Degenerate Diffusion in Complex Amphiphilic Network Structures

复杂两亲网络结构中的简并扩散

• 批准号: 1802863
• 负责人: Shibin Dai
• 金额: $ 8.62万
• 依托单位: University of Alabama Tuscaloosa
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-08-01 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1802863&HistoricalAwards=false
• 关键词: Degenerate; Diffusion; Complex; Amphiphilic; Network

The principal investigator studies complex network structures in amphiphilic mixtures under a framework that includes degenerate diffusion and functionalized Cahn-Hilliard (FCH) energy. Network structures in complex systems have close relations to phase transitions, materials science, and mathematical biology. He develops methods to model and analyze the development of structures in amphiphilic mixtures and their properties. Such systems include biological membranes and polymer materials like polymer electrolyte membranes. Biological membranes play critical roles in biological processes such as protein transportation, drug encapsulation and delivery. Polymer electrolyte membranes are key ingredients of fuel cells that are able to efficiently produce clean energy and are a promising replacement for traditional batteries. Their effectiveness is directly related to their fine structures. In the course of this project, a graduate student and an undergraduate student are trained.The principal investigator concentrates on the influence of degenerate diffusion on the dynamics of complex amphiphilic structures, the variational properties of the functionalized Cahn-Hilliard energy, and their relation to amphiphilic structures. He formulates bilayers, filamentous pores, micelles, and defect structures such as open edges, end caps, and triple junctions, as minimizers of the FCH energy, and relates them to variational properties of the FCH energy under various geometric constraints. By building degenerate diffusion into the FCH equation, he is able to model biologically significant phenomena such as the co-existence of bilayer vesicles of various sizes and shapes, the diffusion of lipid molecules along lipid bilayer membranes, and the impermeability of bilayers. He studies the evolution of the defects and the sensitivity of their energies to parametric variation, and identifies the energetic cost for the defects to form. The tools developed in this project have wide applications in the modeling of other physical and biological systems, and in the study of other problems in applied mathematics related to nonlinear PDEs.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.

主要研究员研究两亲性混合物中的复杂网络结构，包括简并扩散和官能化的Cahn-Hilliard（FCH）能量。 复杂系统中的网络结构与相变、材料科学和数学生物学有着密切的联系。 他开发了建模和分析两亲性混合物及其性质的结构发展的方法。 这样的系统包括生物膜和聚合物材料，如聚合物电解质膜。 生物膜在蛋白质转运、药物包封和释放等生物过程中起着重要作用。 聚合物电解质膜是燃料电池的关键成分，能够高效生产清洁能源，是传统电池的有前途的替代品。 它们的有效性与它们的精细结构直接相关。 本项目培养了一名研究生和一名本科生，主要研究方向是简并扩散对复杂两亲性结构动力学的影响，功能化Cahn-Hilliard能量的变分性质，以及它们与两亲性结构的关系。 他制定了双层，丝状孔，胶束和缺陷结构，如开放的边缘，端盖，和三重连接，作为FCH能量的最小化，并将它们与各种几何约束下的FCH能量的变分性质。 通过在FCH方程中建立简并扩散，他能够模拟生物学上重要的现象，例如各种大小和形状的双层囊泡的共存，脂质分子沿着脂质双层膜的扩散，以及双层的不渗透性。 他研究了缺陷的演化及其能量对参数变化的敏感性，并确定了缺陷形成的能量成本。 该项目开发的工具在其他物理和生物系统的建模以及与非线性偏微分方程相关的应用数学中的其他问题的研究中具有广泛的应用。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。