Diffusion, Dissipation Enhancement, and Mixing

扩散、耗散增强和混合

• 批准号: 2108080
• 负责人: Gautam Iyer
• 金额: $ 31.77万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2108080&HistoricalAwards=false
• 关键词: Diffusion; Dissipation; Enhancement; Mixing

Diffusion and mixing are key physical phenomena that arise in applications ranging from micro-fluids to meteorology, to cosmology. Diffusion tends to spread out clusters and tries to disperse them, while mixing weaves the clusters and tends to intersperse layers of one cluster with another. This project seeks to quantify their interaction and determine how it impacts the dynamics of physical and chemical fluid systems. Improving the understanding of how they interact has both direct and indirect consequences in scientific areas, such as the study of chemotaxis, of phase separation of binary mixtures including alloys, and of the earth's magnetic field. The research will be carried out with active involvement from students and postdoctoral associates, who will be trained across a broad range of fields.This project will examine several issues concerning enhanced dissipation, diffusion, and mixing. In incompressible fluids, stirring induces mixing by filamentation and facilitates the formation of small scales. Diffusion, on the other hand, efficiently damps small scales and the balance between these two phenomena can lead to enhanced dissipation - the tendency of solutions to dissipate energy faster than normal. Four goals of the project are to construct simple and explicit family of flows that enhance dissipation by an arbitrarily large amount; to use dissipation enhancement to address physically meaningful questions concerning nonlinear partial differential equations; to obtain sharp estimates for the dissipation enhancement in terms of the mixing rates; and to investigate residual diffusivity, and the effect of dissipation enhancement on the long-time behavior of magnetic fields.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.

扩散和混合是在从微流体到气象学再到宇宙学的各种应用中出现的关键物理现象。扩散倾向于分散星团并试图分散它们，而混合则编织星团，并倾向于将一个星团的层散布到另一个星团。这个项目试图量化它们的相互作用，并确定它如何影响物理和化学流体系统的动力学。提高对它们如何相互作用的理解在科学领域具有直接和间接的影响，例如研究趋化性、研究包括合金在内的二元混合物的相分离以及研究地球磁场。这项研究将在学生和博士后伙伴的积极参与下进行，他们将在广泛的领域接受培训。这个项目将研究几个关于增强耗散、扩散和混合的问题。在不可压缩流体中，搅拌通过丝状化诱导混合，并促进形成小水垢。另一方面，扩散有效地抑制了小尺度，这两种现象之间的平衡可能会导致增强的消散--解决方案比正常情况下更快地消散能量的趋势。该项目的四个目标是构建简单和显式的流族，以增加任意数量的耗散；使用耗散增强来解决与非线性偏微分方程有关的物理意义问题；根据混合率获得对耗散增强的精确估计；以及调查剩余扩散率以及耗散增强对磁场长期行为的影响。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Growth of Sobolev norms and loss of regularity in transport equations

• DOI: 10.1098/rsta.2021.0024
• 发表时间: 2022-06-13
• 期刊: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
• 影响因子: 5
• 作者: Crippa, Gianluca;Elgindi, Tarek;Mazzucato, Anna L.
• 通讯作者: Mazzucato, Anna L.