US-Cameroon Cooperative Research: Pade Approximants and the Physics of Waves

该奖项支持高露洁大学物理和天文学系的Prabasaj Paul教授和喀麦隆Buea大学物理系的Daniel Nkemzi教授之间为期两年的合作研究项目。他们将研究Pade近似在电磁波散射问题和具有最大带隙的光子材料中的应用。粗糙表面的电磁波散射问题在物理学和数学的许多分支中都具有重要意义。使用一些强大的数学技术，多点Pade近似，两位研究人员将研究波在具有非常大的粗糙度参数的不平坦表面上的散射，以及光通过具有空间变化的折射率的区域的传输。散射矩阵的Pade近似将保持两个重要的性质，即互易性和么正性。研究人员预计，他们的模型将比现有的基于经典扰动序列的数学模型产生更好的结果。这项研究结合了Paul教授在凝聚态物质和量子物理方面的专业知识和Nkemzi教授在应用数学方面的知识，主要是在波传播方面。研究结果有望增加关于粗糙表面的波散射的新知识，并将应用于数学和物理的许多领域。

0218015PaulThis award supports a two-year collaborative research project between Professor Prabasaj Paul, with the Department of Physics and Astronomy at Colgate University, and Professor Daniel Nkemzi, with the Department of Physics at the University of Buea, in Cameroon. They will investigate the application of Pade approximants to the problems of scattering of electromagnetic waves, and of photonic materials with maximal bandgaps. The problem of electromagnetic wave scattering from rough surfaces is important to many branches of physics and mathematics. Using some powerful mathematical techniques, the multipoint Pade approximants, the two researchers will investigate the scattering of waves off uneven surfaces with very large roughness parameters, as well as the transmission of light through regions with a spatially varying refractive index. The Pade approximants of the scattering matrix will preserve two important properties, reciprocity and unitarity. The investigators expect their model to yield better results than existing mathematical models that are based on a classical perturbation series. The study combines Professor Paul's expertise in condensed matter and quantum physics with Professor Nkemzi's knowledge of applied mathematics, principally in wave propagation.The results are expected to add new knowledge about wave scattering from rough surfaces, and will have application to many areas of mathematics and physics.