title: Interface pattern formation in nonlinear dissipative systems.
abstract: 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 pattern 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 science (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 Thomson. Two-dimensional finger-shaped patterns, observed in flame fronts and the ensembled average shape of the diffusion-limited aggregation pattern, have been shown to be similar to Saffman-Taylor finger shapes. 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.
authors.affiliation: Metals and Ceramics Sciences, Ames Laboratory (US-DOE) and Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011, USA. trivedi@ameslab.gov
authors.forename: Rohit
authors.initials: R
authors.lastname: Trivedi
authors.forename: Shan
authors.initials: S
authors.lastname: Liu
authors.forename: Scott
authors.initials: S
authors.lastname: Williams
mesh_terms: D000497:Alloys / Q000737:chemistry*; D002164:Camphor / Q000737:chemistry*; D008422:Materials Testing / Q000379:methods*; D008962:Models, Theoretical; D009570:Nitriles / Q000737:chemistry*; D017711:Nonlinear Dynamics; D012212:Rheology / Q000379:methods*; D012680:Sensitivity and Specificity; D013499:Surface Properties; D014783:Viscosity
chemical_list: D000497:Alloys; D009570:Nitriles; C010337:succinonitrile; D002164:Camphor