Birth, Death and Flight: A Theory of Malthusian Flocks

TL;DR

This paper develops a comprehensive theory for Malthusian flocks, self-propelled systems with reproduction and death, revealing their unique order, scaling laws, and fluctuation behaviors across all spatial dimensions.

Contribution

It provides an exact spatio-temporal scaling framework for Malthusian flocks, highlighting their distinct properties compared to immortal flocks, including the absence of sound waves and giant fluctuations.

Findings

Existence of long-ranged order in 2D systems.

Exact determination of spatio-temporal scaling in all dimensions.

Persistent number fluctuations propagating along flock motion.

Abstract

I study "Malthusian Flocks": moving aggregates of self-propelled entities (e.g., organisms, cytoskeletal actin, microtubules in mitotic spindles) that reproduce and die. Long-ranged order (i.e., the existence of a non-zero average velocity $<\vec v (\vec r, t) >\ne \vec 0$) is possible in these systems, even in spatial dimension $d=2$. Their spatio-temporal scaling structure can be determined exactly in all spatial dimensions; furthermore, they lack both the longitudinal sound waves and the giant number fluctuations found in immortal flocks. Number fluctuations are very {\it persistent}, and propagate along the direction of flock motion, but at a different speed.