Symmetry Properties of Confined Convective States
نویسنده
چکیده
This paper is a commentary on the experimental observation observations of Bensimon et al. [1] of convection of a binary fluid mixture in a fluid annulus. They observed a convective pattern that is time periodic, but with non-zero amplitude confined to a stationary sector of the annulus. The symmetry properties of this state are paradoxical. There is no subgroup of the spatio-temporal symmetry group of the experiment that preserves the confined state, but different aspects of the confined states can be associated with different symmetry subgroups. Solutions to a model partial differential equation are displayed here which are reminiscent of the confined states observed in the experiments of Bensimon et al. The convection experiments that motivate this work were conducted with ethyl alcohol water mixtures in a “thin” annulus. The height and crosssectional width of the annulus were comparable and much smaller than the circumference of the annulus. The states observed at the onset of convection are patterns of approximately fifty rolls that propagate at uniform speed as traveling waves. By first decreasing the Rayleigh number when the fluid is in a state of uniform traveling waves and increasing it again, Bensimon et al. were able to stabilize a pattern of traveling waves that was confined to a sector of the annulus. In one sector of the annulus, the fluid was conducting while, in the complementary sector, the fluid propagated as a pattern of rolls moving with constant speed from one boundary point of the sector to the other.
منابع مشابه
Dispersion of passive tracers in a confined convective flow
A confined convective flow is experimentally studied at different Rayleigh numbers. Particle Tracking Velocimetry (PTV) technique is used both to reconstruct Lagrangian trajectories and to evaluate Eulerian flow field. Dispersion properties of the flow are investigated by means of Lagrangian statistics on particle displacements. For each run of the experiment, single particle statistics have be...
متن کاملConvective effects on a propagating reaction front
Unstable concentration gradients inherent in traveling chemical waves can give rise to buoyancy-driven convection, altering the speed of the wave. When an excitable Belousov– Zhabotinsky reaction system is confined within a sufficiently narrow, vertical two-dimensional channel, convection arises at a symmetry-breaking bifurcation point. The observed linear rate of change of wave speed with the ...
متن کاملA DFT study of the nuclear magnetic properties of fullerenes
The stable configurations, electronic structure and magnetic properties of B16N16, B8C24, Al and P inserted (BC3)8 was studied by performing density functional theory (DFT) calculations of the NMR parameters. The results indicate that B8C24 has semiconductivity property and be effectively modified by inserti...
متن کاملInvestigation of electron and hydrogenic-donor states confined in a permeable spherical box using B-splines
Effects of quantum size and potential shape on the spectra of an electron and a hydrogenic-donor at the center of a permeable spherical cavity have been calculated, using linear variational method. B-splines have been used as basis functions. By extensive convergence tests and comparing with other results given in the literature, the validity and efficiency of the method were confirmed.
متن کامل