Intrinsic Equations of Motion for Interfaces in Models of Solidification
凝固模型中界面的固有运动方程
基本信息
- 批准号:9306326
- 负责人:
- 金额:$ 6万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:1993
- 资助国家:美国
- 起止时间:1993-07-15 至 1996-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
A methodology is proposed for deriving equations of motion for interfaces in transition between two phases, such as the solidification of a liquid into a solid, in the asymptotic limit of small diffusion. The investigator will show that the velocity of the interface is a function of its local geometry, described by so-called intrinsic quantities such as the curvature. This model allows the computation of the radius at which a growing spherical particle becomes unstable and may allow a deeper understanding of the complex dendritic structures seen in solidification. The problem of the solidification of a liquid has many industrial applications, such as the growing of a quartz crystal from a melt for use in semiconductor devices like computer chips. For these applications it is desirable to grow smooth, regular crystals. Unfortunately, many substances tend to grow into irregular snowflake-like dendrites. In this study the investigator proposes a methodology for reducing the complex equations governing solidification to a relatively simple geometric description. This reduction should allow the prediction of the transition from regular to dendritic solidification. It may also give some insight into the process by which irregular dendritic structures form and grow.
提出了一种在小扩散渐近极限下推导两相过渡界面运动方程的方法,例如液体凝固成固体。研究者将证明界面的速度是其局部几何的函数,由所谓的固有量如曲率来描述。该模型可以计算球形颗粒在生长过程中变得不稳定的半径,并且可以更深入地了解凝固过程中所见的复杂枝晶结构。液体凝固的问题有许多工业应用,例如从熔体中生长出用于计算机芯片等半导体器件的石英晶体。对于这些应用,需要生长光滑、规则的晶体。不幸的是,许多物质往往会长成不规则的雪花状树突。在这项研究中,研究者提出了一种方法,以减少复杂的方程控制凝固相对简单的几何描述。这种还原可以预测从规则凝固到枝晶凝固的转变。它还可能对不规则树突结构形成和生长的过程提供一些见解。
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)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Andrew Bernoff其他文献
Andrew Bernoff的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Andrew Bernoff', 18)}}的其他基金
Optimizing the Mathematics Postdoctoral Experience: A Teaching and Research Postdoctoral Fellowship at Harvey Mudd College
优化数学博士后体验:哈维穆德学院的教学和研究博士后奖学金
- 批准号:
0839966 - 财政年份:2009
- 资助金额:
$ 6万 - 项目类别:
Standard Grant
Collaborative research MSPA-ENG: Dynamics of interfacial domains
合作研究 MSPA-ENG:界面域动力学
- 批准号:
0730630 - 财政年份:2007
- 资助金额:
$ 6万 - 项目类别:
Standard Grant
RUI: Stability and Dynamics of Self-Similarity in Evolution Equations
RUI:进化方程中自相似性的稳定性和动力学
- 批准号:
9971969 - 财政年份:1999
- 资助金额:
$ 6万 - 项目类别:
Continuing Grant
Mathematical Sciences: Postdoctoral Research Fellowship
数学科学:博士后研究奖学金
- 批准号:
8905509 - 财政年份:1989
- 资助金额:
$ 6万 - 项目类别:
Fellowship Award
相似海外基金
Learning equations of motion for coupled spatio-temporal processes
学习时空耦合过程的运动方程
- 批准号:
2745609 - 财政年份:2022
- 资助金额:
$ 6万 - 项目类别:
Studentship
Construction of a new mathematical model of grain boundary motion and development in the theory of differential equations
晶界运动新数学模型的构建及微分方程理论的发展
- 批准号:
22K03376 - 财政年份:2022
- 资助金额:
$ 6万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Open quantum dynamics theory of excition, electron and proton transfer processes: Hierarchical equations of motion approach
激发、电子和质子转移过程的开放量子动力学理论:层次运动方程方法
- 批准号:
21H01884 - 财政年份:2021
- 资助金额:
$ 6万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Study of singularity of the equations of fluids and stochasticity of turbulence from the view point of vortex motion
从涡运动的角度研究流体方程的奇异性和湍流的随机性
- 批准号:
19H00641 - 财政年份:2019
- 资助金额:
$ 6万 - 项目类别:
Grant-in-Aid for Scientific Research (A)
Structure of stationary solutions and motion of interfaces in bistable reaction-diffusion equations
双稳态反应扩散方程中平稳解的结构和界面运动
- 批准号:
15K17569 - 财政年份:2015
- 资助金额:
$ 6万 - 项目类别:
Grant-in-Aid for Young Scientists (B)
Reduced Hierachal Equations of Motion for Exciton and electron transfer ssystems: Application to nonlinear response
激子和电子转移系统的简化层次运动方程:在非线性响应中的应用
- 批准号:
26248005 - 财政年份:2014
- 资助金额:
$ 6万 - 项目类别:
Grant-in-Aid for Scientific Research (A)
Nonlocal interaction equations and applications to collective motion of individuals
非局部相互作用方程及其在个体集体运动中的应用
- 批准号:
1414396 - 财政年份:2013
- 资助金额:
$ 6万 - 项目类别:
Standard Grant
Mathematical analysis for nonlinear parabolic equations with degeneracy and mathematical models of grain boundary motion
简并非线性抛物型方程的数学分析及晶界运动数学模型
- 批准号:
25800086 - 财政年份:2013
- 资助金额:
$ 6万 - 项目类别:
Grant-in-Aid for Young Scientists (B)
Large time behavior of the solutions to the equations of fluid motion.
流体运动方程解的大时间行为。
- 批准号:
23540211 - 财政年份:2011
- 资助金额:
$ 6万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Nonlocal interaction equations and applications to collective motion of individuals
非局部相互作用方程及其在个体集体运动中的应用
- 批准号:
1109805 - 财政年份:2011
- 资助金额:
$ 6万 - 项目类别:
Standard Grant