Reduced Models for Transport of Particles in Heterogeneous Media

异质介质中粒子传输的简化模型

• 批准号: 1813943
• 负责人: Alexei Novikov
• 金额: $ 28万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-08-01 至 2022-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1813943&HistoricalAwards=false
• 关键词: Reduced; Models; Transport; Particles; Heterogeneous

The overall objective of this project is to study physical systems in heterogeneous environments. Heterogeneous environments are ubiquitous. Some examples are ocean flows, atmospheric turbulence, oil-bearing sands, and biological tissues. Understanding overall properties of such media is relevant to aspects of virtually every branch of science and engineering; especially materials science, chemical engineering, geophysics, medical imaging and fluid dynamics. One of the projects of this research concerns changes in salinity or chlorofluorocarbon on the surface of the ocean. Oceanic vortices may dramatically change mixing rates of various chemical compounds. The aim of this project is to estimate these rates in simpler mathematical models to illuminate the mechanisms present in the full problem. Another project of this research concerns light propagation through the atmosphere. The main source of distortion in these devices comes from atmospheric turbulence. The aim of this project is to understand the mechanism of this distortion.This work carries out mathematical studies of particle propagation in cluttered environments and of convection-diffusion processes in fluids. The first project concentrates on the effect of long-range correlations. This is a novel direction in the theory of propagation in random media, and approximate models of propagation in slowly decorrelating media are not yet developed. The goal is to explain how long-range correlations lead to time-scale separation of various phenomena. The second project concentrates on the interaction of the standard and the fractional diffusion with incompressible flows. The intellectual challenge of the proposed work is to understand this interaction for incompressible flows with large amplitude. This is particularly relevant to understanding diffusion in turbulent flows.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.

该项目的总体目的是在异质环境中研究物理系统。异质环境无处不在。一些例子是海洋流动，大气湍流，含油沙子和生物组织。了解这种媒体的整体特性与几乎每个科学和工程分支的各个方面有关；特别是材料科学，化学工程，地球物理学，医学成像和流体动力学。这项研究的一个项目涉及海洋表面上的盐度或氯氟化碳的变化。海洋涡流可能会大大改变各种化合物的混合速率。该项目的目的是在更简单的数学模型中估算这些速率，以阐明整个问题中存在的机制。 这项研究的另一个项目涉及大气中的光传播。这些设备中失真的主要来源来自大气湍流。该项目的目的是了解这种失真的机制。这项工作对混乱环境中的粒子传播和流体中的对流扩散过程进行了数学研究。第一个项目集中于远程相关性的影响。这是在随机介质中传播理论中的一个新方向，尚未开发出缓慢反相关的介质中传播的近似模型。目的是解释距离相关性多长时间导致各种现象的时间尺度分离。第二个项目集中于标准的相互作用以及与不可压缩流的分数扩散。拟议工作的智力挑战是了解这种相互作用的幅度不高的不可压缩流。这与理解动荡流的扩散尤其重要。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的评论标准来评估值得支持的。

项目成果

Random walk methods for Monte Carlo simulations of Brownian diffusion on a sphere

球体上布朗扩散蒙特卡罗模拟的随机游走方法

• DOI: 10.1016/j.amc.2019.124670
• 发表时间: 2020
• 期刊: Applied Mathematics and Computation
• 影响因子: 4
• 作者: Novikov, A.;Kuzmin, D.;Ahmadi, O.
• 通讯作者: Ahmadi, O.

Fast Signal Recovery From Quadratic Measurements

从二次测量中快速恢复信号

• DOI: 10.1109/tsp.2021.3067140
• 发表时间: 2021
• 期刊: IEEE Transactions on Signal Processing
• 影响因子: 5.4
• 作者: Moscoso, Miguel;Novikov, Alexei;Papanicolaou, George;Tsogka, Chrysoula
• 通讯作者: Tsogka, Chrysoula

Synthetic Aperture Imaging With Intensity-Only Data

仅强度数据的合成孔径成像

• DOI: 10.1109/tci.2019.2919272
• 发表时间: 2020
• 期刊: IEEE Transactions on Computational Imaging
• 影响因子: 5.4
• 作者: Moscoso, Miguel;Novikov, Alexei;Papanicolaou, George;Tsogka, Chrysoula
• 通讯作者: Tsogka, Chrysoula

Three-dimensional imaging from single-element holographic data

单元素全息数据的三维成像

• DOI: 10.1364/josaa.402396
• 发表时间: 2020
• 期刊: Journal of the Optical Society of America A
• 作者: Moscoso, M.;Novikov, A.;Papanicolaou, G.;Tsogka, C.
• 通讯作者: Tsogka, C.

Feeble Fish in Time‐Dependent Waters and Homogenization of the G‐equation

时间上的弱鱼——相关水域和 G 方程的均质化

• DOI: 10.1002/cpa.21878
• 发表时间: 2020
• 期刊: Communications on Pure and Applied Mathematics
• 影响因子: 3
• 作者: Burago, Dmitri;Ivanov, Sergei;Novikov, Alexei
• 通讯作者: Novikov, Alexei