Incompressible polar active fluids with quenched disorder in dimensions $d> 2$

TL;DR

This paper develops a hydrodynamic theory for incompressible polar active fluids with quenched disorder, revealing their ability to maintain coherent motion despite disorder and providing exact scaling exponents in dimensions 2 to 5.

Contribution

It introduces a novel hydrodynamic framework for active fluids with quenched disorder and derives exact scaling exponents in multiple dimensions.

Findings

Active fluids can sustain coherent motion despite quenched disorder.

Linearized hydrodynamics fails to describe scaling behavior in 2 to 5 dimensions.

Exact dimension-dependent scaling exponents are obtained.

Abstract

We present a hydrodynamic theory of incompressible polar active fluids with quenched disorder. This theory shows that such fluids can overcome the disruption caused by the quenched disorder and move coherently, in the sense of having a non-zero mean velocity in the hydrodynamic limit. However, the scaling behavior of this class of active systems cannot be described by linearized hydrodynamics in spatial dimensions between 2 and 5. Nonetheless, we obtain the exact dimension-dependent scaling exponents in these dimensions.