Ni. Lebovka et Nv. Vygornitskii, HOW DOES THE GEOMETRY AFFECT THE CRITICALITY IN 2-COMPONENT SPREADINGPHENOMENA, Journal of physics. A, mathematical and general (Print), 31(46), 1998, pp. 9199-9208
We study numerically the two-component spreading model (SMK) for conca
ve and convex radial growth two-dimensional geometries. The seed is ch
osen to be an occupied circle line, and the growth spreads inside the
circle (concave geometry) or outside the circle (convex geometry). On
the basis of a generalized diffusion-annihilation equation for domain
evolution, we derive mean-field relations that describe quite well the
results of numerical investigations. We conclude that the intrinsic u
niversality of the SMK does not depend on the geometry, and that the d
ependence of criticality on curvature observed in numerical experiment
s is only an apparent effect. We discuss the dependence of the apparen
t critical exponent chi(a) upon the growth geometry and initial condit
ions.