Challenges in Systems with Semctic and Nematic Order

具有近序和向列序的系统面临的挑战

基本信息

项目摘要

Proposal: DMS-0405853PI: Georg DolzmannInstitution: University of Maryland College ParkTitle: Challenges in Systems with Smectic and Nematic OrderABSTRACTMany physical systems that can be found both in nature and in modern technological applications possess internal degrees of freedom at a microscopic scale with tremendous impact on the macroscopic properties of the system. A lot of fundamental research has been directed in the past decades towards developing mathematical theories that allow one to `bridge the scales', i.e., to understand analytically the mechanisms that relate microscopic and macroscopic structures, to predict the response of these materials to applied forces, and to design algorithmic strategies that allow an efficient simulation of the system. A successful completion of this program would ultimately allow one to `tailor--make smart materials' for key--technological applications. The principal investigator plans to addresses key questions within this general framework with special emphasis on two particular systems with excellent potential for technological applications. The first system is a special class of elastomers that combine the entropic response of polymer networks with the orientational instabilities of liquid crystals. The other systems are lipid bilayer membranes (bio-membranes), which form the vast majority of all membranes in biological systems. The molecules in each of the layers tend to have a nematic order and are uniformly arranged in domains of macroscopic sizes. Key issues concern the influence of the internal structure of the two layers on the macroscopic shape and elasticity of the membranes, the formation of domains within the layer, and their stability. Potential applications include artificial blood cells and mechanisms for drug delivery. From the point of view of the general mathematical framework, this proposal is concerned with the analysis of variational problems that arise in the modeling of these systems and addresses questions of existence and regularity of solutions which are closely related to structural properties of the variational integrals. An improved understanding of the analytical aspects is also at the heart of efficient algorithms for the numerical simulation of the systems mentioned above, and it is expected that a combined analytical and numerical approach will lead to significant progress in the understanding of the complex physical systems.Many modern materials have striking elastic properties that allow novel technological applications. Frequently these surprising properties are related to internal degrees of freedom and patterns (so-called microstructures) that form in the materials at a scale much smaller than the size of the sample itself (nanoscale). This proposal aims at developing analytical and numerical tools for the prediction and simulation of these effects, with special emphasis on two particular systems, a class of rubber-type materials (with potential applications as artificial muscles or light guiding devices) and bio-membranes (possible applications include drug delivery mechanisms).
提案:DMS-0405853 PI:Georg Dolzmann机构:马里兰州大学帕克题目:近晶和向列有序系统的挑战摘要在自然界和现代技术应用中可以发现的许多物理系统都具有微观尺度的内部自由度,对系统的宏观性质具有巨大的影响。在过去的几十年里,许多基础研究都致力于发展数学理论,使人们能够“桥接尺度”,即,分析理解与微观和宏观结构相关的机制,预测这些材料对作用力的反应,并设计算法策略,以实现系统的有效模拟。该方案的成功完成将最终使人们能够为关键技术应用“量身定做智能材料”。首席研究员计划在这个总体框架内解决关键问题,特别强调两个具有良好技术应用潜力的特定系统。第一个系统是一类特殊的弹性体,它联合收割机了聚合物网络的熵响应和液晶的取向不稳定性。其他系统是脂质双层膜(生物膜),其形成生物系统中所有膜的绝大多数。每一层中的分子倾向于具有有序性,并且均匀地排列在宏观尺寸的区域中。关键问题涉及两层的内部结构对膜的宏观形状和弹性、层内域的形成及其稳定性的影响。潜在的应用包括人造血细胞和药物输送机制。从一般的数学框架的角度来看,这个建议是关注的变分问题的分析,出现在这些系统的建模和地址的存在性和规律性的解决方案,这是密切相关的变分积分的结构特性的问题。对分析方面的更好理解也是上述系统的数值模拟的有效算法的核心,预计分析和数值相结合的方法将导致对复杂物理系统的理解取得重大进展。许多现代材料具有惊人的弹性特性,允许新的技术应用。通常,这些令人惊讶的特性与材料中形成的内部自由度和图案(所谓的微观结构)有关,这些图案的尺度远小于样品本身的尺寸(纳米级)。该提案旨在开发用于预测和模拟这些效应的分析和数值工具,特别强调两个特定系统,一类橡胶类材料(具有人工肌肉或光导装置的潜在应用)和生物膜(可能的应用包括药物输送机制)。

项目成果

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Konstantina Trivisa其他文献

On the Motion of a Viscous Compressible Radiative-Reacting Gas
  • DOI:
    10.1007/s00220-006-1534-7
  • 发表时间:
    2006-03-09
  • 期刊:
  • 影响因子:
    2.600
  • 作者:
    Donatella Donatelli;Konstantina Trivisa
  • 通讯作者:
    Konstantina Trivisa
On a free boundary problem for polymeric fluids: global existence of weak solutions

Konstantina Trivisa的其他文献

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{{ truncateString('Konstantina Trivisa', 18)}}的其他基金

RTG: The Mathematics of Quantum Information Science
RTG:量子信息科学的数学
  • 批准号:
    2231533
  • 财政年份:
    2023
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
On the Dynamics of Nonlinear Systems in Applied Sciences: From Theory, Computations, and Experiments to Insights
应用科学中的非线性系统动力学:从理论、计算、实验到见解
  • 批准号:
    2008568
  • 财政年份:
    2020
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
On the Dynamics of Nonlinear Systems in Applied Sciences
应用科学中的非线性系统动力学
  • 批准号:
    1614964
  • 财政年份:
    2016
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
ON THE DYNAMICS, STRUCTURE AND STABILITY OF CERTAIN NONLINEAR SYSTEMS IN APPLIED SCIENCES
应用科学中某些非线性系统的动力学、结构和稳定性
  • 批准号:
    1211519
  • 财政年份:
    2012
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
ON THE DYNAMICS OF CERTAIN NONLINEAR SYSTEMS IN APPLIED SCIENCES: TRANSPORT, MOTION AND MIXING
应用科学中某些非线性系统的动力学:输运、运动和混合
  • 批准号:
    1109397
  • 财政年份:
    2011
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
On the Dynamics, Structure and Stability of Certain Nonlinear Systems in Applied Sciences
应用科学中某些非线性系统的动力学、结构和稳定性
  • 批准号:
    0807815
  • 财政年份:
    2008
  • 资助金额:
    --
  • 项目类别:
    Continuing Grant
PECASE: Systems of Conservation Laws and Related Models in Applied Sciences - Math Awareness and Outreach
PECASE:应用科学中的守恒定律体系和相关模型 - 数学意识和推广
  • 批准号:
    0239063
  • 财政年份:
    2003
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Hyperbolic Systems of Conservation Laws - Viscous Conservation Laws - Applications
守恒定律的双曲系统 - 粘性守恒定律 - 应用
  • 批准号:
    0196157
  • 财政年份:
    2000
  • 资助金额:
    --
  • 项目类别:
    Standard Grant
Hyperbolic Systems of Conservation Laws - Viscous Conservation Laws - Applications
守恒定律的双曲系统 - 粘性守恒定律 - 应用
  • 批准号:
    0072496
  • 财政年份:
    2000
  • 资助金额:
    --
  • 项目类别:
    Standard Grant

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