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曲面物理和力学:最佳基本微分算子对

DOI: 10.6052/1000-0879-12-218, PP. 1-7

Keywords: 曲面物理和力学,经典梯度,形状梯度,最佳基本微分算子对

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Abstract:

曲面物理和力学中有两个独立的基本微分算子(即"基本微分算子对").本文综述如下主题在所有的基本微分算子对中,经典梯度▽(···)和形状梯度▽(···)的配对[[▽,▽]]是最佳的.具体内容包括(1)基本微分算子对的形式并不唯一;(2)内积的可交换性确立了[[▽,▽]]优于其他基本微分算子对的"最佳"地位;(3)基于[[▽,▽]]可以最佳地构造曲面物理和力学的高阶标量微分算子,因而[[▽,▽]]是构造曲面物理和力学微分方程的最佳"基本砖块";(4)[[▽,▽]]在软物质曲面物理和力学中普遍存在.

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