Mathematical Sciences: Mathematical Studies of Wave Propagation

数学科学：波传播的数学研究

• 批准号: 9510492
• 负责人: Cheryl Hile
• 金额: $ 1.79万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-15 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9510492&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Wave; Propagation

9510492 Hile This work is supported by a Research Planning Grant for Women Scientists and Engineers Award. The goal of the research is two-fold: (i) to understand which higher-order dispersive and nonlinear effects cause the asymmetry apparent in certain one-dimensional solutions of Maxwell's equations describing ultra-short optical soliton-like pulses, and to determine if a corresponding extended nonlinear Schroedinger equation can be developed to describe the asymmetric pulses produced in pulse- compression experiments; and (ii) to determine the physical parameters responsible for the divergence or collapse of two-dimensional ultra-short spatial solitons propagating in a planar waveguide. The project will also involve planning activities in collaboration with a senior mathematician from industry to determine the feasibility of developing an innovative technique for efficiently predicting high-frequency radar cross-section statistics for realistic, complex targets. Over the last decade, optical fiber communication systems have played a vital role in revolutionizing the telecommunications industry. Though this technology has progressed very rapidly, advances continue to be made in the design of these systems. Areas of current research in the field, which hold great interest and challenge for mathematicians, involve physical phenomena and processes that exploit the nonlinear effects in optical materials. These physical phenomena and processes include optical solitons, optical pulse compression, and optical switching. This project will involve goals and planning activities that include developing and analyzing mathematical models of these nonlinear phenomena and processes in order to improve the design of optical communications systems. The National Science Foundation's mandate to ensure the vitality of the Nation's scientific enterprise includes concern for the quality, composition, distribution and effectiveness of the human resou rce base in science and engineering. Within this context, the Foundation is committed to enhancing the current rate of participation of women in science and engineering careers, in general, and as active participants in all of its programs. Research Planning Grant awards are made: (1) to help increase the number of new women investigators participating in NSF's research programs; and, (2) to facilitate preliminary studies and other activities related to the development of competitive research projects and proposals by women who have not previously had independent Federal research funding. Research Planning Grants are one-time awards that may be used for preliminary work to determine the feasibility of a proposed line of inquiry, and/or for other activities that will facilitate proposal development.

小行星9510492 这项工作得到了女科学家研究规划补助金的支持 工程师奖。 研究的目标有两个方面：（一） 了解哪些高阶色散和非线性效应导致 麦克斯韦方程某些一维解的不对称性 方程描述超短光孤子脉冲，并确定 如果相应的扩展非线性薛定谔方程可以 描述脉冲压缩实验中产生的非对称脉冲; 2确定脉冲压缩实验中的物理参数 导致了二维超短脉冲的发散或崩溃 空间孤子在平面波导中的传播。 该项目还将 涉及与高级数学家合作的规划活动 从行业来确定开发创新的可行性 用于有效预测高频雷达截面的技术 针对现实复杂目标的统计数据。 在过去的十年中，光纤通信系统发挥了重要作用。 在电信业革命中发挥着重要作用。 虽然这 技术发展非常迅速，在以下方面继续取得进展： 这些系统的设计。 该领域目前的研究领域， 对数学家们来说是巨大的兴趣和挑战，涉及物理 利用光学非线性效应的现象和过程 材料. 这些物理现象和过程包括光学 孤子、光脉冲压缩和光开关。 该项目将 涉及目标和计划活动，包括开发和分析 这些非线性现象和过程的数学模型， 以改进光通信系统的设计。 国家科学基金会的任务是确保 国家的科学事业包括对质量，成分， 科学和技术领域人力资源基础的分配和有效性 工程. 在此背景下，基金会致力于加强 目前妇女参与科学和工程的比例 职业生涯，一般来说，并作为其所有计划的积极参与者。 研究规划补助金的颁发：（1）帮助增加 新的女性研究人员参与国家科学基金会的研究计划;以及， (2)促进与《公约》有关的初步研究和其他活动， 由妇女制定有竞争力的研究项目和建议， 以前没有独立的联邦研究基金。 研究 规划赠款是一次性奖励，可用于前期工作 确定拟议调查路线的可行性，和/或其他 有助于提案制定的活动。