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

A kinetic model and scaling properties for non-equilibrium clustering of self-propelled particles

We demonstrate that the clustering statistics and the corresponding phase transition to non-equilibrium clustering found in many experiments and simulation studies with self-propelled particles (SPPs) with alignment can be obtained from a simple kinetic model. The key elements of this approach are the scaling of the cluster cross-section with the cluster mass -- characterized by an exponent $\alpha$ -- and the scaling of the cluster perimeter with the cluster mass -- described by an exponent $\beta$. The analysis of the kinetic approach reveals that the SPPs exhibit two phases: i) an individual phase, where the cluster size distribution (CSD) is dominated by an exponential tail that defines a characteristic cluster size, and ii) a collective phase characterized by the presence of non-monotonic CSD with a local maximum at large cluster sizes. At the transition between these two phases the CSD is well described by a power-law with a critical exponent $\gamma$, which is a function of $\alpha$ and $\beta$ only. The critical exponent is found to be in the range $0.8 < \gamma < 1.5$ in line with observations in experiments and simulations

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

Fluctuations and the role of collision duration in reaction-diffusion systems

In a reaction-diffusion system, fluctuations in both diffusion and reaction events, have important effects on the steady-state statistics of the system. Here, we argue through extensive lattice simulations, mean-field type arguments, and the Doi-Peliti formalism that the collision duration statistics -- i.e., the time two particles stay together in a lattice site -- plays a leading role in determining the steady state of the system. We obtain approximate expressions for the average densities of the chemical species and for the critical diffusion coefficient required to sustain the reaction

Superdiffusion, large-scale synchronization and topological defects

We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby introducing an additional, independent source of fluctuations, thus constituting the intrinsic nonequilibrium nature of the temporal dynamics. We employ this paradigmatic model system to discuss how the emergence of order is affected by motion of individual entities. In particular, we consider both, normal diffusive motion and superdiffusion. A non-Hamiltonian field theory including multiplicative noise terms is derived which describes the nonequilibrium dynamics at the macroscale. This theory reveals a defect-mediated transition from incoherence to quasi long-range order for normal diffusion of oscillators in two dimensions, implying a power-law dependence of all synchronization properties on system size. In contrast, superdiffusive transport suppresses the emergence of topological defects, thereby inducing a continuous synchronization transition to long-range order in two dimensions. These results are consistent with particle-based simulations.Comment: 7 pages, 5 figures, submitted to Phys. Rev.

Self-propelled rods exhibit a novel phase-separated state characterized by the presence of active stresses and the ejection of polar clusters

We study collections of self-propelled rods (SPR) moving in two dimensions for packing fractions less than or equal to 0.3. We find that in the thermodynamical limit the SPR undergo a phase transition between a disordered gas and a novel phase-separated system state. Interestingly, (global) orientational order patterns -- contrary to what has been suggested -- vanish in this limit. In the found novel state, the SPR self-organize into a highly dynamical, high-density, compact region - which we call aggregate - which is surrounded by a disordered gas. Active stresses build inside aggregates as result of the combined effect of local orientational order and active forces. This leads to the most distinctive feature of these aggregates: constant ejection of polar clusters of SPR. This novel phase-separated state represents a novel state of matter characterized by large fluctuations in volume and shape, related to mass ejection, and exhibits positional as well as orientational local order. SPR systems display new physics unseen in other active matter systems due to the coupling between density, active stresses, and orientational order (such coupling cannot be reduced simply to a coupling between speed and density).Comment: to appear in PR

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

Correlations in complex networks under attack

For any initial correlated network after any kind of attack where either nodes or edges are removed, we obtain general expressions for the degree-degree probability matrix and degree distribution. We show that the proposed analytical approach predicts the correct topological changes after the attack by comparing the evolution of the assortativity coefficient for different attack strategies and intensities in theory and simulations. We find that it is possible to turn an initial assortative network into a disassortative one, and vice versa, by fine-tuning removal of either nodes or edges. For an initial uncorrelated network, on the other hand, we discover that only a targeted edge-removal attack can induce such correlations