapping leads to genuine subdiffusive motion of the active particles. We indicate how these findings can be used to fabricate a filter of active particles.Comment: to appear in Phys. Rev. Let

Optimal noise maximizes collective motion in heterogeneous media

We study the effect of spatial heterogeneity on the collective motion of self-propelled particles (SPPs). The heterogeneity is modeled as a random distribution of either static or diffusive obstacles, which the SPPs avoid while trying to align their movements. We find that such obstacles have a dramatic effect on the collective dynamics of usual SPP models. In particular, we report about the existence of an optimal (angular) noise amplitude that maximizes collective motion. We also show that while at low obstacle densities the system exhibits long-range order, in strongly heterogeneous media collective motion is quasi-long-range and exists only for noise values in between two critical noise values, with the system being disordered at both, large and low noise amplitudes. Since most real system have spatial heterogeneities, the finding of an optimal noise intensity has immediate practical and fundamental implications for the design and evolution of collective motion strategies.Comment: to appear in Phys. Rev. Let

Emergent vortices in populations of colloidal rollers

Coherent vortical motion has been reported in a wide variety of populations including living organisms (bacteria, fishes, human crowds) and synthetic active matter (shaken grains, mixtures of biopolymers), yet a unified description of the formation and structure of this pattern remains lacking. Here we report the self-organization of motile colloids into a macroscopic steadily rotating vortex. Combining physical experiments and numerical simulations, we elucidate this collective behavior. We demonstrate that the emergent-vortex structure lives on the verge of a phase separation, and single out the very constituents responsible for this state of polar active matter. Building on this observation, we establish a continuum theory and lay out a strong foundation for the description of vortical collective motion in a broad class of motile populations constrained by geometrical boundaries

Universal statistics of epithelial tissue topology

Cells forming various epithelial tissues have a strikingly universal distribution for the number of their edges. It is generally assumed that this topological feature is predefined by the statistics of individual cell divisions in growing tissue but existing theoretical models are unable to predict the observed distribution. Here we show experimentally, as well as in simulations, that the probability of cellular division increases exponentially with the number of edges of the dividing cell and show analytically that this is responsible for the observed shape of cell-edge distribution

Bursts of activity in collective cell migration

Dense monolayers of living cells display intriguing relaxation dynamics, reminiscent of soft and glassy materials close to the jamming transition, and migrate collectively when space is available, as in wound healing or in cancer invasion. Here we show that collective cell migration occurs in bursts that are similar to those recorded in the propagation of cracks, fluid fronts in porous media and ferromagnetic domain walls. In analogy with these systems, the distribution of activity bursts displays scaling laws that are universal in different cell types and for cells moving on different substrates. The main features of the invasion dynamics are quantitatively captured by a model of interacting active particles moving in a disordered landscape. Our results illustrate that collective motion of living cells is analogous to the corresponding dynamics in driven, but inanimate, systems