Computational Methods for Heteroepitaxial Growth, Grain Boundary Motion, and High Frequency Wave Propagation
异质外延生长、晶界运动和高频波传播的计算方法
基本信息
- 批准号:0810113
- 负责人:
- 金额:$ 25.64万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2008
- 资助国家:美国
- 起止时间:2008-07-01 至 2013-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This proposal involves three projects. The first concerns modeling andefficient simulation of heteroepitaxial growth using kinetic Monte Carlo and will build from prior NSF support which resulted in thedevelopment of a Fourier multigrid method for the fast solution ofdiscrete elastic equations for complex geometries. This work will be extended to develop methods for obtaining inexpensive upper bonds onrates, the use of local computations for elastic equations, and the inclusion ofintermixing of multiple species. The second project involves the simulation of grain boundary motion in two and three dimensions usinga recently developed multiphase variational level set framework whichallows one to systematically deduce level set equations for a network ofgrains moving under curvature flow. We plan to extend this formulation to allow the simulation of thousands of seeds by using only a few level setfunctions. The efficient computation of high frequency wave propagation and the semi-classical limit of the Schrodinger equation is the thirdproject. The proposed algorithm is based on the observation that most of the time, in these limiting regimes, the solutions are very localized in the wavenumber domain. This can be exploited by solving the equations in thisdomain using a fast local convolution. It is planned to update the solutionsby the computation of the matrix exponential using a Krylov subspaceapproach.Each of the proposed projects has the potential to have a significant impact on problems that are both fundamental and technologically important. Heteroepitaxial growth is scientifically interesting since it has effectson both nanoscales and mesoscales. It is technologically relevant sincequantum dot materials are made in this way. Our proposed techniques willgreatly increase the simulation speed thereby facilitating model development.The study of grain boundary motion using curvature flow is a classic problem in applied and computational mathematics which has importance in material science. Since there are no robust simulations of a large number grains in three dimensions the proposed project should have significant impact. The efficient computation of high frequency wave propagation has important facets ranging from antenna design to seismic sensing. On the other hand,fast simulation of the semi-classical limit of the Schrodinger equation could provide deeper insight into chemical reaction dynamics, molecular-surface scattering, and photodissociation, for example.
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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Peter Smereka其他文献
Wetting of elastic solid on nanopillars
纳米柱上弹性固体的润湿
- DOI:
- 发表时间:
2014 - 期刊:
- 影响因子:8.6
- 作者:
Maxim Ignasco;Yukio Saito;Peter Smereka;and Olivier Pierre-Louis - 通讯作者:
and Olivier Pierre-Louis
Peter Smereka的其他文献
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{{ truncateString('Peter Smereka', 18)}}的其他基金
Computation of the Semiclassical Limit of Schroedinger's Equation, Anisotropic Grain Growth, and Epitaxial Growth Using Kinetic Monte Carlo
使用动力学蒙特卡罗计算薛定谔方程的半经典极限、各向异性晶粒生长和外延生长
- 批准号:
1115252 - 财政年份:2011
- 资助金额:
$ 25.64万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Modeling and Computation of Crystalline Nanostructures
FRG:合作研究:晶体纳米结构的建模和计算
- 批准号:
0854870 - 财政年份:2009
- 资助金额:
$ 25.64万 - 项目类别:
Standard Grant
Efficient Computation of Epitaxial Growth
外延生长的高效计算
- 批准号:
0509124 - 财政年份:2005
- 资助金额:
$ 25.64万 - 项目类别:
Standard Grant
Computational Methods for Problems in Material Science
材料科学问题的计算方法
- 批准号:
0207402 - 财政年份:2002
- 资助金额:
$ 25.64万 - 项目类别:
Standard Grant
Mathematical Sciences: "CAREER Program: Peter Smereka
数学科学:“职业计划:Peter Smereka
- 批准号:
9625190 - 财政年份:1996
- 资助金额:
$ 25.64万 - 项目类别:
Standard Grant
Mathematical Sciences: Postdoctoral Research Fellowship
数学科学:博士后研究奖学金
- 批准号:
9007329 - 财政年份:1990
- 资助金额:
$ 25.64万 - 项目类别:
Fellowship Award
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