7 research outputs found
Role of particle conservation in self-propelled particle systems
Actively propelled particles undergoing dissipative collisions are
known to develop a state of spatially distributed coherently moving clusters.
For densities larger than a characteristic value, clusters grow in time and form
a stationary well-ordered state of coherent macroscopic motion. In this work
we address two questions. (i) What is the role of the particles’ aspect ratio in
the context of cluster formation, and does the particle shape affect the system’s
behavior on hydrodynamic scales? (ii) To what extent does particle conservation
influence pattern formation? To answer these questions we suggest a simple
kinetic model permitting us to depict some of the interaction properties between
freely moving particles and particles integrated in clusters. To this end, we
introduce two particle species: single and cluster particles. Specifically, we
account for coalescence of clusters from single particles, assembly of single
particles on existing clusters, collisions between clusters and cluster disassembly.
Coarse graining our kinetic model, (i) we demonstrate that particle shape (i.e.
aspect ratio) shifts the scale of the transition density, but does not impact the
instabilities at the ordering threshold and (ii) we show that the validity of particle
conservation determines the existence of a longitudinal instability, which tends to amplify density heterogeneities locally, and in turn triggers a wave pattern
with wave vectors parallel to the axis of macroscopic order. If the system is in
contact with a particle reservoir, this instability vanishes due to a compensation
of density heterogeneities
A Critical Assessment of the Boltzmann Approach for Active Systems
Generic models of propelled particle systems posit that the emergence of
polar order is driven by the competition between local alignment and noise.
Although this notion has been confirmed employing the Boltzmann equation, the
range of applicability of this equation remains elusive. We introduce a broad
class of mesoscopic collision rules and analyze the prerequisites for the
emergence of polar order in the framework of kinetic theory. Our findings
suggest that a Boltzmann approach is appropriate for weakly aligning systems
but is incompatible with experiments on cluster forming systems.Comment: 11 pages, 3 figure
Longitudinal Response of Confined Semiflexible Polymers
The longitudinal response of single semiflexible polymers to sudden changes
in externally applied forces is known to be controlled by the propagation and
relaxation of backbone tension. Under many experimental circumstances,
realized, e.g., in nano-fluidic devices or in polymeric networks or solutions,
these polymers are effectively confined in a channel- or tube-like geometry. By
means of heuristic scaling laws and rigorous analytical theory, we analyze the
tension dynamics of confined semiflexible polymers for various generic
experimental setups. It turns out that in contrast to the well-known linear
response, the influence of confinement on the non-linear dynamics can largely
be described as that of an effective prestress. We also study the free
relaxation of an initially confined chain, finding a surprising superlinear
t^(9/8) growth law for the change in end-to-end distance at short times.Comment: 18 pages, 1 figur
Bridging the gap between single-cell migration and collective dynamics
Motivated by the wealth of experimental data recently available, we present a cellularautomaton-based modeling framework focussing on high-level cell functions and their concerted effect on cellular migration patterns. Specifically, we formulate a coarse-grained description of cell polarity through self-regulated actin organization and its response to mechanical cues. Furthermore, we address the impact of cell adhesion on collective migration in cell cohorts. The model faithfully reproduces typical cell shapes and movements down to the level of single cells, yet allows for the efficient simulation of confluent tissues. In confined circular geometries, we find that specific properties of individual cells (polarizability;contractility) influence the emerging collective motion of small cell cohorts. Finally, we study the properties of expanding cellular monolayers (front morphology;stress and velocity distributions) at the level of extended tissues
Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems
Kinetic theories constitute one of the most promising tools to decipher the characteristic spatiotemporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides a natural translation between a particle-level description of the system’s dynamics and the corresponding hydrodynamic fields. Yet, the intricate mathematical structure of the Boltzmann equation substantially limits the progress toward a full understanding of this equation by solely analytical means. Here, we propose a general framework to numerically solve the Boltzmann equation for self-propelled particle systems in two spatial dimensions and with arbitrary boundary conditions. We discuss potential applications of this numerical framework to active matter systems and use the algorithm to give a detailed analysis to a model system of self-propelled particles with polar interactions. In accordance with previous studies, we find that spatially homogeneous isotropic and broken-symmetry states populate two distinct regions in parameter space, which are separated by a narrow region of spatially inhomogeneous, density-segregated moving patterns. We find clear evidence that these three regions in parameter space are connected by first-order phase transitions and that the transition between the spatially homogeneous isotropic and polar ordered phases bears striking similarities to liquid-gas phase transitions in equilibrium systems. Within the density-segregated parameter regime, we find a novel stable limit-cycle solution of the Boltzmann equation, which consists of parallel lanes of polar clusters moving in opposite directions, so as to render the overall symmetry of the system’s ordered state nematic, despite purely polar interactions on the level of single particles