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

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

1998-06-26

arxiv.org/abs/cond-mat/9806320v1

Physics

Condensed Matter

Statistical Mechanics

Uses iopart.cls, 11 pages with 8 postscript figures embedded

Scientific paper

10.1088/0305-4470/31/46/010

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.

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