Variational Models for Self-Assembly and Pattern Formation: Analysis and Computation

自组装和图案形成的变分模型：分析和计算

• 批准号: RGPIN-2015-04488
• 负责人: Choksi, Rustum
• 金额: $ 2.26万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635631
• 关键词: Variational; Models; Self; Assembly; Pattern

Self-assembly, a process whereby a disordered system of components forms an organized, structured pattern solely as a consequence of component interactions, is both ubiquitous in nature and important for the synthesis of many designer materials. Many systems which exhibit self-assembly and pattern formation may be viewed as energy-driven; therefore, one can successfully capture and analyze the phenomena via minimization of some, often postulated, free energy defined over all possible configurations. The resulting variational problems involve highly non-trivial energy landscapes and are mathematically and computationally very challenging. In this proposal we will study three such variational models (and connections between them) from the point of view of mathematical analysis and computation. A common theme will be the focus on nonlocal problems and global techniques, i.e. those whose vision extends beyond the local study of critical points and the analysis of their stability.

自组装，一个过程，其中一个无序的系统的组件形成一个有组织的，结构化的模式，仅仅作为一个结果的组件相互作用，是无处不在的性质和重要的合成许多设计材料。许多表现出自组装和图案形成的系统可以被视为能量驱动的;因此，人们可以通过最小化定义在所有可能的配置上的一些通常假设的自由能来成功地捕获和分析这些现象。由此产生的变分问题涉及高度非平凡的能源景观，在数学和计算上非常具有挑战性。在这个建议中，我们将研究三个这样的变分模型（以及它们之间的联系）从数学分析和计算的角度来看。一个共同的主题将是对非局部问题和全球技术的关注，即那些视野超越临界点的局部研究和稳定性分析的人。