A Mathematical Theory of Microscale Hydrodynamic Cloaking and Shielding by Electro-Osmosis

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-02-12 DOI:10.1137/23m1554837

Hongyu Liu, Zhi-Qiang Miao, Guang-Hui Zheng

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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 262-284, February 2024.
Abstract. In this paper, we develop a general mathematical framework for perfect and approximate hydrodynamic cloaking and shielding of electro-osmotic flow, which is governed by a coupled PDE system via the field-effect electro-osmosis. We first establish the representation formula of the solution of the coupled system using the layer potential techniques. Based on the Fourier series, the perfect hydrodynamic cloaking and shielding conditions are derived for the control region with the cross-sectional shape being an annulus or a confocal ellipses. Then we further propose an optimization scheme for the design of approximate cloaks and shields within general geometries. The well-posedness of the optimization problem is proved. In particular, the conditions that can ensure the occurrence of approximate cloaks and shields for general geometries are also established. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking and shielding.

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微尺度水动力隐形和电渗透屏蔽的数学理论

SIAM 应用数学杂志》第 84 卷第 1 期第 262-284 页，2024 年 2 月。摘要本文建立了电渗流完美和近似流体力学隐形和屏蔽的一般数学框架，电渗流受场效应电渗耦合 PDE 系统支配。我们首先利用层势技术建立了耦合系统解的表示公式。基于傅里叶级数，我们推导出了横截面形状为环形或共焦椭圆形的控制区域的完美流体力学隐形和屏蔽条件。然后，我们进一步提出了在一般几何形状下设计近似隐形和屏蔽的优化方案。我们证明了优化问题的拟合性。特别是，我们还确定了确保在一般几何形状下出现近似斗篷和防护罩的条件。我们的理论发现得到了各种数值结果的验证和补充。本文的结果还为更复杂的流体力学隐形和屏蔽提供了数学基础。

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

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.