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Numerical exploration of the spiral state in the pattern formation of the Swift-Hohenberg equation on a sphere

Gotoh Fumitoshi Generalis Sotos C. Itano Tomoaki 30335187 関西大学

2021.03.20

概要

Spiral states are commonly observed in pattern formation on a sphere. Li et al.(Phys. Rev. E, Vol. 71, 016301 [2005]) previously proposed a method to generate the spiral states by adopting mixed modes with adjacent wavenumbers like l = l0, l0 + 1, as the initial condition of a time- developing numerical simulation. Herein, using the Swift-Hohenberg equation as an example, we show that Li’s empirical method can be successful only in particular regions of parameter space. Tracing the state by a continuation method generated from the static state via three symmetry breakings, the spiral state may be regarded as a resonant state generated by the combination of a few degenerate unstable modes with different azimuthal wave numbers.

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参考文献

[1] P. C. Matthews. Pattern formation on a sphere. Phys Rev E, 67(3):036206, 2003.

[2] C. M. R. Fowler. The solid earth, 2004.

[3] F. H. Busse. Patterns of convection in spherical shells. J Fluid Mech, 72(1):67–85, 1975.

[4] P. Zhang, K. Liao, and K. Zhang. Patterns in spherical rayleigh-b´enard convection: A giant spiral roll and its dislocations. Phys Rev E, 66:055203(R), 2002.

[5] L. Li, P. Zhang, X. Liao, and K. Zhang. Multiplicity of nonlinear thermal convection in a spherical shell. Phys Rev E, 71:016301, 2005.

[6] S. Rachel and P. Matthews. Symmetric spiral patterns on spheres. SIAM J. Applied Dynamical Systems, 10(3):1177–1211, 2011.

[7] T. Itano, T. Ninomiya, K. Konno, and M. Sugihara-Seki. J. Phys. Soc. Jpn, 84:103401, 2015.

[8] J. B. Swift and P.C. Hohenberg. Hydrodynamic fluctuations at the convective instability. Phys Rev A, 15:319–328, 1977.

[9] R. Gabbrielli. A new counter-example to kelvin’s conjecture on minimal surfaces. Philosophical Magazine Letters, 89:483–491, 2009.

[10] N. Schaeffer. Efficient spherical harmonic transforms aimed at pseudospectral numerical sim- ulations. Geochemistry,　Geophysics, Geosystems, 14(3):751–758, 2013.

[11] M. Frigo and S. G. Johnson. The design and implementation of FFTW3. Proceedings of the IEEE, 93(2):216–231, 2005. Special issue on “Program Generation, Optimization, and Platf orm Adaptation”.

[12] T. Akinaga, T. Itano, and S. Generalis. Symmetry breaking perturbative flows to retrieve resonant modes in plane shear layers. Arxiv preprint flu-dyn http://arxiv.org/abs/1503.02625, 2015.

[13] T. Akinaga, T. Itano, and S. Generalis. Convection induced by instabilities in the presence of a transverse seepage. Chaos, Solitons and Fractals, 91:533–543, 2016.

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