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- W2018286884 abstract "Asymptotic analysis and finite-element simulations are used to explore the nonlinear dynamics present in cellular interface patterns that arise in thin-film directional solidification, as caused by the presence of a codimension-two bifurcation at a specific value of the spatial wavelength for the cells. For certain parameter sets, the quadratic nonlinearities that dominate the dynamics because of 2:1 spatial resonance give rise to secondary steady-state bifurcation and to time-periodic states with periods that scale as ${mathrm{ensuremath{delta}}}^{mathrm{ensuremath{-}}3/2}$, where ensuremath{delta} measures the distance from the parameter values for the codimension-two state. The structure of this dynamics is explored in closed form for a modified Swift-Hohenberg equation and for the two-sided, solutal model for directional solidification. The asymptotic results for directional solidification are verified by finite-element numerical simulations for small amplitude cells." @default.
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- W2018286884 date "1994-05-01" @default.
- W2018286884 modified "2023-10-16" @default.
- W2018286884 title "Long-time-scale dynamics observed in directional solidification of a binary alloy" @default.
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- W2018286884 doi "https://doi.org/10.1103/physrevb.49.12724" @default.
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