Abstract
Meso-scale turbulence was originally observed experimentally in various suspensions of swimming bacteria, as well as in the collective motion of active colloids. The corresponding large scale dynamical patterns were reproduced in a simple model of a polar fluid, assuming a constant density of active particles. Recent, more detailed studies in a variety of experimental realizations of active polar fluids revealed additional interesting aspects, such as anomalous velocity statistics and clustering phenomena. Those phenomena cannot be explained by currently available models for active polar fluids. Herein, we extend the continuum model suggested by Dunkel et al to include density variations and a local feedback between the local density and self-propulsion speed of the active polar particles. If the velocity decreases strong enough with the density, a linear stability analysis of the resulting model shows that, in addition to the short-wavelength instability of the original model, a long-wavelength instability occurs. This is typically observed for high densities of polar active particles and is analogous to the well-known phenomenon of motility-induced phase separation (MIPS) in scalar active matter. We determine a simple phase diagram indicating the linear instabilities and perform systematic numerical simulations for the various regions in the corresponding parameter space. The interplay between the well understood short-range instability (leading to meso-scale turbulence) and the long-range instability (associated with MIPS) leads to interesting dynamics and novel phenomena concerning nucleation and coarsening processes. Our simulation results display a rich variety of novel patterns, including phase separation into domains with dynamically changing irregularly shaped boundaries. Anomalous velocity statistics are observed in all phases where the system segregates into regions of high and low densities. This offers a simple explanation for their occurrence in recent experiments with bacterial suspensions.
Highlights
Exploring active matter has become a popular subject in contemporary physics leading to many new insights into a large variety of intriguing systems
Active systems are ubiquitous in nature, thereby drawing interest from different scientific communities and offering a wealth of surprising dynamic phenomena [1, 2, 3, 4, 5, 6]
More recent reviews have focused on the prominent role of models with alignment interaction [14] and on anisotropic, self-propelled particles [15] as well as on the large variety of computational approaches to active matter [16] and on a roadmap outlining a multitude of promising directions for the field [17]
Summary
Exploring active matter has become a popular subject in contemporary physics leading to many new insights into a large variety of intriguing systems. Considering steric interactions and alignment individually gives rise to MIPS [42, 43, 44] and global order in Vicsek-like models [45, 46, 47, 48] respectively, while meso-scale turbulence results from the combination of alignment and hydrodynamics [23, 29, 30, 31]. Our model features elements from all three of these prominent theories of active matter (MIPS, global order, meso-scale turbulence) and connects them in a minimalist fashion. In the fourth section we present numerical solutions of our model, sketch a phase portrait and discuss the observed anomalous velocity statistics
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