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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 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.

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Figure 1: A comparison of the Saffman–Taylor finger shape with the shape of a cell in directional solidification.
Figure 2: Shapes of cells in an array in directional solidification.

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Acknowledgements

This work was supported by the Office of Microgravity, NASA, and funded through the Marshall Space Flight Center.

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Correspondence to Rohit Trivedi.

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Trivedi, R., Liu, S. & Williams, S. Interface pattern formation in nonlinear dissipative systems. Nature Mater 1, 157–159 (2002). https://doi.org/10.1038/nmat749

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