Universality in Incompressible Active Fluid: Effect of Non-local Shear Stress
arXiv:2007.11032 · doi:10.1103/PhysRevE.102.032616
Abstract
Phase transitions in active fluids attracted significant attention within the last decades. Recent results show [L. Chen et al., New J. Phys. 17, 042002 (2015)] that an order-disorder phase transition in incompressible active fluids belongs to a new universality class. In this work, we further investigate this type of phase transition and focus on the effect of long-range interactions. This is achieved by introducing a non-local shear stress into the hydrodynamic description, which leads to superdiffusion of the velocity field, and can be viewed as a result of the active particles performing Levy walks. The universal properties in the critical region are derived by performing a perturbative renormalization group analysis of the corresponding response functional within the one-loop approximation. We show that the effect of non-local shear stress decreases the upper critical dimension of the model, and can lead to the irrelevance of the active fluid self-advection with the resulting model belonging to an unusual 'long-range Model A' universality class not reported before. Moreover, when the degree of non-locality is sufficiently high all non-linearities become irrelevant and the mean-field description is valid in any spatial dimension.
arXiv commentAccepted for publication in Phys. Rev. E
References in corpus (41)
- Novel type of phase transition in a system of self-driven particles
- Active Particles in Complex and Crowded Environments
- Collective motion
- Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
- Motility-Induced Phase Separation
- Flocks, herds, and schools: A quantitative theory of flocking
- Spontaneous motion in hierarchically assembled active matter
- Scale-free correlations in bird flocks
- Meso-scale turbulence in living fluids
- Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles
- Onset of collective and cohesive motion
- Collective motion of self-propelled particles interacting without cohesion
- Diffusive transport without detailed balance in motile bacteria: Does microbiology need statistical physics?
- Superfluid transport of information in turning flocks of starlings
- Active Jamming: Self-propelled soft particles at high density
- Boltzmann and hydrodynamic description for self-propelled particles
- Spontaneous flow transition in active polar gels
- Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
- Crystallization in a dense suspension of self-propelled particles
- The Role of Projection in the Control of Bird Flocks
- A Reanalysis of the Hydrodynamic Theory of Fluid, Polar-Ordered Flocks
- Self-organized Vortex State in Two-dimensional Dictyostelium Dynamics
- Sound waves and the absence of Galilean invariance in flocks
- New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion
- Tuning the random walk of active colloids
- Minimal continuum theories of structure formation in dense active fluids
- Anomalous scaling regimes of a passive scalar advected by the synthetic velocity field
- The role of correlations in the collective behaviour of microswimmer suspensions
- Diffusion of individual birds in starling flocks
- Active glasses
- Anomalous glassy dynamics in simple models of dense biological tissue
- Anomalous scaling of a passive scalar advected by the synthetic compressible flow
- Critical Phenomenon of the Order-Disorder Transition in Incompressible Flocks
- Anomalous scaling of a passive scalar advected by the turbulent velocity field with finite correlation time: Two-loop approximation
- An improved $\eps$ expansion for three-dimensional turbulence: two-loop renormalization near two dimensions
- Dynamical renormalization group approach to the collective behaviour of swarms
- Field theory of directed percolation with long-range spreading
- Turbulent compressible fluid: renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields
- Swimming suppresses correlations in dilute suspensions of pusher microorganisms
- Edge instability in incompressible planar active fluids
- Renormalization group crossover in the critical dynamics of field theories with mode coupling terms