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Volume 16, Issue 5
On Field Concentration Between Nearly-Touching Multiscale Inclusions in the Quasi-Static Regime

Youjun Deng, Lingzheng Kong, Hongyu Liu & Liyan Zhu

Adv. Appl. Math. Mech., 16 (2024), pp. 1252-1276.

Published online: 2024-07

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  • Abstract

Strong field concentration may occur between two nearly-touching high-contrast material inclusions due to an incident field. The degree of concentration is characterised by the blowup rate of the underlying gradient field. This phenomenon has received considerable attention in the literature due to its practical implications in the theory of composite materials. However, most of the existing studies are concerned with the static cases. In this paper, we present a comprehensive numerical investigation of this intriguing phenomenon associated to the Helmholtz system in the quasi-static frequency regime. On the one hand, we present extensive numerical results to corroborate the theoretical findings in [16], and on the other hand, we derive new findings that cannot be handled by the theoretical analysis yet. Our focus is on the static effect, frequency effect, the geometric (curvature) effect to the gradient estimates.

  • AMS Subject Headings

35J25, 35C20, 78A40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-16-1252, author = {Deng , YoujunKong , LingzhengLiu , Hongyu and Zhu , Liyan}, title = {On Field Concentration Between Nearly-Touching Multiscale Inclusions in the Quasi-Static Regime}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {16}, number = {5}, pages = {1252--1276}, abstract = {

Strong field concentration may occur between two nearly-touching high-contrast material inclusions due to an incident field. The degree of concentration is characterised by the blowup rate of the underlying gradient field. This phenomenon has received considerable attention in the literature due to its practical implications in the theory of composite materials. However, most of the existing studies are concerned with the static cases. In this paper, we present a comprehensive numerical investigation of this intriguing phenomenon associated to the Helmholtz system in the quasi-static frequency regime. On the one hand, we present extensive numerical results to corroborate the theoretical findings in [16], and on the other hand, we derive new findings that cannot be handled by the theoretical analysis yet. Our focus is on the static effect, frequency effect, the geometric (curvature) effect to the gradient estimates.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0104}, url = {http://global-sci.org/intro/article_detail/aamm/23293.html} }
TY - JOUR T1 - On Field Concentration Between Nearly-Touching Multiscale Inclusions in the Quasi-Static Regime AU - Deng , Youjun AU - Kong , Lingzheng AU - Liu , Hongyu AU - Zhu , Liyan JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1252 EP - 1276 PY - 2024 DA - 2024/07 SN - 16 DO - http://doi.org/10.4208/aamm.OA-2023-0104 UR - https://global-sci.org/intro/article_detail/aamm/23293.html KW - Field concentration, gradient estimates, Helmholtz system, high-contrast inclusions, blow up, quasi-static, multi-scale, curvature. AB -

Strong field concentration may occur between two nearly-touching high-contrast material inclusions due to an incident field. The degree of concentration is characterised by the blowup rate of the underlying gradient field. This phenomenon has received considerable attention in the literature due to its practical implications in the theory of composite materials. However, most of the existing studies are concerned with the static cases. In this paper, we present a comprehensive numerical investigation of this intriguing phenomenon associated to the Helmholtz system in the quasi-static frequency regime. On the one hand, we present extensive numerical results to corroborate the theoretical findings in [16], and on the other hand, we derive new findings that cannot be handled by the theoretical analysis yet. Our focus is on the static effect, frequency effect, the geometric (curvature) effect to the gradient estimates.

Deng , YoujunKong , LingzhengLiu , Hongyu and Zhu , Liyan. (2024). On Field Concentration Between Nearly-Touching Multiscale Inclusions in the Quasi-Static Regime. Advances in Applied Mathematics and Mechanics. 16 (5). 1252-1276. doi:10.4208/aamm.OA-2023-0104
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