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

9510513奥尔森这项工作得到了女科学家和工程师奖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混合物在线性和各向同性情况下的行为。提出了新的近似方法，绕过了有效介质理论的一些缺陷。将使用平均能量方法，而不是平均压力方法。国家科学基金会的任务是确保联合国科学事业的活力，其中包括对科学和工程人力资源基础的质量、组成、分布和有效性的关注。在这一背景下，基金会致力于提高目前妇女在科学和工程职业中的参与率，并积极参与其所有方案。研究规划补助金的颁发有：(1)帮助增加参与国家科学基金会研究项目的新女性研究人员的数量；(2)促进与开发竞争性研究项目有关的初步研究和其他活动，以及由以前没有独立联邦研究资助的女性提出的建议。研究规划补助金是一种一次性奖励，可用于初步工作，以确定拟议调查路线的可行性，和/或用于促进提案制定的其他活动。

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.