LEAPS-MPS: Network Statistics of Rupturing Foams

LEAPS-MPS：破裂泡沫的网络统计

• 批准号: 2316289
• 负责人: Joseph Klobusicky
• 金额: $ 21.49万
• 依托单位: University of Scranton
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-01-01 至 2025-12-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2316289&HistoricalAwards=false
• 关键词: LEAPS; MPS; Network; Statistics; Rupturing

Foams form when pockets of air are trapped inside a liquid or solid material. The structures and symmetries found in foams have drawn the attention of pure mathematicians for centuries, but physical properties of foams, both desirable and undesirable, are also highly relevant in industry and manufacturing. This project will study statistical properties of two-dimensional foams in a controlled setting through compressing a soap foam between two transparent plates and heating to induce edge breaking. The network dynamics will be then captured through image processing algorithms. The underlying differential equations for modeling ruptures, a variation of the so-called coagulation equations describing sticky particle aggregation, will also be rigorously analyzed. Because the elimination of foam is vital in multiple industrial processes such as in the production of detergents, the project aims to generate data directly related to rates of foam reduction to shed light on how to optimize this process. The project includes undergraduate research training opportunities and outreach activities to local high schools focused on data science.The study of microstructure, or composition of materials at small scales, is critical for understanding material properties at the macroscopic level. While much has been written about the coarsening of microstructure via gas diffusion across cell walls, this project will focus on the experimental generation and theoretical modeling of two-dimensional foams with edge rupture induced by heating. Using cell-tracking algorithms commonly found in morphology, the project will examine the evolving network statistics such as topological frequencies, coarsening rates, and the creation and growth of massive cells. Because the second-order reaction of cell merging resulting from rupture can be modeled through processes like the Smoluchowski coagulation equation, this project will consider a class of these equations inspired by this merging and will focus on rigorously deriving properties of the resulting cluster statistics. The long-term goal being to use the experimental, computational, and theoretical methods developed in this study for constructing a general theory of coarsening processes.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.

当空气被困在液体或固体材料中时，泡沫就形成了。在泡沫中发现的结构和对称性几个世纪以来一直引起纯数学家的注意，但泡沫的物理性质，无论是理想的还是不理想的，也与工业和制造业密切相关。该项目将研究二维泡沫的统计特性，在受控环境下，通过将肥皂泡沫压缩在两个透明板之间并加热以诱导边缘断裂。然后通过图像处理算法捕获网络动态。模拟破裂的基本微分方程，即描述粘性颗粒聚集的所谓凝聚方程的一种变体，也将被严格分析。由于泡沫的消除在洗涤剂生产等多个工业过程中至关重要，因此该项目旨在生成与泡沫减少率直接相关的数据，以阐明如何优化这一过程。该项目包括本科生研究培训机会，以及向以数据科学为重点的当地高中开展推广活动。微观结构的研究，或材料在小尺度上的组成，对于在宏观层面上理解材料的性质是至关重要的。虽然已经有很多关于通过气体扩散穿过细胞壁使微观结构变粗的文章，但本项目将重点研究加热引起边缘破裂的二维泡沫的实验生成和理论建模。使用形态学中常见的细胞跟踪算法，该项目将检查不断发展的网络统计数据，如拓扑频率、粗化率以及大量细胞的产生和生长。由于破裂导致的细胞合并的二级反应可以通过Smoluchowski凝聚方程等过程来建模，因此该项目将考虑一类受这种合并启发的方程，并将重点放在严格推导所得到的簇统计特性上。长期目标是利用本研究中开发的实验、计算和理论方法来构建粗化过程的一般理论。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。