DYNAMICAL MODEL OF OSCILLATORY ZONING IN PLAGIOCLASE WITH NONLINEAR PARTITION RELATION

We present a nonlinear dynamical model for oscillatory zoning in plagi oclase based on a simple isothermal constitutive undercooling mechanis m. A phenomenological partitioning is introduced to relate the concent ration of An in the melt at the interface with the concentration in th e solid. The non-linearities in the model result from the coupling of the growth velocity with the local An concentration and from the bound ary condition at the interface. The consideration of a nonlinear bound ary condition is new and generalizes previous nonlinear growth models. It is shown that parameter values exist for which oscillatory solutio ns are possible via a Hopf bifurcation. As the system is driven furthe r out of equilibrium, the model shows the development of chaotic solut ions via a period-doubling sequence.