The transition between quasi-static and fully dynamic for interfaces

Renormalization group and scaling theory have been used to determine the large time growth exponent for the characteristic length, R(t), of an interface in the form R(t) ∼ tβ. The exponent β is different in the two cases: quasi-static, in which the time derivative in the heat equation is suppressed, and the fully dynamic system. This paper examines the transition between the two regimes through an examination of the Greenʹs function for elliptic equations as a limit of the fundamental solution for parabolic equations. The key interface equation can be written as a sum of two terms: the elliptic (c = 0) and parabolic. For c = 0, the exponent β can take on values in a continuous spectrum. As c takes on finite values, a unique exponent is selected from this spectrum.