F213 Rayleigh-Benard 対流における正六角形格子上のパターン形成 : 5 次の振幅方程式

概要

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Pattern formation in Rayleigh-Benard convection has been analyzed on a hexagonal lattice. We considered the convections with reflectional symmetry in the horizontal midplane and without it It is well-known that the cubic amplitude equations are not generic in the case where the convection has the reflectional symmetry. We derived the quintic amplitude equations of dimension six by means of the center manifold reduction in each case. The equations including the quintic non-linear terms correspond to the universal unfolding of the Γ_s-equivalent normal form under the symmetry group Γ_s=(D_6+T^2)〓Z_2. For Rayleigh-Benard convection with the density which is a quadratic function of the temperature, we numerically determined the coefficients included in the equations. It was clarified that rolls and hexagons are possible to be realized as stable primary bifurcation branches.
2002-07-23