Topology of Three Dimensional Manifolds and the Embedding Problems in Minimal Surface Theory

1980 ◽  
Vol 112 (3) ◽  
pp. 441 ◽  
Author(s):  
William H. Meeks ◽  
Shing-Tung Yau
Keyword(s):  
Minimal Surface ◽  
Three Dimensional ◽  
Surface Theory

Unsteady Lifting Surface Theory for a Rotating Cascade of Swept Blades

1989 ◽  
Author(s):  
Hidekazu Kodama ◽  
Masanobu Namba
Keyword(s):  
Three Dimensional ◽  
Acoustic Power ◽  
Aerodynamic Characteristics ◽  
Blade Loading ◽  
Surface Theory ◽  
Numerical Examples ◽  
Lifting Surface ◽  
Blade Flutter ◽  
Annular Cascade ◽  
Remarkable Reduction

A lifting surface theory is developed to predict the unsteady three-dimensional aerodynamic characteristics for a rotating subsonic annular cascade of swept blades. A discrete element method is used to solve the integral equation for the unsteady blade loading. Numerical examples are presented to demonstrate effects of the sweep on the blade flutter and on the acoustic field generated by interaction of rotating blades with a convected sinusoidal gust. It is found that increasing the sweep results in decrease of the aerodynamic work on vibrating blades and also remarkable reduction of the modal acoustic power of lower radial orders for both forward and backward sweeps.

Application of Lifting-Surface Theory to the Prediction of Hydroelastic Response of Hydrofoil Boats

1968 ◽  
Vol 12 (04) ◽  
pp. 286-301
Author(s):  
C. J. Henry
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Mode Shapes ◽  
Operator Technique ◽  
Elastic Mode ◽  
Surface Theory ◽  
Lifting Surface ◽  
Modes Of Vibration ◽  
Elastic Modes

In this report a theoretical procedure is developed for the prediction of the dynamic response elastic or rigid body, of a hydrofoil-supported vehicle in the flying condition— to any prescribed transient or periodic disturbance. The procedure also yields the stability indices of the response, so that dynamic instabilities such as flutter can also be predicted. The unsteady hydrodynamic forces are introduced in the equations of motion for the elastic vehicle in terms of the indicia I pressure-response functions, which are de rived herein from lifting-surface theory. Thus, the predicted vehicle-response includes the effects of three-dimensional unsteady flow conditions at specified forward speed. The natural frequencies and elastic modes of vibration of the vehicle and foil system in the absence of hydrodynamic effects are presumed known. A numerical procedure is presented for the solution of the downwash integral equations relating the unknown indicial pressure distributions to the specified elastic-mode shapes. The procedure is based on use of the generalized-lift-operator technique together with the collocation method.

A Survey on Classical Minimal Surface Theory

2012 ◽  
Author(s):  
William Meeks ◽  
Joaquín Pérez
Keyword(s):  
Minimal Surface ◽  
Surface Theory

Development and Industrial Application of the “All-Over-Controlled Vortex Distribution Method” for Designing Radial and Mixed Flow Impellers

1992 ◽  
Author(s):  
S. J. Wang ◽  
M. J. Yuan ◽  
G. Xi ◽  
S. X. Liu ◽  
D. T. Qi ◽  
...  
Keyword(s):  
Flow Field ◽  
Centrifugal Compressor ◽  
Inverse Method ◽  
Three Dimensional ◽  
Industrial Applications ◽  
Mixed Flow ◽  
Distribution Method ◽  
Stream Surface ◽  
Surface Theory ◽  
Performance Curves

Sixteen years ago an inverse method of designing radial, mixed flow impellers was proposed by the first author of this paper, which was based on a quasi-three-dimensional stream surface theory. The contradictions between the full controlling of the flow field in the whole impeller and the designed bables’ smooth machinability can be perfectly resolved with the above method (So it is called “all-over-controlled vortex distribution method”). This paper presents the developments and industrial applications of the above method in the last decade. Two single centrifugal compressor model stages with the 3-D impellers designed by this method are studied in detail, and several performance curves of the multistage centrifugal compressors designed by this method are also presented.

scholarly journals A generalization of a completeness lemma in minimal surface theory

2014 ◽  
Vol 37 (2) ◽  
pp. 506-517
Author(s):  
Yûsuke Okuyama ◽  
Katsutoshi Yamanoi
Keyword(s):  
Minimal Surface ◽  
Surface Theory
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