Birth, Death, and Horizontal Flight: Malthusian flocks with an easy plane in three dimensions

TL;DR

This paper develops a theoretical framework for three-dimensional Malthusian flocks, where entities move coherently in a plane while being born and dying, and derives their universal scaling exponents exactly.

Contribution

It introduces a novel theory for 3D Malthusian flocks with planar velocity preference and calculates their universal scaling exponents exactly.

Findings

Exact dynamical exponent z=3/2

Anisotropy exponent ζ=3/4

Roughness exponent χ=-1/2

Abstract

I formulate the theory of three dimensional "Malthusian flocks" -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion -- whose constituents all have a preference for having their velocity vectors lie parallel to the same two-dimensional plane. I determine the universal scaling exponents characterizing such systems exactly, finding that the dynamical exponent $z=3/2$, the "anisotropy" exponent $\zeta=3/4$, and the "roughness" exponent $\chi=-1/2$. I also give the scaling laws implied by these exponents.