Dynamical renormalization group calculation of a two-phase sharp interface model.
The temporal evolution of an interface separating two phases is studied using renormalization group and scaling theory and exact calculation of a sharp interface model incorporating surface tension and kinetic undercooling. Under conditions favoring rapid solidification the characteristic length, R(t), varies as t(1/2) while the total surface area of the interface, S(t), varies as t((d-1)/2). This complements the results of Jasnow and Vinals who found R(t) approximately t in the quasistatic regime. The transition in exponents from R(t) approximately t to R(t) approximately t(1/2), as solidification proceeds from the quasistatic to the rapid solidification regime, suggests a complex evolution toward a self-similar late stage growth.
Caginalp
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University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.