Research and Education in Physical Mathematics
物理数学研究与教育
基本信息
- 批准号:0605031
- 负责人:
- 金额:$ 28.76万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2006
- 资助国家:美国
- 起止时间:2006-08-15 至 2010-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
BrennerDMS-0605031 The investigator focuses on the coupling of the analyticalmethods of applied mathematics to numerical computation, in thecontext of both research and education. The topics consideredaddress a range of problems in engineering and science using acombination of approximate analysis, computation, and experiments. The investigator and his colleagues conduct the following projects:(1) A mathematical analysis of ion beam sputtering, aimed at bothimproving understanding of the surface patterns producedtechnique (e.g. why do particular morphologies form for given sets of conditions?) and at understanding whether ion beams can be used to create and control prespecified surface morphologies;(2) Studies of the self-assembly of two-dimensional elasticsheets into three-dimensional structures. Here there areimportant issues both with respect to assembly kinetics and indetermining the shape of the sheet that leads to the lowestenergy structure, when folded into a given topology;(3) An analysis of the shapes of pollen grains, and themechanisms through which they dry up; and(4) A mathematical analysis of droplet impact on a solid substrate -- in particular, whether or not a droplet produces a splash depends on an as yet unknown event that occurs immediately after the impact. The educational activities center around the general issue of howthe concepts of applied mathematics should be taught, given theprevalence of computation. The two main issues addressed are:How can computers be used to increase the mathematical (as opposed to computational) sophistication of students? And secondly, how should mathematical modeling be taught, in order to clearly differentiate modeling (which produces understanding of aphenomenon) from computer graphics (which produces a picturereproducing it)? The investigator is developing new courses (andmodifications of old courses) to address these issues. Over the past decade, computers, and computer simulations,play an ever increasing role in science and scientific arguments. It is clear this trend will continue. On the other hand, forcomplicated systems there are serious issues in understandingwhen to judge whether a computer simulation is correct. Thisproject addresses this general question both in the context ofspecific research projects and also through the development ofeducational courses and tools to help students learn how toanswer this question. The research projects include analyses ofcomplex, technologically important phenomena for which bothcomputer simulation and mathematical analysis can be combined. These project include a study of ion beam sputtering, a complexprocess that occurs when surfaces are irradiated with high energyions. The investigator and his colleagues study this problemusing both computer simulations and analytic methods, coupledwith experiments, in an effort to understand whether ion beamscan create specific, technologically useful, patterns in asurface. Another project studies the self-assembly of elasticsheets, in an effort to understand whether it is possible tocreate small objects which self-assemble into useful componentsin three dimensions. A third project studies the process when adroplet of liquid splashes on a solid substrate. Despite theubiquity of this phenomenon it is not known why a droplet createsa splash. On the educational front, the project aims to developmaterial to teach students both how to carry out computersimulations, and equally importantly how to evaluate whether theyare correct.
Brenner DMS-0605031研究人员在研究和教育的背景下,重点关注应用数学的分析方法与数值计算的耦合。所考虑的主题结合了近似分析、计算和实验,解决了工程和科学中的一系列问题。研究人员和他的同事们开展了以下项目:(1)离子束溅射的数学分析,目的是提高对所产生的表面图案的理解,以及如何利用这一技术(例如,为什么在给定的条件下会形成特定的形貌?)以及了解离子束是否可以用来创造和控制预先指定的表面形貌;(2)研究二维弹性薄片到三维结构的自组装。这里有两个重要的问题,既涉及组装动力学,也涉及不确定当折叠成给定拓扑时导致最低能量结构的薄片的形状;(3)分析花粉颗粒的形状,以及它们通过其干燥的机制;以及(4)液滴对固体基质的影响的数学分析--尤其是,液滴是否产生飞溅取决于撞击后立即发生的未知事件。鉴于计算的普及,教育活动围绕着如何教授应用数学的概念这一普遍问题展开。解决的两个主要问题是:如何使用计算机来提高学生的数学(而不是计算)的复杂性?其次,应该如何教授数学建模,以便清楚地区分建模(它产生对现象的理解)和计算机图形学(它产生一幅再现它的图片)?研究人员正在开发新的课程(以及对旧课程的修改)来解决这些问题。在过去的十年里,计算机和计算机模拟在科学和科学争论中发挥着越来越大的作用。很明显,这一趋势将继续下去。另一方面,对于复杂的系统,在理解何时判断计算机模拟是否正确方面存在严重的问题。这个项目在具体研究项目的背景下,也通过开发教育课程和工具来帮助学生学习如何回答这个问题,来解决这个普遍问题。研究项目包括对复杂的、技术上重要的现象的分析,计算机模拟和数学分析可以结合起来。这些项目包括对离子束溅射的研究,这是一种当表面受到高能离子照射时发生的复杂过程。这位研究人员和他的同事们使用计算机模拟和分析方法,结合实验来研究这个问题,以努力了解离子束是否可以在表面产生特定的、技术上有用的图案。另一个项目研究弹性薄片的自组装,试图了解是否有可能创造出可以自我组装成三维有用组件的小物体。第三个项目研究液体在固体衬底上飞溅的过程。尽管这种现象无处不在,但人们并不知道为什么一滴水会产生飞溅。在教育方面,该项目旨在开发教材,教学生如何进行计算机模拟,以及同样重要的是如何评估他们是否正确。
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 Brenner其他文献
Modelling Spatio-Temporal Comprehension in Situated Human-Robot Dialogue as Reasoning about Intentions and Plans
将情境人机对话中的时空理解建模为意图和计划的推理
- DOI:
- 发表时间:
2007 - 期刊:
- 影响因子:0
- 作者:
G. Kruijff;Michael Brenner - 通讯作者:
Michael Brenner
An infantile case of Alexander disease unusual for its MRI features and a GFAP allele carrying both the p.Arg79His mutation and the p.Glu223Gln coding variant
- DOI:
10.1007/s00415-009-0147-4 - 发表时间:
2009-04-01 - 期刊:
- 影响因子:4.600
- 作者:
Maria Teresa Dotti;Rosaria Buccoliero;Andrew Lee;J. Raphael Gorospe;Daniel Flint;Paolo Galluzzi;Silvia Bianchi;Camilla D’Eramo;Sakkubai Naidu;Antonio Federico;Michael Brenner - 通讯作者:
Michael Brenner
A novel glial fibrillary acidic protein mRNA lacking exon 1.
一种缺乏外显子 1 的新型神经胶质原纤维酸性蛋白 mRNA。
- DOI:
- 发表时间:
1995 - 期刊:
- 影响因子:0
- 作者:
Diana Zelenika;Brigitte Grima;Michael Brenner;Bernard Pessac - 通讯作者:
Bernard Pessac
Practical Applications of Homomorphic Encryption
同态加密的实际应用
- DOI:
10.5220/0003969400050014 - 发表时间:
2018 - 期刊:
- 影响因子:0
- 作者:
Michael Brenner;H. Perl;Matthew Smith - 通讯作者:
Matthew Smith
Fast confidential search for bio-medical data using Bloom filters and Homomorphic Cryptography
使用布隆过滤器和同态密码术对生物医学数据进行快速机密搜索
- DOI:
10.1109/escience.2012.6404484 - 发表时间:
2012 - 期刊:
- 影响因子:0
- 作者:
H. Perl;Yassene Mohammed;Michael Brenner;Matthew Smith - 通讯作者:
Matthew Smith
Michael Brenner的其他文献
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{{ truncateString('Michael Brenner', 18)}}的其他基金
DMREF: Collaborative Research: Digital Magnetic Handshake Materials, Structures, and Machines
DMREF:合作研究:数字磁握手材料、结构和机器
- 批准号:
1921619 - 财政年份:2019
- 资助金额:
$ 28.76万 - 项目类别:
Standard Grant
Research and Education in Physical Mathematics
物理数学研究与教育
- 批准号:
1715477 - 财政年份:2017
- 资助金额:
$ 28.76万 - 项目类别:
Standard Grant
REU Site: Team Research in Computational and Applied Mathematics (TRiCAM)
REU 网站:计算与应用数学团队研究 (TRiCAM)
- 批准号:
1460870 - 财政年份:2015
- 资助金额:
$ 28.76万 - 项目类别:
Standard Grant
Research and Education in Physical Mathematics
物理数学研究与教育
- 批准号:
1411694 - 财政年份:2014
- 资助金额:
$ 28.76万 - 项目类别:
Standard Grant
DMREF: Self Assembly with DNA-Labeled Colloidal Particles and DNA Nanostructures
DMREF:使用 DNA 标记的胶体颗粒和 DNA 纳米结构进行自组装
- 批准号:
1435964 - 财政年份:2014
- 资助金额:
$ 28.76万 - 项目类别:
Standard Grant
Research and Education in Physical Mathematics
物理数学研究与教育
- 批准号:
0907985 - 财政年份:2009
- 资助金额:
$ 28.76万 - 项目类别:
Standard Grant
Research and Education in Physical Mathematics
物理数学研究与教育
- 批准号:
0305873 - 财政年份:2003
- 资助金额:
$ 28.76万 - 项目类别:
Standard Grant
CAREER PROPOSAL IN PHYSICAL MATHEMATICS
物理数学职业建议
- 批准号:
0296056 - 财政年份:2001
- 资助金额:
$ 28.76万 - 项目类别:
Standard Grant
CAREER PROPOSAL IN PHYSICAL MATHEMATICS
物理数学职业建议
- 批准号:
9733030 - 财政年份:1998
- 资助金额:
$ 28.76万 - 项目类别:
Standard Grant
Mathematical Investigations of Nonlinear Free Boundary Problems in Stokes Flow
斯托克斯流中非线性自由边界问题的数学研究
- 批准号:
9803167 - 财政年份:1998
- 资助金额:
$ 28.76万 - 项目类别:
Standard Grant
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