Triangulation of Branching Contours Using Area Minimization

1998 ◽  
Vol 08 (04) ◽  
pp. 389-406 ◽  
Author(s):  
Mu Hong ◽  
Thomas W. Sederberg ◽  
Krzysztof S. Klimaszewski ◽  
Kazufumi Kaneda
Keyword(s):  
Surface Area ◽  
Piecewise Linear ◽  
New Method ◽  
Minimum Surface ◽  
Area Minimization ◽  
Current Algorithm ◽  
Minimum Surface Area ◽  
Minimal Area

This paper presents a new method for reconstructing piecewise linear surfaces from planar polygonal contours that branch. For non-branching contours, experience has shown that the piecewise linear surface of minimum surface area which connects a pair of contours often provides a good solution. The current algorithm extends this idea by searching for the surface of minimal area which connects two contours comprised of more than one polygon. Several examples that justify this heuristic are provided.

Geometry and Soap Bubbles

1964 ◽  
Vol 47 (364) ◽  
pp. 205-208
Author(s):  
R. W. Calvert
Keyword(s):  
Surface Area ◽  
Soap Films ◽  
Soap Bubbles ◽  
Minimum Surface ◽  
Minimum Surface Area

Owing to the tendency of soap films to form the minimum surface area the surfaces of bubbles are spherical and intersect at 120°.

ADSORPTION OF STERICALLY HINDERED PHENOLS ON CARBON

1959 ◽  
Vol 37 (8) ◽  
pp. 1235-1240 ◽  
Author(s):  
Owen H. Wheeler ◽  
Eric M. Levy
Keyword(s):  
Surface Area ◽  
Hydroxyl Group ◽  
Sterically Hindered Phenols ◽  
Freundlich Isotherms ◽  
Minimum Surface ◽  
Alkyl Groups ◽  
Hindered Phenols ◽  
Sterically Hindered ◽  
Minimum Surface Area

The Freundlich isotherms for the adsorption of some ortho-alkylated phenols on carbon from cyclohexane solution have been determined. The minimum surface area covered by the adsorbed phenols is compared with the area of the molecules themselves. Large alkyl groups ortho to the hydroxyl group greatly reduce the adsorption.

Polyhedral carbon nanofoams with minimum surface area partitions produced using silica nanofoams as templates

Carbon ◽  
2010 ◽  
Vol 48 (11) ◽  
pp. 3121-3130 ◽  
Author(s):  
Linda L. Hussami ◽  
Robert W. Corkery ◽  
Lars Kloo
Keyword(s):  
Surface Area ◽  
Minimum Surface ◽  
Minimum Surface Area

scholarly journals OPTIMIZATION OF VESSELS SIZES FROM THE CONDITIONS OF THE MINIMUM HULL SURFACE AREA

2020 ◽  
Vol 2018 (1) ◽  
pp. 61-63
Author(s):  
Sergey Scherbin ◽  
Bogdan Vnukov ◽  
Konstantin Gordeev
Keyword(s):  
Surface Area ◽  
Minimum Surface ◽  
Minimum Surface Area ◽  
Optimal Diameter

The method of optimization of vessels sizes for the reasons of the minimum surface area of the hull is considered. The dependences of the optimal diameter, height and minimum surface area of the tank body on the volume are obtained.

A New Method to Find the Forced Response of Nonlinear Systems with Dry Friction

2021 ◽  
Author(s):  
Gregory L. Altamirano ◽  
Meng-Hsuan Tien ◽  
Kiran D'Souza
Keyword(s):  
Dry Friction ◽  
Coulomb Friction ◽  
Nonlinear Response ◽  
Piecewise Linear ◽  
Time Integration ◽  
Nonlinear Behavior ◽  
Forced Response ◽  
New Method ◽  
Analysis Tools ◽  
Compatibility Constraint

Abstract Coulomb friction has an influence on the behavior of numerous mechanical systems. Coulomb friction systems or dry friction systems are nonlinear in nature. This nonlinear behavior requires complex and time demanding analysis tools to capture the dynamics of these systems. Recently, efforts have been made to develop efficient analysis tools able to approximate the forced response of systems with dry friction. The objective of this paper is to introduce a methodology that assists in these efforts. In this method, the piecewise-linear nonlinear response is separated into individual linear responses that are coupled together through compatibility constraint equations. The new method is demonstrated on a number of systems of varying complexity. The results obtained by the new method are validated through the comparison with results obtained by time integration. The computational savings of the new method is also discussed.

Analytical Results on a Chaotic Piecewise-Linear O.D.E.

1984 ◽  
Vol 39 (4) ◽  
pp. 342-348
Author(s):  
B. Uehleke ◽  
O. E. Rössler
Keyword(s):  
Analytical Methods ◽  
Hormonal Regulation ◽  
Piecewise Linear ◽  
New Method ◽  
Analytical Results

A variant to the well known Danziger-Elmergreen equation of hormonal regulation is analyzed geometrically by analytical methods. The new method of Poincaré half maps is employed. Several chaotic regimes are found.

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