scholarly journals Transitions between streamline topologies of structurally stable Hamiltonian flows in multiply connected domains

2015 ◽  
Vol 307 ◽  
pp. 22-41 ◽  
Author(s):  
Takashi Sakajo ◽  
Tomoo Yokoyama
Keyword(s):  
Multiply Connected Domains ◽  
Multiply Connected ◽  
Hamiltonian Flows ◽  
Structurally Stable

scholarly journals Word representation of streamline topologies for structurally stable vortex flows in multiply connected domains

2013 ◽  
Vol 469 (2150) ◽  
pp. 20120558 ◽  
Author(s):  
Tomoo Yokoyama ◽  
Takashi Sakajo
Keyword(s):  
Stream Function ◽  
Contour Plot ◽  
Hamiltonian Vector Field ◽  
Multiply Connected Domains ◽  
Two Dimensional ◽  
Inviscid Flows ◽  
Multiply Connected ◽  
Word Representation ◽  
Multiple Obstacles ◽  
Structurally Stable

Let us consider incompressible and inviscid flows in two-dimensional domains with multiple obstacles. The instantaneous velocity field becomes a Hamiltonian vector field defined from the stream function, and it is topologically characterized by the streamline pattern that corresponds to the contour plot of the stream function. The present paper provides us with a procedure to construct structurally stable streamline patterns generated by finitely many point vortices in the presence of the uniform flow. Starting from some basic structurally stable streamline patterns in a disc of low genus, i.e. a disc with a small number of holes, we repeat some fundamental operations that append a streamline pattern by increasing one genus to them. Owing to the inductive procedure, one can assign a sequence of operations as a representing word to each structurally stable streamline pattern. We also give the canonical expression for the word representation, which allows us to make a catalogue of all possible structurally stable streamline patterns in a combinatorial manner. As an example, we show all streamline patterns in the discs of genus 1 and 2.

Conformal and Quasiconformal Mappings of Close Multiply-Connected Domains

2002 ◽  
Vol 9 (2) ◽  
pp. 367-382
Author(s):  
Z. Samsonia ◽  
L. Zivzivadze
Keyword(s):  
Integral Equations ◽  
Quasiconformal Mappings ◽  
Multiply Connected Domains ◽  
Multiply Connected

Abstract Doubly-connected and triply-connected domains close to each other in a certain sense are considered. Some questions connected with conformal and quasiconformal mappings of such domains are studied using integral equations.

scholarly journals Eigenvalues of the negative Laplacian for arbitrary multiply connected domains

1996 ◽  
Vol 19 (3) ◽  
pp. 581-586
Author(s):  
E. M. E. Zayed
Keyword(s):  
Boundary Conditions ◽  
Spectral Function ◽  
Three Dimensions ◽  
Bounded Domains ◽  
Multiply Connected Domains ◽  
Multiply Connected ◽  
Asymptotic Formulae ◽  
Negative Laplacian

The purpose of this paper is to derive some interesting asymptotic formulae for spectra of arbitrary multiply connected bounded domains in two or three dimensions, linked with variation of positive distinct functions entering the boundary conditions, using the spectral function∑k=1∞{μk(σ1,…,σn)+P}−2asP→∞. Further results may be obtained.

Conformal parameterization for multiply connected domains: combining finite elements and complex analysis

2013 ◽  
Vol 30 (4) ◽  
pp. 441-455 ◽  
Author(s):  
Everett Kropf ◽  
Xiaotian Yin ◽  
Shing-Tung Yau ◽  
Xianfeng David Gu
Keyword(s):  
Finite Elements ◽  
Complex Analysis ◽  
Multiply Connected Domains ◽  
Multiply Connected

Shape Interrogation by Medial Axis Transform

1990 ◽  
Author(s):  
N. M. Patrikalakis ◽  
H. N. Gursoy
Keyword(s):  
Finite Element ◽  
Medial Axis ◽  
Multiply Connected Domains ◽  
Medial Axis Transform ◽  
Curved Boundaries ◽  
Multiply Connected ◽  
Maximum Thickness ◽  
Surface Patches ◽  
Geometric Representations ◽  
Shape Characteristics

Abstract In this paper we develop a new interrogation method based on the medial axis transform to extract some important global shape characteristics from geometric representations. These shape characteristics include constrictions, maximum thickness points, and associated length scales; isolation of holes and their proximity information; and a set of topologically simple subdomains decomposing a complex domain. The algorithm we develop to compute the medial axis transform of planar multiply connected shapes with curved boundaries can automatically identify these characteristics. Higher level algorithms for generation of finite element meshes of planar multiply connected domains, adaptive triangulation and approximation of trimmed curved surface patches and other engineering applications using the medial axis transform are also discussed.

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