Identification and Classification of Off-Vertex Critical Points for Contour Tree Construction on Unstructured Meshes of Hexahedra

2021 ◽  
pp. 1-1
Author(s):  
Marius Klaus Koch ◽  
Paul H J Kelly ◽  
Peter Vincent
Keyword(s):  
Critical Points ◽  
Unstructured Meshes ◽  
Tree Construction ◽  
Contour Tree

scholarly journals Proposal for the classification of critical points by order

1973 ◽  
Vol 44 (1) ◽  
pp. 25-26 ◽  
Author(s):  
T.S. Chang ◽  
A. Hankey ◽  
H.E. Stanley
Keyword(s):  
Critical Points

scholarly journals On solutions of the Chazy equation

2021 ◽  
pp. 51-59
Author(s):  
Kiryl G. Atrokhau ◽  
Elena V. Gromak
Keyword(s):  
Differential Equation ◽  
Critical Points ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Elliptic Functions ◽  
Third Order ◽  
Chazy Equation ◽  
Painlevé Property ◽  
Necessary And Sufficient

The Chazy system determines the necessary and sufficient conditions for the absence of movable critical points of solutions of the particular third order differential equation that was considered by Chazy in one of the first papers on the classification of higher-order ordinary differential equations with respect to the Painlevé property. The solution of the complete Chazy system in the case of constant poles has been already obtained. However, the question of integrating the Chazy equation remained open until now. In this paper, we prove that in the case of constant poles, under some additional conditions, this equation is integrated in elliptic functions.

On the Existence and the Classification of Critical Points for Non-Smooth Functionals

1995 ◽  
Vol 47 (4) ◽  
pp. 684-717 ◽  
Author(s):  
G. Fang
Keyword(s):  
Critical Point ◽  
Critical Points ◽  
Metric Space ◽  
Critical Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Topological Properties ◽  
Smooth Case ◽  
Continuous Functionals

AbstractWe extend the min-max methods used in the critical point theory of differentiable functionals on smooth manifolds to the case of continuous functionals on a complete metric space. We study the topological properties of the min-max generated critical points in this new setting by adopting the methodology developed by Ghoussoub in the smooth case. Many old and new results are extended and unified and some applications are given.

scholarly journals Qualitative Analysis of the Dynamics of a Two-Component Chiral Cosmological Model

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 195
Author(s):  
Viktor Zhuravlev ◽  
Sergey Chervon
Keyword(s):  
Asymptotic Behavior ◽  
Cosmological Model ◽  
Qualitative Analysis ◽  
Critical Points ◽  
Scalar Fields ◽  
Two Component ◽  
Different Types ◽  
Asymptotic Dynamics

We present a qualitative analysis of chiral cosmological model (CCM) dynamics with two scalar fields in the spatially flat Friedman–Robertson–Walker Universe. The asymptotic behavior of chiral models is investigated based on the characteristics of the critical points of the selfinteraction potential and zeros of the metric components of the chiral space. The classification of critical points of CCMs is proposed. The role of zeros of the metric components of the chiral space in the asymptotic dynamics is analysed. It is shown that such zeros lead to new critical points of the corresponding dynamical systems. Examples of models with different types of zeros of metric components are represented.

scholarly journals Some examples of critical points for the total mean curvature functional

2000 ◽  
Vol 43 (3) ◽  
pp. 587-603 ◽  
Author(s):  
Josu Arroyo ◽  
Manuel Barros ◽  
Oscar J. Garay
Keyword(s):  
Critical Points ◽  
Mean Curvature ◽  
Space Form ◽  
Total Curvature ◽  
Constant Scalar Curvature ◽  
Real Space ◽  
Closed Curves ◽  
Three Sphere ◽  
Total Mean Curvature

AbstractWe study the following problem: establish existence and classification of closed curves which are critical points for the total curvature functional, defined on spaces of curves in a Riemannian manifold. This problem is completely solved in a real space form. Next, we give examples of critical points for this functional in a class of metrics with constant scalar curvature on the three sphere. Also, we obtain a rational one-parameter family of closed helices which are critical points for that functional in ℂℙ2 (4) when it is endowed with its usual Kaehlerian structure. Finally, we use the principle of symmetric criticality to get equivariant submanifolds, constructed on the above curves, which are critical points for the total mean curvature functional.

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