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

波散射和衍射工程问题的概率随机游走解

• 批准号: 0408381
• 负责人: David Bogy
• 金额: $ 24万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-09-01 至 2007-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0408381&HistoricalAwards=false
• 关键词: Probabilistic; Random; Walk; Solutions; Engineering

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.

波散射和绕射工程问题的概率随机游走解。波的散射和衍射是声学、光学、电磁学和地震学中的重要现象。 例如，我们如何通过测量物体散射波的振幅和相位来识别物体的形状和大小？波散射的严格描述长期以来一直与繁琐的公式相关联，这些公式需要大量昂贵的计算和博士学位。水平知识。然而，这种情况可能很快就会改变，由于所提出的新方法的发展，波传播，提供数学上精确的解决方案，在一个简单的形式访问平均本科生，甚至高中生。这种波的研究方法直到世纪才发表，但它已经使人们有可能得到一些长期存在的问题的简单而严格的解决方案，包括任意角度的平面扇形屏衍射的3D问题，或任意形状的表面破裂腔和裂纹的半空间中声波衍射的2D问题。这里提出的研究包括进一步发展的方法，解决重要的应用问题和整合的方法在加州大学伯克利分校提供的研究生课程。