Tangential Tensor Fields on Deformable Surfaces – How to Derive Consistent L2-Gradient Flows

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

IMA Journal of Applied Mathematics Pub Date : 2024-02-19 DOI:10.1093/imamat/hxae006

Ingo Nitschke, Souhayl Sadik, Axel Voigt

引用次数: 0

Abstract

We consider gradient flows of surface energies which depend on the surface by a parameterization and on a tangential tensor field. The flow allows for dissipation by evolving the parameterization and the tensor field simultaneously. This requires the choice of a notation for independence. We introduce different gauges of surface independence and show their consequences for the evolution. In order to guarantee a decrease in energy, the gauge of surface independence and the time derivative have to be chosen consistently. We demonstrate the results for a surface Frank-Oseen-Hilfrich energy.

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可变形曲面上的切向张量场--如何推导一致的 L2 梯度流

我们考虑的是表面能量的梯度流，它取决于表面的参数化和切向张量场。这种流动通过同时演化参数化和张量场来实现耗散。这就需要选择一个独立的符号。我们引入了表面独立性的不同量纲，并展示了它们对演化的影响。为了保证能量的减少，必须一致地选择表面独立性的量规和时间导数。我们演示了表面弗兰克-奥森-希尔弗里希能量的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IMA Journal of Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

24 months

期刊介绍： The IMA Journal of Applied Mathematics is a direct successor of the Journal of the Institute of Mathematics and its Applications which was started in 1965. It is an interdisciplinary journal that publishes research on mathematics arising in the physical sciences and engineering as well as suitable articles in the life sciences, social sciences, and finance. Submissions should address interesting and challenging mathematical problems arising in applications. A good balance between the development of the application(s) and the analysis is expected. Papers that either use established methods to address solved problems or that present analysis in the absence of applications will not be considered. The journal welcomes submissions in many research areas. Examples are: continuum mechanics materials science and elasticity, including boundary layer theory, combustion, complex flows and soft matter, electrohydrodynamics and magnetohydrodynamics, geophysical flows, granular flows, interfacial and free surface flows, vortex dynamics; elasticity theory; linear and nonlinear wave propagation, nonlinear optics and photonics; inverse problems; applied dynamical systems and nonlinear systems; mathematical physics; stochastic differential equations and stochastic dynamics; network science; industrial applications.