Equilibrium shapes of microparacrystals in chain hydrocarbons and ammonia catalysts

Polymer ◽  
1979 ◽  
Vol 20 (9) ◽  
pp. 1091-1094 ◽  
Author(s):  
R. Hosemann ◽  
F.J. Baltá-Calleja
Keyword(s):  
Equilibrium Shapes

Common volume functions and diffraction line profiles of polyhedral domains

2012 ◽  
Vol 45 (6) ◽  
pp. 1162-1172 ◽  
Author(s):  
Alberto Leonardi ◽  
Matteo Leoni ◽  
Stefano Siboni ◽  
Paolo Scardi
Keyword(s):  
Diffraction Pattern ◽  
Excellent Agreement ◽  
Numerical Algorithm ◽  
Theoretical Description ◽  
Fast Computation ◽  
Line Profiles ◽  
Cubic Materials ◽  
Equilibrium Shapes ◽  
The Common ◽  
Volume Functions

A general numerical algorithm is proposed for the fast computation of the common volume function (CVF) of any polyhedral object, from which the diffraction pattern of a corresponding powder can be obtained. The theoretical description of the algorithm is supported by examples ranging from simple equilibrium shapes in cubic materials (Wulff polyhedra) to more exotic non-convex shapes, such as tripods or hollow cubes. Excellent agreement is shown between patterns simulated using the CVF and the corresponding ones calculated from the atomic positionsviathe Debye scattering equation.

Mechanics of membrane–membrane adhesion

2011 ◽  
Vol 16 (8) ◽  
pp. 872-886 ◽  
Author(s):  
Ashutosh Agrawal
Keyword(s):  
Lipid Vesicles ◽  
Spontaneous Curvature ◽  
Interface Conditions ◽  
Point Boundary ◽  
Lagrange Equations ◽  
Equilibrium Conditions ◽  
Numerical Studies ◽  
Curvature Elasticity ◽  
Equilibrium Shapes ◽  
Membrane Adhesion

Curvature elasticity is used to derive the equilibrium conditions that govern the mechanics of membrane–membrane adhesion. These include the Euler–Lagrange equations and the interface conditions which are derived here for the most general class of strain energies permissible for fluid surfaces. The theory is specialized for homogeneous membranes with quadratic ‘Helfrich’-type energies with non-uniform spontaneous curvatures. The results are employed to solve four-point boundary value problems that simulate the equilibrium shapes of lipid vesicles that adhere to each other. Numerical studies are conducted to investigate the effect of relative sizes, osmotic pressures, and adhesion-induced spontaneous curvature on the morphology of adhered vesicles.

Equilibrium Shapes and Vibrations of Thin Elastic Rod

1987 ◽  
Vol 56 (7) ◽  
pp. 2309-2324 ◽  
Author(s):  
Hideo Tsuru
Keyword(s):  
Elastic Rod ◽  
Equilibrium Shapes ◽  
Thin Elastic Rod

scholarly journals Equilibrium Shapes of Large Trans-Neptunian Objects

2017 ◽  
Vol 850 (1) ◽  
pp. L9 ◽  
Author(s):  
Nicolas Rambaux ◽  
Daniel Baguet ◽  
Frederic Chambat ◽  
Julie C. Castillo-Rogez
Keyword(s):  
Equilibrium Shapes

Equilibrium shapes and bifurcation of captive dielectric drops subjected to electric fields

1994 ◽  
Vol 33 (1) ◽  
pp. 61-86 ◽  
Author(s):  
A. Ramos ◽  
A. Castellanos
Keyword(s):  
Electric Fields ◽  
Equilibrium Shapes

Equilibrium shapes of acoustically levitated drops

1986 ◽  
Vol 79 (5) ◽  
pp. 1335-1338 ◽  
Author(s):  
Eugene H. Trinh ◽  
Chaur‐Jian Hsu
Keyword(s):  
Equilibrium Shapes

EQUIVALENCE OF THE TWO METHODS IN CALCULATING THE EQUILIBRIUM SHAPES OF CYLINDRICAL VESICLES

1999 ◽  
Vol 13 (16) ◽  
pp. 547-553
Author(s):  
SHAOGUANG ZHANG ◽  
ZHONGCAN OUYANG ◽  
JIXING LIU
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
The Other ◽  
General Shape ◽  
Calculus Of Variation ◽  
And Topology ◽  
Shape Equation ◽  
Equilibrium Shapes ◽  
Comparison Of The Results ◽  
The Relationship

So far, two methods are often used in solving the equilibrium shapes of vesicles. One method is by starting with the general shape equation and restricting it to the shapes with particular symmetry. The other method is by assuming the symmetry and topology of the vesicle first and treating it with the calculus of variation to get a set of ordinary differential equations. The relationship between these two methods in the case of cylindrical vesicles, and a comparison of the results are given.

The stability of pendent liquid drops. Part 2. Axial symmetry

1974 ◽  
Vol 63 (3) ◽  
pp. 487-508 ◽  
Author(s):  
E. Pitts
Keyword(s):  
Surface Tension ◽  
Energy Change ◽  
Maximum Volume ◽  
Experimental Conditions ◽  
Liquid Drops ◽  
Stable Equilibria ◽  
Equilibrium Shapes ◽  
The Stability ◽  
The Many ◽  
Horizontal Support

In a drop of liquid which hangs below a horizontal support or a t the end of a tube, the forces due to surface tension, pressure and gravity are in equilibrium. Amongst the many possible equilibrium shapes of the drop, only those which are stable occur naturally. The calculus of variations has been used to determine theoretically the stable equilibria, by calculating the energy change when the liquid in equilibrium experiences axially symmetrical perturbations under physically realistic constraints. If the energy change can be made negative, the drop is unstable. With this criterion, stable equilibria have been identified through which the naturally growing drops evolve until they reach a maximum volume, when they become unstable. These results are illustrated by calculations relating to typical experimental conditions.

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