Minimization of instabilities in growing interfaces: a variational approach.
The Mullins-Sekerka and the electric breakdown instabilities are well known to lead to the spontaneous formation of a variety of complex spatial structures, among them dendritic crystal shapes, and treelike electric discharge patterns. Controlling such systems by suppressing predominantly excited solutions offers the opportunity to manipulate and stabilize these patterns in a defined way for a wide range of technological applications. In this work, we employ a variational approach which enables one to systematically search for the ideal conditions under which the patterns grow, but where interfacial deformations are efficiently minimized. The effectiveness of our variational control method is illustrated via linear stability calculations on both two-dimensional and three-dimensional contour-dynamics models for crystal growth and electric discharge phenomena.
Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
Eduardo O
EO
Dias
Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
José A
JA
Miranda