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.

形状内存合金和带有表面活性剂的微流体散装是所谓的新型材料的例子，它们是由单分子厚的界面层连接的多相散装组成。在外延生长制造过程中，诸如位错和晶界等物质缺陷是界面层，其迁移可能导致致命的塑性变形。该项目将重点介绍新型材料中界面层和微流动流的迁移模式的数学分析，以了解其机制并预测其模式。例如，提供对其演变的准确理论预测，例如，微流体设备的设计和降低制造成本。 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 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耦合的散装动力学不会破坏领先顺序的材料缺陷的慢动作模式。第二个目标是系统地将Onsager的线性响应原则推广到与拓扑变化的交互式动态有关的障碍问题。研究人员的目标是为微流体流的几何运动提供新的相位场模型，该模型在拓扑变化发生时自动建立在交互式层的迁移机制中。这个新模型以及数学验证将揭示隐藏的变分原理和选择标准。该变异原理将结合通用复杂系统的固体流体，固体互动机制和连贯的微型麦克罗结构。该奖项反映了NSF的法定任务，并被认为是通过基金会的智力优点和更广泛影响的评估标准通过评估来获得的支持。