Electromagnetically Driven Flow Between Concentric Spheres: Experiments and Simulations

2016 ◽  
pp. 253-264
Author(s):  
A. Figueroa ◽  
J. A. Rojas ◽  
J. Rosales ◽  
F. Vázquez
Keyword(s):  
Concentric Spheres

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.

The capacitance of a system of concentric spheres

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

Aristotle's Unmoved Movers

Traditio ◽  
1946 ◽  
Vol 4 ◽  
pp. 1-30 ◽  
Author(s):  
Philip Merlan
Keyword(s):  
Middle Ages ◽  
The Other ◽  
World Picture ◽  
The Earth ◽  
Concentric Spheres ◽  
The One ◽  
The Universe ◽  
The Middle Ages

According to Aristotle all heavenly movement is ultimately due to the activity of forty-seven (or fifty-five) ‘unmoved movers'. This doctrine is highly remarkable in itself and has exercised an enormous historical influence. It forms part of a world-picture the outlines of which are as follows. The universe consists of concentric spheres, revolving in circles. The outermost of these bears the fixed stars. The other either bear planets or, insofar as they do not, contribute indirectly to the movements of the latter. Each sphere is moved by the one immediately surrounding it, but also possesses a movement of its own, due to its mover, an unmoved, incorporeal being. (It was these beings which the schoolmen designated as theintelligentiae separatae.) The seemingly irregular movements of the planets are thus viewed as resulting from the combination of regular circular revolutions. The earth does not move and occupies the centre of the universe. Such was Aristotle's astronomic system, essential parts of which were almost universally adopted by the Arabic, Jewish, and Christian philosophers of the Middle Ages.

Capacitance of concentric spheres

1973 ◽  
Vol 8 (2) ◽  
pp. 122-123
Author(s):  
R Brown
Keyword(s):  
Concentric Spheres

Evaluation of Secondary Flow between Rotating Concentric Spheres Using a Perturbation Method

2021 ◽  
Vol 412 ◽  
pp. 49-72
Author(s):  
R. Leticia Corral Bustamante ◽  
Antonino H. Pérez ◽  
Alfredo L. Márquez
Keyword(s):  
Perturbation Method ◽  
Secondary Flow ◽  
Analytical Method ◽  
Analytic Solution ◽  
Previous Analysis ◽  
Secondary Flows ◽  
Newtonian Flow ◽  
New Approach ◽  
Concentric Spheres ◽  
Method Show

A new approach to evaluate the Newtonian flow between concentric rotating spheres is introduced in this paper. A general analytic solution to the problem is deduced using a perturbation method that takes into account the primary and secondary flows produced between the spheres, as well as an alternative analytical method. In order to exemplify the results of the previous analysis, six particular cases were studied. The results of the perturbation method show that under certain circumstances the secondary flow is no negligible, as is usually considered, but it is comparable to the value of the primary one. While the analytical method allows us to simulate the flow with results very similar to those of other authors.

scholarly journals On the Moving Trajectory of a Ball in a Viscous Liquid between Two Concentric Rigid Spheres

2018 ◽  
Vol 23 (4) ◽  
pp. 77
Author(s):  
Sergey Gladkov ◽  
Sophie Bogdanova
Keyword(s):  
Differential Equations ◽  
Coordinate System ◽  
Viscous Liquid ◽  
Nonlinear Differential Equations ◽  
Reaction Force ◽  
Arbitrary Point ◽  
System Of Equations ◽  
Rigid Spheres ◽  
Dynamic Motion ◽  
Concentric Spheres

In the paper, the dynamic motion of a point ball with a mass of m , sliding in a viscous liquid between two concentric spheres under the influence of gravity and viscous and dry resistance, is investigated. In addition, it is considered that the ball starts its motion from some arbitrary point M 0 = M ( θ 0 , φ 0 ) . A system of nonlinear differential equations in a spheroidal coordinate system is obtained for the angular variables θ and φ to account for all the forces acting on the ball. The dependence of the reaction force on the angular variables is found, and the solution of the resulting system of equations is numerically analyzed. The projections of the trajectories on the plane x − y ,   y − z ,   x − z are found.

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