94 research outputs found
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 -- and the scaling of the cluster perimeter with the
cluster mass -- described by an exponent . 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 , which is a function
of and only. The critical exponent is found to be in the range
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 . We show, through simulations and analytical
calculations, that the mean square displacement of particles exhibits two
regimes as function of the density of obstacles and . We find
that at low values of , particle motion is diffusive and characterized
by a diffusion coefficient that displays a minimum at an intermediate obstacle
density . We observe that in high obstacle density regions and for
large 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
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
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.
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
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