Bulk-Interface Coupled Response in Novel Materials: Pattern Formation and Interactive Migration

新型材料中的体界面耦合响应：图案形成和交互式迁移

基本信息

批准号：
2204288
负责人：
Yuan Gao
金额：
$ 18.23万
依托单位：
Purdue University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-09-01 至 2025-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2204288&HistoricalAwards=false
关键词：
Bulk Interface Coupled Response Novel

项目摘要

Shape-memory alloys and microfluidic bulks with surfactants are examples of so-called novel materials, which are composites of multi-phase bulks connected by single-molecule-thick interfacial layers. In epitaxial growth manufacturing processes, material defects such as dislocations and grain boundaries are interfacial layers, whose migration may lead to fatal plastic deformation. This project will focus on the mathematical analysis of migration patterns of interfacial layers and microfluidic flows in novel materials to understand their mechanisms and predict their patterns. Providing accurate theoretical predictions of their evolution will advance, for instance, the design of microfluidic devices and lower manufacturing costs. The training of undergraduate students and high school students will be integrated into this interdisciplinary research project.The first scientific goal of this project is to develop a novel decomposition for bulk-interface interactive dynamics and use it to predict the pattern formation of a multilayer transition profile. Using quantitative estimates based on the global stability of partial differential equations with dynamic boundary conditions and a reduced invariant manifold for the slow-motion persistence of the multilayer pattern, the main intent is to show that the coupled bulk dynamics does not destroy the slow-motion pattern of material defects at the leading order. The second goal is to systematically generalize Onsager’s linear response principle to obstacle problems for interactive dynamics with topological changes. The investigator aims to derive a new phase field model for geometric motions of microfluidic flows, which automatically builds in migration mechanisms of interfacial layers whenever topological changes happen. This new model, together with mathematical validations, will unveil the hidden variational principle and a selection criterion. This variational principle will incorporate solid-fluid, solid-solid interactive mechanisms, and coherent micro-macro structures for general complex systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

形状记忆合金和含有表面活性剂的微流体块体是所谓的新型材料的例子，它们是由单分子厚界面层连接的多相块体的复合材料，在外延生长制造过程中，位错和晶界等材料缺陷。是界面层，其迁移可能导致致命的塑性变形，该项目将重点对新型材料中的界面层迁移模式和微流体流动进行数学分析，以了解其机制并进行预测。提供其演化的准确理论预测将促进微流体装置的设计和降低制造成本，并将对本科生和高中生的培训纳入这一跨学科研究项目。该项目的第一个科学目标。该项目的目的是开发一种新颖的体界面交互动力学分解方法，并使用它来预测多层转变轮廓的模式形成，该方法基于具有动态边界条件的偏微分方程的全局稳定性和减少的不变流形。多层图案的慢运动持久性，主要目的是证明耦合体动力学不会破坏前导阶材料缺陷的慢运动图案，第二个目标是系统地推广 Onsager 的线性响应原理对障碍问题。研究人员的目标是导出一种用于微流体流动几何运动的新相场模型，每当发生拓扑变化时，该模型就会自动构建界面层的迁移机制。隐藏的变分原理和选择标准。该变分原理将结合一般复杂系统的固-液、固-固相互作用机制以及连贯的微观-宏观结构。该奖项反映了 NSF 的法定使命，并通过使用评估被认为值得支持。基金会的智力价值和更广泛的影响审查标准。