Probabilistic Random Walk Solutions of Engineering Problems in Wave Scattering and Diffraction

加州大学伯克利分校NSF提案#0408381波散射和绕射是声学、光学、电磁学和地震中的重要现象。例如，我们如何识别一个物体的形状和大小，测量它散射的波的幅度和相位？长期以来，对波散射的严格描述一直与繁琐的公式有关，这些公式需要大量昂贵的计算和博士水平的知识。然而，由于拟议的波传播新方法的发展，这种情况可能很快就会改变，这种方法以一种普通本科生甚至高中生都能接触到的简单形式提供数学上的精确解。这种研究波浪的方法直到21世纪才发表，但它已经使人们有可能得到许多长期存在的问题的简单而严格的解，包括任意角度的平面扇形屏幕的三维绕射问题，或者带有表面破裂的空穴和任意形状的裂纹的半空间中声波的二维绕射问题。这里提出的研究包括进一步发展该方法，解决重要的应用问题，并将该方法整合到加州大学伯克利分校提供的研究生课程中。

AbstractProbablistic Random Walk Solutions of Engineering Problems in Wave Scattering and DiffractionDavid B. Bogy, UC BerkeleyNSF Proposal #0408381Wave scattering and diffraction are important phenomena in acoustics, optics, electromagnetics and earthquakes. For example, how do we identify the shape and size of an object measuring the amplitudes and phases of the waves it scatterers? The rigorous description of wave scattering has long been associated with cumbersome formulas that require large and expensive calculations and Ph.D. level knowledge. However, the situation may soon be changed due to the development of the proposed novel approach to wave propagation that provides mathematically exact solutions in a simple form accessible to average undergraduates or even high-school students. This approach to wave studies was not published until the 21st century, but it already has made it possible to get simple but rigorous solutions of a number of long-standing problems, including the 3D problem of diffraction by a plane sectorial screen of arbitrary angle, or the 2D problem of diffraction of acoustical waves in a half-space with surface breaking cavities and cracks of arbitrary shape. The research proposed here included further development of the method, solution of important applied problems and integration of the method into graduate courses offered at UC Berkeley.