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Long wavelength instabilities of perfectly square planforms in nonlinear convection

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Abstract

The long wavelength instabilities of square planforms are studied using amplitude equations which describe the general interaction of two orthogonal coupled roll patterns. In addition to the zig-zag, two-dimensional and three-dimensional Eckhaus instabilities, a truly three-dimensional rectangular instability is found. Nonlinear phase diffusion equations are derived close to the onset of the instabilities.

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Authors
  1. Rebecca B. Hoyle
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Additional information

University of Gambridge, Gambridge, United Kingdom. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 8, pp. 788–792, August, 1993.

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Hoyle, R.B. Long wavelength instabilities of perfectly square planforms in nonlinear convection. Radiophys Quantum Electron 36, 532–535 (1993). https://doi.org/10.1007/BF01038428

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  • DOI: https://doi.org/10.1007/BF01038428

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