Mathematical Sciences: Computations in Fluids and Materials
数学科学:流体和材料计算
基本信息
- 批准号:9707494
- 负责人:
- 金额:$ 23.1万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:1997
- 资助国家:美国
- 起止时间:1997-08-01 至 2001-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
9707494 Michael Shelley These projects concern dynamics and pattern formation in complex fluids, and singularity formation and topological transitions in Newtonian fluids. The first project considers the hydrodynamics of slender elastic filaments, such as arise in liquid crystal flows, the dynamics of phospho-lipid bilayer tubes, and in the dynamics of biological polymers. Building tractable computational models, that account for hydrodynamic interactions of the filament with itself, relies on discriminating exploitation of slenderness. This still gives a computationally intensive problem with high-order time-step constraints from elasticity, interaction integrals with singular kernels, and integral equations to be solved at every time-step. The second project continues towards an understanding of topological transitions of fluid/fluid interfaces between immiscible liquids. The fundamental questions are: How does surface tension provoke or mediate transitions? What characterizes the singularity? What physics needs to be added to follow the transition? And what is left of the singularity in its aftermath? Building upon previous work on such singularities in the Kelvin-Helmholtz instability between immiscible fluids, it is proposed to study, computationally and analytically, singularities and transitions in jets that separate immiscible fluids, both by using sharp interface models, and fluid models that have viscosity and allow some miscibility. The third project studies the effect of shear-thinning, a property shared with many non-Newtonian fluids and liquid crystal flows, on the development of the Saffman-Taylor instability. Some of the modelling work has already been done, yielding a natural non-Newtonian version of Darcy's law, relating the fluid velocity to the solution of a nonlinear elliptic problem. It is proposed to now simulate the full nonlinear dynamics of such a bubble expanding into a shear-thinning liquid. This is a very challenging comp utational problem as it involves the solution of nonlinear elliptic problems on an evolving domain. Much of the fundamental dynamics of fluids and materials -- singularity and pattern formation are two central examples -- will be understood by a progression from mathematical modelling, to developing computational methods and relevant mathematical understanding, and thence to large-scale simulation and data analysis through high-performance computing. The three projects to be pursued here all lie at the intersection of fluid dynamics and materials science, and all illustrate the above statement. In the first project, it is proposed to understand and simulate the dynamics of filamentary structures, as arise in phase transitions of liquid crystalline fluids, the dynamics of phospho-lipid bilayer tubes, and in the dynamics of biological polymers. In first example, such filaments are of potential technological importance in the manufacture of high-strength filaments. The second project continues towards a theoretical understanding of what drives the break-up into droplets of a jet of fluid into a second, different fluid (say, oil and water). While easy and common to observe, such behavior is strongly associated with surface tension, an effect that is still ill-understood, and yet lies at the heart of much basic fluid phenomena. This will be studied by a combination of modelling, analysis, and large-scale computation. The final project concerns the dynamics of shear-thinning liquids flowing in thin gaps. Such flows are important to display device design, and to injection molding. Of particular interest is the instability and pattern formation associated with a gas/liquid interface which is driven but mediated by surface tension. This is an extremely challenging computational problem, requiring the development of new simulational methods.
这些项目涉及复杂流体中的动力学和模式形成,以及牛顿流体中的奇点形成和拓扑转变。第一个项目考虑了细长弹性细丝的流体动力学,如液晶流动中的流体动力学,磷脂双层管的动力学,以及生物聚合物的动力学。建立可处理的计算模型,以解释细丝与自身的流体动力学相互作用,依赖于对细细的鉴别利用。这仍然是一个计算密集的问题,具有高阶时间步约束,从弹性,奇异核的相互作用积分,以及在每个时间步要求解的积分方程。第二个项目继续致力于了解不混相液体之间流体/流体界面的拓扑转变。最基本的问题是:表面张力是如何引发或调解过渡的?奇点的特征是什么?在转变之后需要添加什么物理元素?奇点发生后还剩下什么呢?在先前对非混相流体之间的开尔文-亥姆霍兹不稳定性的奇异性的研究基础上,提出了通过使用尖锐界面模型和具有粘度并允许一些混相的流体模型来研究分离非混相流体的射流中的奇异性和过渡的计算和分析方法。第三个项目研究剪切变薄对Saffman-Taylor不稳定性发展的影响,这是许多非牛顿流体和液晶流动所共有的特性。一些建模工作已经完成,产生了自然的非牛顿版本的达西定律,将流体速度与非线性椭圆问题的解联系起来。现在建议模拟这种气泡膨胀成剪切变薄液体的全部非线性动力学。这是一个非常具有挑战性的计算问题,因为它涉及到在一个演化域上求解非线性椭圆问题。许多流体和材料的基本动力学——奇点和模式形成是两个主要的例子——将通过数学建模,开发计算方法和相关的数学理解,进而通过高性能计算进行大规模模拟和数据分析来理解。这里要进行的三个项目都位于流体动力学和材料科学的交叉点,并且都说明了上述陈述。在第一个项目中,提出了理解和模拟细丝结构的动力学,如液晶流体的相变,磷脂双层管的动力学,以及生物聚合物的动力学。在第一个例子中,这种长丝在制造高强度长丝方面具有潜在的技术重要性。第二个项目继续从理论上理解是什么驱使一股流体的水滴分裂成另一种不同的流体(比如油和水)。虽然很容易观察到,但这种行为与表面张力密切相关,表面张力是一种尚未被理解的效应,但却是许多基本流体现象的核心。这将通过建模、分析和大规模计算的结合来研究。最后一个项目涉及在薄间隙中流动的剪切变薄液体的动力学。这种流动对显示装置设计和注射成型都很重要。特别令人感兴趣的是与气/液界面相关的不稳定性和模式形成,这是由表面张力驱动但介导的。这是一个极具挑战性的计算问题,需要开发新的模拟方法。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Michael Shelley其他文献
Instant Neural Radiance Fields
即时神经辐射场
- DOI:
10.1145/3532833.3538678 - 发表时间:
2022 - 期刊:
- 影响因子:0
- 作者:
T. Müller;Alex Evans;Christoph Schied;Marco Foco;A. Bódis;Isaac Deutsch;Michael Shelley;A. Keller - 通讯作者:
A. Keller
<em>C. Elegans</em> Chromosomes Connect to Centrosomes by Anchoring into the Spindle Network
- DOI:
10.1016/j.bpj.2017.11.2112 - 发表时间:
2018-02-02 - 期刊:
- 影响因子:
- 作者:
Stefanie Redemann;Johannes Baumgart;Norbert Lindow;Michael Shelley;Ehssan Nazockdast;Andrea Kratz;Steffen Prohaska;Jan Brugues;Sebastian Fürthauer;Thomas Müller-Reichert - 通讯作者:
Thomas Müller-Reichert
Michael Shelley的其他文献
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{{ truncateString('Michael Shelley', 18)}}的其他基金
Collaborative research: MODULUS: Nuclear envelope shape change coordination with chromosome segregation in mitosis in fission yeast
合作研究:MODULUS:核膜形状变化与裂殖酵母有丝分裂中染色体分离的协调
- 批准号:
2133261 - 财政年份:2022
- 资助金额:
$ 23.1万 - 项目类别:
Standard Grant
Collaborative Research: Multiscale engineering of active stress in biomaterials
合作研究:生物材料主动应力的多尺度工程
- 批准号:
2004469 - 财政年份:2020
- 资助金额:
$ 23.1万 - 项目类别:
Continuing Grant
Collaborative Research: Multiscale Study of Active Cellular Matter: Simulation, Modeling, and Analysis
合作研究:活性细胞物质的多尺度研究:模拟、建模和分析
- 批准号:
1620331 - 财政年份:2016
- 资助金额:
$ 23.1万 - 项目类别:
Standard Grant
Collaborative Research: Fracture in Soft Organic Solids -The Variational View
合作研究:软有机固体的断裂 - 变分视图
- 批准号:
1615839 - 财政年份:2016
- 资助金额:
$ 23.1万 - 项目类别:
Standard Grant
Collaborative Research: FRG: Understanding and Controlling Active Fluids through Modeling, Simulation, and Experiment
合作研究:FRG:通过建模、模拟和实验理解和控制活性流体
- 批准号:
1463962 - 财政年份:2015
- 资助金额:
$ 23.1万 - 项目类别:
Continuing Grant
Collaborative Research: The Analysis and Simulation of Biologically Active Suspensions
合作研究:生物活性悬浮液的分析与模拟
- 批准号:
0920930 - 财政年份:2009
- 资助金额:
$ 23.1万 - 项目类别:
Standard Grant
Collaborative Research: MSPA-ENG: Interplay of Biosensing and Locomotion in Confined Microfluidic Environments
合作研究:MSPA-ENG:受限微流体环境中生物传感和运动的相互作用
- 批准号:
0700669 - 财政年份:2007
- 资助金额:
$ 23.1万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Dynamics of elastic biostructures in complex fluids
FRG:合作研究:复杂流体中弹性生物结构的动力学
- 批准号:
0652775 - 财政年份:2007
- 资助金额:
$ 23.1万 - 项目类别:
Standard Grant
Dynamics of Fiber Suspensions and their Applications
纤维悬浮液动力学及其应用
- 批准号:
0412203 - 财政年份:2004
- 资助金额:
$ 23.1万 - 项目类别:
Standard Grant
SGER: Proposal forModeling the Dynamics of Shape Change in Liquid Crystal Elastomer Systems
SGER:液晶弹性体系统形状变化动力学建模提案
- 批准号:
0440299 - 财政年份:2004
- 资助金额:
$ 23.1万 - 项目类别:
Standard Grant
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