论文标题
形状优化stokes流中刚体的巨大电阻张量条目
Shapes optimising grand resistance tensor entries for a rigid body in a Stokes flow
论文作者
论文摘要
我们研究了在Stokes流动中运动的刚体的水动力耐药性的最佳形状。在这种低雷诺数制度中，对象的流体动力阻力特性是用大电阻张量中包含的有限参数编码的。将这些参数视为要优化的目标函数，我们使用变化技术的计算来得出一般形状衍生式公式，从而可以指定如何变形体形以提高任何给定的电阻张量输入的目标值。然后，我们描述一种用于数值计算优化形状的实用算法，并将其应用于几个示例。数值结果揭示了有趣的新几何形状时，在优化对强度张量的双基因分子输入时，包括在最大化流体动力和旋转运动之间的耦合时出现手性螺旋形状。这项工作具有良好的适应性适应性，为对微生物的形态功能以及微功能设备设计的未来进步铺平了道路。
We investigate the optimal shapes of the hydrodynamic resistance of a rigid body set in motion in a Stokes flow. In this low Reynolds number regime, the hydrodynamic drag properties of an object are encoded in a finite number of parameters contained in the grand resistance tensor. Considering these parameters as objective functions to be optimised, we use calculus of variations techniques to derive a general shape derivative formula, allowing to specify how to deform the body shape to improve the objective value of any given resistance tensor entry. We then describe a practical algorithm for numerically computing the optimized shapes and apply it to several examples. Numerical results reveal interesting new geometries when optimizing the extra-diagonal inputs to the strength tensor, including the emergence of a chiral helical shape when maximising the coupling between the hydrodynamic force and the rotational motion. With a good level of adaptability to different applications, this work paves the way for a new analysis of the morphological functionality of microorganisms and for future advances in the design of microswimmer devices.
