Some Nonlinear PDEs from Material Science, Biological Sciences, and Fluid Mechanics

材料科学、生物科学和流体力学中的一些非线性偏微分方程

• 批准号: 0708479
• 负责人: Bo Su
• 金额: $ 9.7万
• 依托单位: Iowa State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0708479&HistoricalAwards=false
• 关键词: Some; Nonlinear; PDEs; Material; Science

Su0708479 The purpose of the project is to study several types ofnonlinear partial differential equations that arise in materialscience, solid mechanics, and cell biology. In particular, thegoals of project are to study the relation between a variety ofplate theories and three-dimensional elasticity theory byderiving the asymptotic limit of three-dimensional nonlinearelasticity, to justify the limit of a singularly perturbedfunctional as an Aviles-Giga functional, to investigate theevolution of interfaces in multi-phase polymer crystals growth byaddressing the stability of moving fronts, and to deepenunderstanding of the homogenization limit of parabolic equationsand of systems of elliptic equations in cell biology and polymersciences. The investigator studies nonlinear pertial differentialequations that describe important behaviors of systems inpolymers, materials, and cell biology. Clear understanding ofthe stability of moving interfaces helps control the interfacebetween the melt and crystal to ensure high quality of polymerproduction. Theoretical guided computation of the Young modulusin polymer nanocomposites is important to measure the strength ofmicro-packaging material for computer chips. Identifying thecorrected diffusion process for protein IP3 from cell membrane tohighly convoluted endoplastic reticulum can save huge amounts ofmoney and time in fundamental scientific research in cellbiology.

苏0708479 该项目的目的是研究材料科学、固体力学和细胞生物学中出现的几种非线性偏微分方程。 具体而言，本项目的目标是通过推导三维非线性弹性的渐近极限来研究各种板理论与三维弹性理论之间的关系，证明奇异摄动泛函作为Aviles-Giga泛函的极限，通过解决运动前沿的稳定性来研究多相聚合物晶体生长中界面的演化，并加深对细胞生物学和聚合物科学中抛物型方程和椭圆型方程组的均匀化极限的理解。 研究非线性微分方程，描述聚合物，材料和细胞生物学系统的重要行为。 清楚地认识运动界面的稳定性有助于控制熔体和晶体之间的界面，以确保高质量的聚合物生产。 聚合物纳米复合材料杨氏模量的理论指导计算对于计算机芯片微封装材料的强度测试具有重要意义。 确定蛋白质IP 3从细胞膜到高度卷曲的内质网的正确扩散过程可以节省大量的资金和时间在细胞生物学的基础科学研究。