Displaying similar documents to “About stability of equilibrium shapes”

Shape Correspondence Analysis for Biomolecules Based on Volumetric Eigenfunctions

Tao Liao, Hao-Chih Lee, Ge Yang, Yongjie Jessica Zhang (2015)

Molecular Based Mathematical Biology

Similarity:

The functionality of biomolecules depends on their flexible structures, which can be characterized by their surface shapes. Tracking the deformation and comparing biomolecular shapes are essential in understanding their mechanisms. In this paper, a new spectral shape correspondence analysis method is introduced for biomolecules based on volumetric eigenfunctions. The eigenfunctions are computed from the joint graph of two given shapes, avoiding the sign flipping and confusion in the...

Function spaces and shape theories

Jerzy Dydak, Sławomir Nowak (2002)

Fundamenta Mathematicae

Similarity:

The purpose of this paper is to provide a geometric explanation of strong shape theory and to give a fairly simple way of introducing the strong shape category formally. Generally speaking, it is useful to introduce a shape theory as a localization at some class of “equivalences”. We follow this principle and we extend the standard shape category Sh(HoTop) to Sh(pro-HoTop) by localizing pro-HoTop at shape equivalences. Similarly, we extend the strong shape category of Edwards-Hastings...

On the ersatz material approximation in level-set methods

Marc Dambrine, Djalil Kateb (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a ersatz material approximation [Allaire , (2004) 363–393], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic...