Mathematical Problems from Materials Science
Mathematical Problems from Materials Science
批准号:
0313744
负责人:
Robert Kohn
金额:
$56.3万
依托单位:
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
2003
资助国家:
美国
项目状态:
已结题
起止时间:
2003-07-01 至 2009-06-30
中文摘要
提案:0313744 PI:Robert V. Kohn [kohn@cims.nyu.edu]机构:纽约大学材料科学中的数学问题摘要本项目主要研究数学、物理和材料科学之间的界面问题,特别是(a)能量驱动的晶粒边界图案形成,(B)能量驱动的相混合物和缺陷的粗化。 关于前者:PI将使用基于非相干能量最小化新观点研究扭曲晶界中的图案形成。 关于后者:PI将使用基于耗散和等周不等式的新观点,研究从相分离、晶粒生长和涡旋湮灭的问题。能量驱动的图案形成发生在许多不同的物理系统中;例子包括II型超导体中的涡旋晶格、晶界中的位错图案和由相分离产生的螺旋结构。 这个项目寻求理解-对于特定的,广泛研究的系统-为什么某些模式形成而不是其他模式。这种理解对于解释实验观察至关重要,即对于从对系统形成的模式的观察中推断系统的物理性质至关重要。
英文摘要
Proposal: 0313744PI: Robert V. Kohn [kohn@cims.nyu.edu]Institution: New York UniversityTitle: Mathematical Problems from Materials ScienceABSTRACTThis project addresses topics at the interface between mathematics, physics, and materials science, particularly (a) energy-driven pattern formation in crystalline grain boundaries, and (b) energy-driven coarsening of phase mixtures and defects. Concerning the former: the PI will investigate pattern formation in twist grain boundaries, using a new viewpoint based on minimization of incoherence energy. Concerning the latter: the PI will investigate problems from phase separation, grain growth, and vortex annihilation, using a new viewpoint based on dissipation and isoperimetric inequalities.Energy-driven pattern formation occurs in many different physical systems; examples include vortex lattices in type-II superconductors, dislocation patterns in grain boundaries, and labyrinthine structures created by phase separation. This project seeks an understanding -- for specific, widely studied systems -- why certain patterns form rather than others. Such understanding is crucial for interpreting experimental observations, i.e. for drawing inferences about the physics of a system from observations of the patterns it forms.
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会议论文
Mathematical Aspects of Materials Science and Prediction with Expert Advice
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批准号:2009746
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项目类别:Standard Grant
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资助金额:$19.98万
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财政年份:2020
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负责人:Robert Kohn
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依托单位:
DMREF: Adaptive Fine-Scale Structure Design: From Theory to Fabrication
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批准号:1436591
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项目类别:Standard Grant
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资助金额:$81.77万
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财政年份:2014
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负责人:Robert Kohn
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依托单位:
Mathematical problems from materials science
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批准号:1311833
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项目类别:Continuing Grant
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资助金额:$112.16万
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财政年份:2013
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负责人:Robert Kohn
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依托单位:
Mathematical Problems from Materials Science and Finance
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批准号:0807347
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项目类别:Continuing Grant
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资助金额:$87.61万
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财政年份:2008
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负责人:Robert Kohn
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依托单位:
Modeling, Analysis, and Simulation of Photonic Microstructures
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批准号:0313890
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项目类别:Standard Grant
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资助金额:$32.0万
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财政年份:2003
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负责人:Robert Kohn
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依托单位:
Focused Research Group: Analysis and Simulation of Magnetic Devices
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批准号:0101439
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项目类别:Continuing Grant
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资助金额:$75.06万
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财政年份:2001
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负责人:Robert Kohn
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依托单位:
Mathematical Problems from Materials Science
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批准号:0073047
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项目类别:Continuing Grant
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资助金额:$19.35万
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财政年份:2000
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负责人:Robert Kohn
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依托单位:
Mathematical Sciences: Microstructure and Macroscopic Behavior
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批准号:9402763
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项目类别:Continuing Grant
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资助金额:$125.0万
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财政年份:1994
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负责人:Robert Kohn
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依托单位:
Mathematical Sciences: Mathematical Problems from Materials Sciences
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批准号:9404376
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项目类别:Continuing Grant
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资助金额:$23.36万
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财政年份:1994
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负责人:Robert Kohn
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依托单位:
Mathematical Sciences: Elastodynamic Modelling of Stress Driven Phase Boundary Motion
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批准号:9217151
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项目类别:Standard Grant
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资助金额:$3.0万
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财政年份:1993
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负责人:Robert Kohn
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依托单位:
Mathematical Sciences: NATO Advanced Research Workshop
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批准号:9211780
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项目类别:Standard Grant
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资助金额:$0.4万
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财政年份:1992
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负责人:Robert Kohn
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依托单位:
Mathematical Sciences: Mathematical Problems from Materials Science
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批准号:9102829
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项目类别:Continuing Grant
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资助金额:$20.35万
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财政年份:1991
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负责人:Robert Kohn
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依托单位:
Rapidly Varying Thin Structures With Applications to Structural Design Optimization (Mathematical Sciences)
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批准号:8201308
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项目类别:Standard Grant
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资助金额:$2.55万
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财政年份:1982
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负责人:Robert Kohn
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依托单位:
Mathematical Sciences Postdoctoral Research Fellowship
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批准号:7919146
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项目类别:Fellowship Award
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资助金额:$3.4万
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财政年份:1979
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负责人:Robert Kohn
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依托单位:
Various Research Tasks Related to Energy Information and Data Activities
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批准号:7415285
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项目类别:Standard Grant
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资助金额:$0.0万
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财政年份:1974
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负责人:Robert Kohn
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依托单位:
Linear Activity Analysis of Air Pollution Control
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批准号:7407802
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项目类别:Standard Grant
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资助金额:$3.62万
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财政年份:1974
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负责人:Robert Kohn
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依托单位:
海外基金