TIME-PERIODIC SPATIALLY PERIODIC PLANFORMS IN EUCLIDEAN EQUIVARIANT PARTIAL-DIFFERENTIAL EQUATIONS
UNSPECIFIED. (1995) TIME-PERIODIC SPATIALLY PERIODIC PLANFORMS IN EUCLIDEAN EQUIVARIANT PARTIAL-DIFFERENTIAL EQUATIONS. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 352 (1698). pp. 125-168. ISSN 0962-8428Full text not available from this repository.
In Rayleigh-Benard convection, the spatially uniform motionless state of a fluid loses stability as the Rayleigh number is increased beyond a critical value. In the simplest case of convection in a pure Boussinesq fluid, the instability is a symmetry-breaking steady-state bifurcation that leads to the formation of spatially periodic patterns. However, in many double-diffusive convection systems, the heat-conduction solution actually loses stability via Hopf bifurcation. These hydrodynamic systems provide motivation for the present study of spatiotemporally periodic pattern formation in Euclidean equivariant systems. We call such patterns planforms.
We classify, according to spatio-temporal symmetries and spatial periodicity, many of the time-periodic solutions that may be obtained through equivariant Hopf bifurcation from a group-invariant equilibrium. Instead of focusing on planforms periodic with respect to a specified planar lattice, as has been done in previous investigations, we consider all planforms that are spatially periodic with respect to some planar lattice. Our classification results rely only on the existence of Hopf bifurcation and planar Euclidean symmetry and not on the particular differential equation.
|Item Type:||Journal Article|
|Journal or Publication Title:||PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES|
|Publisher:||ROYAL SOC LONDON|
|Official Date:||15 July 1995|
|Number of Pages:||44|
|Page Range:||pp. 125-168|
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