We deal with the time-harmonic acoustic waves scattered by a large number of small holes, with radius a, a≪1, arbitrarily distributed in a bounded part of the homogeneous background R3. We assume no periodicity in distributing these holes. Using the asymptotic expansions of the scattered field by this cluster, we show that as their number M grows following the law M∼a−s, a→0, the collection of these holes has one of the following behaviors: (1) if s<1, then the scattered fields tend to vanish as a tends to zero, i.e., the cluster is a soft one. (2) if s=1, then the cluster behaves as an equivalent medium modeled by a refraction index, supported in a given bounded domain Ω, which is described by certain geometry properties of the holes and their local distribution. The cluster is a moderate (or intermediate) one. (3) if s>1, with additional conditions, then the cluster behaves as a totally reflecting extended body, modeled by a bounded domain Ω, i.e., the incident waves are totally reflected by the surface of this extended body. The cluster is a rigid one. Explicit errors estimates between the scattered fields due to the cluster of small holes and the ones due to equivalent media (i.e., the refraction index) or the extended body are provided.

中文翻译：

---

一簇小孔散布的声场的特征

我们处理由大量小孔散射的时间谐波声波，半径为a，1，任意分布在均匀背景R3的有界部分中。我们假设没有周期性分布这些漏洞。使用该簇的散射场的渐近展开，我们表明，随着它们的数目M遵循定律M〜a-s，a→0增长，这些孔的集合具有以下行为之一：（1）如果s <1，则散射场趋向于消失，趋向于零，即群集是一个柔软的群集。（2）如果s = 1，则该团簇的行为相当于由折射率建模的等效介质，并在给定的有界域Ω中进行支持，这由孔的某些几何特性及其局部分布来描述。集群是中等（或中等）集群。（3）如果s> 1，在附加条件下，团簇表现为一个全反射的扩展物体，由有界域Ω建模，即入射波被该扩展物体的表面完全反射。集群是一个刚性的集群。提供了由于小孔簇引起的散射场与由于等效介质（即折射率）或扩展体引起的散射场之间的显式误差估计。