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.

这个项目的总体目标是研究异构环境中的物理系统。异构环境无处不在。例如洋流、大气湍流、含油砂和生物组织。了解这种介质的整体特性与科学和工程的几乎每个分支都有关；特别是材料科学、化学工程、地球物理、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盐度或氯氟化碳的变化。海洋涡旋可以极大地改变各种化合物的混合速率。这个项目的目的是用更简单的数学模型来估计这些速率，以阐明在整个问题中存在的机制。这项研究的另一个项目涉及光在大气中的传播。这些装置的主要畸变源来自大气湍流。这个项目的目的是了解这种扭曲的机制。这项工作进行了粒子在杂乱环境中的传播和流体中对流扩散过程的数学研究。第一个项目关注的是长期相关性的影响。这是随机介质中传播理论的一个新方向，目前还没有建立起缓慢去相关介质中传播的近似模型。目标是解释长程相关性如何导致各种现象在时间尺度上的分离。第二个项目集中在标准和分数扩散与不可压缩流的相互作用。所提出的工作的智力挑战是理解这种相互作用的不可压缩流与大振幅。这对于理解湍流中的扩散尤为重要。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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

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

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

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.

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