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.

当空气口袋被困在液体或固体材料中时，泡沫会形成。几个世纪以来，泡沫中发现的结构和对称性吸引了纯数学家的注意，但是在工业和制造业中，泡沫的物理特性都具有理想的和不希望的。该项目将通过压缩两个透明板之间的肥皂泡沫和加热以引起边缘破裂，研究在受控设置中二维泡沫的统计特性。然后将通过图像处理算法捕获网络动力学。用于建模破裂的基本微分方程，即描述粘性颗粒聚集的所谓凝结方程的变化，也将进行严格分析。由于消除泡沫在多个工业过程中至关重要，例如在洗涤剂的生产中，该项目旨在生成与降低泡沫速率直接相关的数据，以阐明如何优化该过程。该项目包括对关注数据科学的当地高中的本科研究培训机会和外展活动。对微观结构的研究或小规模的材料组成，对于理解宏观级别的材料特性至关重要。尽管已经写了很多关于通过气体扩散在细胞壁上进行微结构的文章，但该项目将集中于实验生成和二维泡沫的实验生成和由加热引起的边缘破裂的理论建模。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，例如拓扑频率，变形速率以及大规模细胞的创造和生长。 由于破裂引起的细胞合并的二阶反应可以通过Smoluchowski凝血方程等过程进行建模，因此该项目将考虑受此合并启发的这些方程的类别，并将集中于所得群集统计的严格衍生性能。长期的目标是使用本研究中开发的实验，计算和理论方法来构建一个通用的粗化过程理论。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的影响来通过评估来支持的。