小物体对多体波的散射及其应用
Many-body wave scattering by small bodies and applications
摘要：
本文将多体波散射问题严格地归结为求解一个线性代数方程组，避开了通常的积分方程组。考虑了无限多个小粒子嵌入介质的极限情况，导出了介质中场的极限方程。阻抗边界条件施加在小物体的边界上。Neumann边界条件（声学硬粒子）的情况下也被认为是。应用程序创建所需的折射系数的材料。它被证明，通过嵌入适当数量的小颗粒每单位体积的原始材料与适当的边界阻抗，可以创建一个新的材料与任何所需的折射系数。控制方程是一个标量亥姆霍兹方程，它是通过对波动方程进行傅里叶变换而得到的。
英文摘要：
A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting case of infinitely many small particles embedded into a medium is considered and the limiting equation for the field in the medium is derived. The impedance boundary conditions are imposed on the boundaries of small bodies. The case of Neumann boundary conditions (acoustically hard particles) is also considered. Applications to creating materials with a desired refraction coefficient are given. It is proved that by embedding suitable number of small particles per unit volume of the original material with suitable boundary impedances one can create a new material with any desired refraction coefficient. The governing equation is a scalar Helmholtz equation, which one obtains by Fourier transforming the wave equation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
