转变水力动力学超材料:严格论证形式不变性和具有空间方差的结构设计
Physical review. E
|June 17, 2023
概括
转换光学可以操纵物理场,但通常不是与纳维埃-斯托克斯方程. 然而,滑近似允许Hele-Shaw流的形状不变性,从而使水力动力学超材料设计成为可能.
科学领域:
- 流体动力学 流体动力学
- 超材料是什么?超材料是什么?
- 转换光学是指转换光学.
背景情况:
- 变换光学利用形式不变的规律方程来操纵物理场.
- 最近的努力探索将转换光学应用于由纳维埃-斯托克斯方程控制的水力动力学超材料.
- 对纳维埃-斯托克斯方程的变换光学适用性缺乏严格的分析.
研究的目的:
- 建立转换光学中形状不变性的标准.
- 确定转换光学对纳维埃-斯托克斯方程和相关流体方程的适用性.
- 根据形状不变的流体模型,提出水力动力学元材料的设计.
主要方法:
- 推导出一种形式不变的标准,涉及到米度和亲系连接.
- 分析了纳维埃-斯托克斯和斯托克斯方程的形式不变性.
- 根据滑近似 (Hele-Shaw模型) 对形状不变性进行研究的爬行流.
- 拟议的多层结构具有空间变化的细胞深度.
主要成果:
- 纳维埃-斯托克斯方程和斯托克斯方程缺乏形式不变性,这是由于粘性术语中的亲缘连接.
- 在滑近似 (Hele-Shaw模型) 下的爬行流显示形式不变.
- 在空间上变化的细胞深度可以模仿Hele-Shaw流的异构剪切粘度.
- 证明了滑近似在实现形状不变性方面的关键作用.
结论:
- 转换光学一般不适用于纳维埃-斯托克斯方程.
- 滑近似是水力动态元材料设计中形式不变性的关键.
- 拟议的设计提供了一种可行的方法,用于实验性制造水力动力超材料.
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