Letter abstract
Nature Materials 1, 157 - 159 (2002)
Published online: 13 October 2002 | doi:10.1038/nmat749
Subject Categories: Metals and alloys | Computation, modelling and theory
Interface pattern formation in nonlinear dissipative systems
Rohit Trivedi1, Shan Liu1 & Scott Williams1
The problem of interface pattern selection in nonlinear dissipative systems is critical in many fields of science, occurring in physical, chemical and biological systems. One of the simplest pattern formations is the Saffman–Taylor finger pattern1 that forms when a viscous fluid is displaced by a less viscous fluid. Such finger-shaped patterns have been observed in distinctly different fields of science2, 3, 4 (hydrodynamics, combustion and crystal growth) and this has led to a search for a unified concept of pattern formation, as first proposed by the classic work of D'arcy Thomson5. Two-dimensional finger-shaped patterns, observed in flame fronts6 and the ensembled average shape of the diffusion-limited aggregation pattern, have been shown to be similar to Saffman–Taylor finger shapes7, 8. Here we present experimental studies that establish that the cell shapes formed during directional solidification of alloys can be described by the form of the Saffman–Taylor finger shape equation when a second phase is present in the intercellular region.
- Metals and Ceramics Sciences, Ames Laboratory (US-DOE) and Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011, USA
Correspondence to: Rohit Trivedi1 e-mail: trivedi@ameslab.gov
