Mathematical Sciences: Bounds and Estimates for the Effective Behavior of Inhomogeneous Materials: The Roles of Anisotrophy and Nonlinear Behavior

9510513 Olson这项工作得到了女性科学家和工程师研究规划补助金的支持。拟议研究的目的是阐明材料混合物的行为，特别是在各向异性或非线性行为起重要作用的情况下。有效介质理论和自洽近似已成功地用于预测线性和各向同性情况下的混合物的行为。新的近似提出了规避有效介质理论的一些缺点。将使用平均能量法而不是平均应力法。 国家科学基金会的任务是确保国家科学事业的活力，包括关注科学和工程人力资源基础的质量、组成、分布和有效性。 在这方面，基金会致力于提高妇女目前的参与率 在科学和工程职业生涯中，一般来说， 参与其所有项目。 研究规划补助金的发放：（1）帮助增加新妇女的人数 参与国家科学基金会研究项目的调查人员;（2）促进与以前没有独立的联邦研究基金的妇女制定竞争性研究项目和建议有关的初步研究和其他活动。 研究规划赠款是一次性奖励，可用于初步工作，以确定拟议的调查路线的可行性，和/或其他活动，将促进提案的发展。

9510513 Olson This work is supported by a Research Planning Grant for Women Scientists and Engineers Award. The purpose of the proposed research is to shed light on the behavior of mixtures of materials, particularly in cases where anisotropy or nonlinear behavior plays an important role. Effective medium theories and the self-consistent approximations have been successfully used to pridict behavior of mixtures in linear and isotropic situations. New approximations are proposed which circumvent some of the drawbacks of the effective medium theories. An average energy approach rather than an average stress approach will be used. The National Science Foundations mandate to ensure the vitality of the Nations scientific enterprise includes concern for the quality, composition, distribution and effectiveness of the human resource 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 NSFs research programs; and, (2) to facilitate preliminary studies and other activities related to the development of competitive research projeats 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.