Pattern and wavenumber selection in the wake of fronts

锋面后的模式和波数选择

基本信息

批准号：
1311740
负责人：
Arnd Scheel
金额：
$ 38万
依托单位：
University of Minnesota-Twin Cities
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2013
资助国家：
美国
起止时间：
2013-07-01 至 2017-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1311740&HistoricalAwards=false
关键词：
Pattern wavenumber selection wake fronts

项目摘要

Pattern and wavenumber selection in the wake of frontsIn a variety of chemical, biological, and manufacturing processes, patterns emerge in the wake of interfaces. This proposal is particularly motivated by Liesegang patterns in recurrent precipitation, bacterial colony patterning, and self-organized nano-ripple formation under ion-bombardment of surfaces. In all those contexts, a plethora of regular and complex patterns has been observed as they form in the wake of moving fronts, both experimentally and in direct simulations. Pattern-forming fronts have been poorly understood from a mathematical view point, yet they provide a prime avenue to a systematic understanding of patterning in phase separation processes, surface evolution, and biological growth. A systematic, model-independent understanding of patterning in the wake of fronts, combined with computational tools for quantitative predictions, has the potential to both explain classic 100-year old chemical experiments and shed new lights on biological aggregation mechanisms. Coherent patterns in the wake of fronts allow for clean qualitative and quantitative predictions of patterns. In this respect, the proposed research will give new tools for quantitative, deterministic model validation. Predictions on patterned surface instabilities have potentially high impact in manufacturing processes. The educational aspect of the proposed research involves undergraduate students during two summer REUs and four graduate students.

前沿之后的图案和波数选择在各种化学、生物和制造过程中，图案随着界面而出现。该提议特别受到循环沉淀中的利泽冈模式、细菌菌落模式以及表面离子轰击下自组织纳米波纹形成的启发。在所有这些背景下，无论是在实验还是在直接模拟中，都观察到了在移动锋之后形成的大量规则和复杂的模式。从数学角度来看，人们对图案形成前沿知之甚少，但它们为系统地理解相分离过程、表面演化和生物生长中的图案提供了主要途径。对前沿后的模式进行系统的、独立于模型的理解，结合定量预测的计算工具，有可能解释 100 年前的经典化学实验，并为生物聚集机制提供新的线索。前沿之后的连贯模式可以对模式进行清晰的定性和定量预测。在这方面，拟议的研究将为定量、确定性模型验证提供新工具。对图案表面不稳定性的预测对制造过程具有潜在的重大影响。拟议研究的教育方面涉及两个夏季 REU 期间的本科生和四名研究生。