How the geometry makes the criticality in two - component spreading phenomena?

TL;DR

This paper investigates how the geometry of spreading influences critical phenomena in a two-component model, revealing that apparent differences are due to initial conditions and geometry rather than intrinsic universality.

Contribution

The study demonstrates that the critical behavior in the two-component spreading model is geometry-independent, with apparent variations explained by initial conditions and curvature effects.

Findings

Criticality is geometry-independent in the SMK model.

Apparent critical exponent variations are due to initial conditions.

Mean field relations accurately describe numerical results.

Abstract

We study numerically a two-component A-B spreading model (SMK model) for concave and convex radial growth of 2d-geometries. The seed is chosen to be an occupied circle line, and growth spreads inside the circle (concave geometry) or outside the circle (convex geometry). On the basis of generalised diffusion-annihilation equation for domain evolution, we derive the mean field relations describing quite well the results of numerical investigations. We conclude that the intrinsic universality of the SMK does not depend on the geometry and the dependence of criticality versus the curvature observed in numerical experiments is only an apparent effect. We discuss the dependence of the apparent critical exponent $\chi_{a}$ upon the spreading geometry and initial conditions.