The point-interaction approximation for the fields generated by contrasted bubbles at arbitrary fixed frequencies

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Ammari, Habib¹  Challa, Durga Prasad²  Choudhury, Anupam Pal³  Sini, Mourad³ 

[1] Swiss Fed Inst Technol, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland

[2] Indian Inst Technol Tirupati, Fac Math, Tirupati, Andhra Pradesh, India

[3] Austrian Acad Sci, RICAM, Altenbergerstr 69, A-4040 Linz, Austria

关键词: Bubbly media;    Foldy-Lax approximation;    Effective medium theory;   

DOI  :  10.1016/j.jde.2019.03.010

来源: Elsevier

【 摘 要 】

We deal with the linearized model of the acoustic wave propagation generated by small bubbles in the harmonic regime. We estimate the waves generated by a cluster of M small bubbles, distributed in a bounded domain Omega, with relative densities having contrasts of the order a(beta), beta > 0, where a models their relative maximum diameter, a << 1. We provide useful and natural conditions on the number M, the minimum distance and the contrasts parameter beta of the small bubbles under which the point interaction approximation (called also the Foldy-Lax approximation) is valid. With the regimes allowed by our conditions, we can deal with a general class of such materials. Applications of these expansions in material sciences and imaging are immediate. For instance, they are enough to derive and justify the effective media of the cluster of the bubbles for a class of gases with densities having contrasts of the order a(beta), beta is an element of (3/2, 2) and in this case we can handle any fixed frequency. In the particular and important case beta = 2, we can handle any fixed frequency far or close (but distinct) from the corresponding Minnaert resonance. The cluster of the bubbles can be distributed to generate volumetric metamaterials but also low dimensional ones as metascreens and metawires. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free