MORPHOLOGICAL TRANSITIONS IN LAPLACIAN GROWTH WITH VARIABLE ANISOTROPY

A model of deterministic Laplacian growth with variable anisotropy is simulated an a square lattice. Upon changing a parameter alpha that co ntrols the amount of anisotropy, three clearly distinct morphologies a ppear, separated by sharp transitions. The model is also shown to desc ribe a problem of fluid invasion in a regular array of chambers connec ted by pores, in which case alpha is related to the relative volume of pores and chambers. Particular cases of this model include the usual bond- and site noise reduction cases of the infinite noise reduction m odels of Laplacian growth, whose relation to fluid invasion is discuss ed. The transitions found here can be described as splitting-merging o f dendrites, a phenomenon that has been qualitatively observed in many systems. Two different mechanisms are responsible for the transitions in this model: One of them (splitting transition) is due to the fact that the dendrites originally growing along the main axes become unsta ble and split. The other transition (screening transition) occurs beca use two stable morphologies compete due to long-range screening. Each transition has an associated characteristic length, which is found to diverge at the critical point. The noiseless character and large latti ce sizes of the simulations here presented allow the determination of critical indices associated with these morphological phase transitions , in a similar way to what is done in the case of thermodynamical phas e transitions. The growth velocity is found to behave continuously acr oss one of the transitions and discontinuously across the other. The r ole of the long range screening in producing this difference is discus sed. A phenomenological model is proposed to describe the role of scre ening, which predicts both the existence of a divergent length and a d iscontinuity in the growth velocity.