Displaying similar documents to “Asymptotic Analysis of the Shape and Composition of Alloy Islands in Epitaxial Solid Films”

Shape Correspondence Analysis for Biomolecules Based on Volumetric Eigenfunctions

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

Molecular Based Mathematical Biology

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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...

Existence and uniqueness for the three-dimensional thermoelasticity system in shape memory problems

Irena Pawłow, Antoni Żochowski (2003)

Banach Center Publications

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A thermodynamically consistent model of shape memory alloys in three dimensions is studied. The thermoelasticity system, based on the strain tensor, its gradient and the absolute temperature, generalizes the well-known one-dimensional Falk model. Under simplifying structural assumptions we prove global in time existence and uniqueness of the solution.

Mesh Generation and Flexible Shape Comparisons for Bio-Molecules

Zhanheng Gao, Reihaneh Rostami, Xiaoli Pang, Zhicheng Fu, Zeyun Yu (2016)

Molecular Based Mathematical Biology

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Novel approaches for generating and comparing flexible (non-rigid) molecular surface meshes are developed. The mesh-generating method is fast and memory-efficient. The resulting meshes are smooth and accurate, and possess high mesh quality. An isometric-invariant shape descriptor based on the Laplace- Beltrami operator is then explored for mesh comparing. The new shape descriptor is more powerful in discriminating different surface shapes but rely only on a small set of signature values....

Multi-phase structural optimization via a level set method

G. Allaire, C. Dapogny, G. Delgado, G. Michailidis (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the optimal distribution of several elastic materials in a fixed working domain. In order to optimize both the geometry and topology of the mixture we rely on the level set method for the description of the interfaces between the different phases. We discuss various approaches, based on Hadamard method of boundary variations, for computing shape derivatives which are the key ingredients for a steepest descent algorithm. The shape gradient obtained for a sharp interface involves...

On the ersatz material approximation in level-set methods

Marc Dambrine, Djalil Kateb (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

Function spaces and shape theories

Jerzy Dydak, Sławomir Nowak (2002)

Fundamenta Mathematicae

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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...