Photographic Studies of Convection Patterns Between Concentric Spheres

1965 ◽  
Vol 3 (2) ◽  
Author(s):  
E. H. Bishop ◽  
R. S. Kolflat ◽  
L. R. Mack ◽  
J. A. Scanlan
Keyword(s):  
Concentric Spheres ◽  
Convection Patterns ◽  
Photographic Studies

Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

1983 ◽  
Vol 41 ◽  
pp. 646-647
Author(s):  
Joseph A. Zasadzinski
Keyword(s):  
Liquid Crystalline ◽  
Freeze Fracture ◽  
Continuum Theory ◽  
Closed Surfaces ◽  
Straight Line ◽  
Low Weight ◽  
Concentric Spheres ◽  
Membrane Geometry ◽  
Dupin Cyclides ◽  
Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

Interactions between steady and oscillatory convection in mushy layers

2010 ◽  
Vol 645 ◽  
pp. 411-434 ◽  
Author(s):  
PETER GUBA ◽  
M. GRAE WORSTER
Keyword(s):  
Standing Waves ◽  
Mushy Layer ◽  
Two Dimensional ◽  
Oscillatory Convection ◽  
Mushy Layers ◽  
Theoretical Predictions ◽  
Convection Patterns ◽  
The Stability ◽  
Nonlinear Solutions ◽  
Steady Convection

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.

The capacitance of a system of concentric spheres

1972 ◽  
Vol 7 (8) ◽  
pp. 490-490
Author(s):  
A A Watson
Keyword(s):  
Concentric Spheres
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