scholarly journals The Plateau problem for convex curvature functions

2020 ◽  
Vol 70 (1) ◽  
pp. 1-66
Author(s):  
Graham Smith
Keyword(s):  
Plateau Problem ◽  
Convex Curvature

scholarly journals On the Levi-flat Plateau problem

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Jiří Lebl ◽  
Alan Noell ◽  
Sivaguru Ravisankar
Keyword(s):  
Plateau Problem ◽  
Flat Plateau

scholarly journals The affine Plateau problem

2005 ◽  
Vol 18 (2) ◽  
pp. 253-289 ◽  
Author(s):  
Neil S. Trudinger ◽  
Xu-Jia Wang
Keyword(s):  
Plateau Problem

scholarly journals Kohn-Rossi cohomology and its application to the complex plateau problem, II

2007 ◽  
Vol 77 (1) ◽  
pp. 135-148 ◽  
Author(s):  
Hing Sun Luk ◽  
Stephen S.-T. Yau
Keyword(s):  
Plateau Problem

scholarly journals On solving the plateau problem in parametric form

1983 ◽  
Vol 6 (2) ◽  
pp. 341-361
Author(s):  
Baruch cahlon ◽  
Alan D. Solomon ◽  
Louis J. Nachman
Keyword(s):  
Minimal Surface ◽  
Numerical Method ◽  
Minimal Surfaces ◽  
Plateau Problem ◽  
Parametric Form ◽  
First Variation ◽  
Plateau’S Problem ◽  
Numerical Example ◽  
Plateau's Problem ◽  
The First Variation

This paper presents a numerical method for finding the solution of Plateau's problem in parametric form. Using the properties of minimal surfaces we succeded in transferring the problem of finding the minimal surface to a problem of minimizing a functional over a class of scalar functions. A numerical method of minimizing a functional using the first variation is presented and convergence is proven. A numerical example is given.

Convex Curvature Effects on Film Cooling Adiabatic Effectiveness

2013 ◽  
Author(s):  
James R. Winka ◽  
Joshua B. Anderson ◽  
David G. Bogard ◽  
Michael E. Crawford ◽  
Emily J. Boyd
Keyword(s):  
Film Cooling ◽  
Suction Side ◽  
Surface Curvature ◽  
Radius Of Curvature ◽  
Exact Matching ◽  
Curvature Effects ◽  
Cooling Hole ◽  
Cylindrical Holes ◽  
Series Of Experiments ◽  
Convex Curvature

Surface curvature is known to have significant effects on film cooling performance, with convex curvature inducing increased film effectiveness and concave curvature causing decreased film effectiveness. Generally, these curvature effects have been presumed to scale with 2r/d at the film cooling hole location, where r is the radius of curvature and d is coolant hole diameter. In this study, the validity of this scaling of curvature effects are examined by performing experiments in regions of large and low curvature on a model vane. Single rows of cylindrical holes were placed at various locations along the high curvature section of the suction side of the vane. For the first series of experiments, a single row of holes was placed at two locations with different local surface curvature. The coolant hole diameters were then adjusted to match 2r/d values. Results from these experiments showed that there was better correspondence of film performance when using the 2r/d scaling, but there was not an exact matching of performance. A second series of experiments focused on evaluating the effects of curvature downstream of the coolant holes. One row of holes was placed at a position upstream of the highest curvature, while another row was placed at a downstream position such that the radius of curvature was equivalent for the two rows of holes. Results indicated that the local radius of curvature is not sufficient in understanding the performance of film cooling. Instead, the curvature envelope downstream of the coolant holes plays a significant role on the performance of film cooling for cylindrical holes.

The impact of streamwise convex curvature on the supersonic turbulent boundary layer

2017 ◽  
Vol 29 (11) ◽  
pp. 116106 ◽  
Author(s):  
Qian-cheng Wang ◽  
Zhen-guo Wang ◽  
Yu-xin Zhao
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Convex Curvature ◽  
The Impact
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