Hydrodynamics of Liquid Crystals and Extremum Problems for Eigenvalues

液晶流体动力学和特征值极值问题

基本信息

  • 批准号:
    1501000
  • 负责人:
  • 金额:
    $ 62.5万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2015
  • 资助国家:
    美国
  • 起止时间:
    2015-06-01 至 2020-05-31
  • 项目状态:
    已结题

项目摘要

This proposal is for a deep theoretical study on a class of complex fluids including both the liquid crystals which have been widely used in display devices and charged biological fluids which are extremely important in modern medicine and life sciences. Of particular interests are their intriguing and complex dynamical phenomena as well as formations of patterns and singularities. The modeling, analysis and simulations involved in understanding these complex fluids are theoretically very important and challenging. It needs new ideas and methods, and hence it would advance our knowledge which would be applicable to many other scientific problems as well.More specifically, the proposal consists of two parts. The first part is to study partial differential equations that describe the hydrodynamics of liquid crystals and related complex fluid models. The main focus of this part of the research will be to study global existence of suitable weak solutions of liquid crystal flows in the Ericksen-Leslie theory; the global existence of solutions of Oldroyd B-model of incompressible visco-elastic fluids; the inviscid incompressible magneto-hydrodynamic system and, in general, coupled nonlinear dynamics of fluids with other geometric objects. The second part is to study a large class of extremum problems of elliptic eigenvalues. Such problems also arise in optimal designs, pattern formations and other applications in material sciences and condense matter physics. The partial differential equations (PDE) that the PI plans to study involve nonlinear couplings between equations that describe transport, phase-field, mapping or geometric object's evolutions and that of Navier Stokes equations. They may be of both parabolic and hyperbolic nature and possess singularities or multiple scales. The variational problems for eigenvalues and eigenfunctions that linked with underlying domains are classical and fundamental. These are fascinating and challenging problems that require new ideas and methods, which could lead to new directions of research or programs in the analysis of PDE and calculus of variations. The proposed research activity is an important and integral part of the PI's training program of under-graduate, graduate, and post-doctoral students.
本论文的目的是对一类复杂流体进行深入的理论研究,这类复杂流体既包括在显示器件中广泛应用的液晶,也包括在现代医学和生命科学中极为重要的带电生物流体。特别感兴趣的是他们的有趣和复杂的动力学现象,以及形成的模式和奇点。理解这些复杂流体所涉及的建模、分析和模拟在理论上非常重要且具有挑战性。它需要新的思想和方法,因此,它将促进我们的知识,这将适用于许多其他科学问题。第一部分是研究描述液晶流体力学的偏微分方程和相关的复杂流体模型。这部分研究的主要重点是研究Ericksen-Leslie理论中液晶流动的整体弱解的存在性;不可压缩粘弹性流体的Oldroyd B模型的整体解的存在性;无粘不可压缩磁流体动力学系统以及一般情况下流体与其他几何对象的耦合非线性动力学。第二部分研究了一大类椭圆型特征值的极值问题。这些问题也出现在最佳设计,图案形成和材料科学和凝聚态物理学中的其他应用中。PI计划研究的偏微分方程(PDE)涉及描述输运、相场、映射或几何对象演化的方程与Navier Stokes方程之间的非线性耦合。它们可以是抛物线和双曲线性质的,并且具有奇异性或多重尺度。与区域相关的特征值和特征函数的变分问题是经典的基本问题。这些都是迷人的和具有挑战性的问题,需要新的思想和方法,这可能会导致新的研究方向或程序在偏微分方程和变分分析。拟议的研究活动是PI的本科生,研究生和博士后学生培训计划的重要组成部分。

项目成果

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Fang-Hua Lin其他文献

The singular set of an energy minimizing map fromB 4 toS 2
  • DOI:
    10.1007/bf02567926
  • 发表时间:
    1990-12-01
  • 期刊:
  • 影响因子:
    0.600
  • 作者:
    Robert Hardt;Fang-Hua Lin
  • 通讯作者:
    Fang-Hua Lin
Plateau's problem for H-convex curves
  • DOI:
    10.1007/bf01277607
  • 发表时间:
    1987-12-01
  • 期刊:
  • 影响因子:
    0.600
  • 作者:
    Fang-Hua Lin
  • 通讯作者:
    Fang-Hua Lin

Fang-Hua Lin的其他文献

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{{ truncateString('Fang-Hua Lin', 18)}}的其他基金

Hydrodynamics of Liquid Crystals and Heat Flow of Harmonic Maps
液晶的流体动力学和谐波图的热流
  • 批准号:
    2247773
  • 财政年份:
    2023
  • 资助金额:
    $ 62.5万
  • 项目类别:
    Standard Grant
Calculus of Variations and Partial Differential Equations
变分和偏微分方程微积分
  • 批准号:
    1955249
  • 财政年份:
    2020
  • 资助金额:
    $ 62.5万
  • 项目类别:
    Standard Grant
Analysis of Complex Fluids and Moving Phase Boundaries
复杂流体和移动相边界的分析
  • 批准号:
    1159313
  • 财政年份:
    2012
  • 资助金额:
    $ 62.5万
  • 项目类别:
    Continuing Grant
FRG: Collaborative Research: Emerging issues in the sciences involving non standard diffusion
FRG:协作研究:涉及非标准扩散的科学中的新问题
  • 批准号:
    1065964
  • 财政年份:
    2011
  • 资助金额:
    $ 62.5万
  • 项目类别:
    Standard Grant
Analysis on Faddeev, Skyrme and Some Complex Fluid Models
Faddeev、Skyrme及一些复杂流体模型分析
  • 批准号:
    0700517
  • 财政年份:
    2007
  • 资助金额:
    $ 62.5万
  • 项目类别:
    Continuing Grant
Analysis of Topological Singularities and Their Dynamics
拓扑奇点及其动力学分析
  • 批准号:
    0201443
  • 财政年份:
    2002
  • 资助金额:
    $ 62.5万
  • 项目类别:
    Continuing Grant
Analysis of Defect Measures and Their Applications
缺陷测量分析及其应用
  • 批准号:
    9706862
  • 财政年份:
    1997
  • 资助金额:
    $ 62.5万
  • 项目类别:
    Continuing Grant
Analysis of Defect Measures and Their Applications
缺陷测量分析及其应用
  • 批准号:
    9896391
  • 财政年份:
    1997
  • 资助金额:
    $ 62.5万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Mathematical Theory of Liquid Crystals and Free Boundaries
数学科学:液晶和自由边界的数学理论
  • 批准号:
    9401546
  • 财政年份:
    1994
  • 资助金额:
    $ 62.5万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Presidential Young Investigator Award
数学科学:总统青年研究员奖
  • 批准号:
    9149555
  • 财政年份:
    1991
  • 资助金额:
    $ 62.5万
  • 项目类别:
    Continuing Grant

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研究和探索一维范德华材料中的Luttinger liquid物理和摩尔超晶格物理
  • 批准号:
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Design and Analysis of Structure Preserving Discretizations to Simulate Pattern Formation in Liquid Crystals and Ferrofluids
模拟液晶和铁磁流体中图案形成的结构保持离散化的设计和分析
  • 批准号:
    2409989
  • 财政年份:
    2024
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    $ 62.5万
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Lubrication by Lamellar Liquid Crystals - An in-situ investigation of thin films with Brewster Angle microscopy technology
层状液晶润滑 - 使用布鲁斯特角显微镜技术对薄膜进行原位研究
  • 批准号:
    EP/Y023277/1
  • 财政年份:
    2024
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Conference: 2023 Liquid Crystals GRC and GRS: Learning from Nature to Transform Technology through Liquid Crystal Science
会议:2023 液晶 GRC 和 GRS:向自然学习,通过液晶科学转变技术
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    2318184
  • 财政年份:
    2023
  • 资助金额:
    $ 62.5万
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Hierarchically Ordered Structures by Frustration Design of Liquid Crystals and Its Functional Exploration
液晶的分层有序结构及其功能探索
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  • 财政年份:
    2023
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通过机器学习预测相变行为以解释分子排列及其在光功能液晶中的应用
  • 批准号:
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  • 财政年份:
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    $ 62.5万
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    Grant-in-Aid for JSPS Fellows
Flow-Induced Structures in Lyotropic Chromonic Liquid Crystals
溶致发色液晶中的流动诱导结构
  • 批准号:
    2245163
  • 财政年份:
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Mathematical Problems Modeling Nematic Liquid Crystals: from Macroscopic to Microscopic Theories
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