Kinetics, Hydrodynamics and Stochastodynamics of Cellular Structure Coarsening

TL;DR

This paper provides a comprehensive analysis of cellular structure coarsening using kinetic, hydrodynamic, and stochastodynamic theories, revealing new patterning effects and stochastic fluctuations across different scales.

Contribution

It introduces a unified approach to cellular coarsening analysis across microscopic, mesoscopic, and macroscopic levels, including a novel stochastic fluctuation phenomenon.

Findings

Identification of a diffusion-reaction equation with negative diffusion coefficient

Discovery of space-correlated stochastic fluctuations in cell interface density

Demonstration of pattern formation in cellular structures

Abstract

For the first time the phenomenon of cellular structure coarsening are consistently analysed from the positions of kinetic, hydrodynamic and stochastodynamic theories of nonequilibrium statistical systems. Thereby micro-, meso- and macroscopic levels of approach are distinguished. At the microscopic level the cellular structure is describe by a probability distribution function in a phase space of cell coordinates and of cell sizes. A kinetic equation for the function is written and a development to a hydrodynamic equation of a mesoscopic cell medium is realised. It has the form of a diffusion-reaction equation with a negative "diffusion" coefficient and with a cell interface density playing the role of concentration. Its analysis reveals a new effect of macroscopic patterning in the cell medium: existence of space-correlated stochastic fluctuations of the cell interface density.