Collective Motion of Micro-organisms from Field Theoretical Viewpoint

TL;DR

This paper models the collective motion of micro-organisms and the formation of red tide as a phase transition using a field-theoretical approach, deriving an equation of state similar to Van der Waals.

Contribution

It introduces a novel field-theoretical model linking micro-organism interactions to phase transition phenomena like red tide formation.

Findings

Red tide formation is modeled as a phase transition from gas to liquid.

Derived a Van der Waals type equation of state for micro-organism density.

Estimated the critical density for red tide generation.

Abstract

We analyze the collective motion of micro-organisms in the fluid and consider the problem of the red tide. The red tide is produced by the condensation of the micro-organisms, which might be a similar phenomenon to the condensation of the strings. We propose a model of the generation of the red tide. By considering the interaction between the micro- organisms mediated by the velocity fields in the fluid, we derive the Van der Waals type equation of state, where the generation of the red tide can be regarded as a phase transition from the gas of micro-organisms to the liquid. (The number density of micro-organisms which generates the red tide is order estimated.)