EAGER: Develop Robust Light-Scattering Computational Capability Based on the Method of Separation of Variables in Spheroidal Coordinates for Small-to-Large Spheroids

EAGER：基于从小到大球体的球体坐标中的变量分离方法，开发鲁棒的光散射计算能力

• 批准号: 2153239
• 负责人: Ping Yang
• 金额: $ 19.96万
• 依托单位: Texas A&M University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-12-01 至 2023-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2153239&HistoricalAwards=false
• 关键词: EAGER; Develop; Robust; Light; Scattering

Dust aerosols affect global climate by partially absorbing and reflecting incoming sunlight and heat energy emitted by the atmosphere and the surface. The optical properties of dust particles are critical to reducing uncertainties in the current knowledge of the role of dust aerosols in the climate system, and thus are important for predicting future climate. The dust particle optical properties are also fundamental for inferring dust aerosol characteristics from space-borne and ground-based remote sensing observations. Dust particles are almost exclusively nonspherical. It has been extensively demonstrated that the spheroidal particle shape model represents a quantum leap forward, compared to the spherical model, for computing the optical properties of nonspherical particles. At present, the optical properties of small-to-large particles can be computed only for spheres. There is a pressing need to have an exact and robust computational capability to compute the optical properties of spheroidal particles. Leveraging advances in computational mathematics, advances in electromagnetic scattering theories, and modern computer technologies and computer coding techniques, this project aims to develop a novel program to compute the optical properties of spheroidal particle in the small-to-large particle size range. Because many bacteria, microweeds, oceanic particles, and interstellar dust particles have approximately spheroidal shapes, the outcome of this project will also find extensive applications in climate science (particularly the radiative energy budget in the climate system), remote sensing, industry, bio-optics, oceanic optics, astrophysics, planetary sciences, and other fields beyond atmospheric sciences. Because this project focuses on a major unsolved interdisciplinary problem and because of significant challenges, particularly from the perspective of computational electromagnetics and mathematics, this project is exploratory but potentially transformative, i.e., “high risk – high payoff”. In addition to its scientific merit, this project contains an educational component to train an early-career researcher in the interdisciplinary area mentioned above. This project aims to solve light scattering by a spheroid in spheroidal coordinates. Although solving the electromagnetic wave equation via the method of separation of variables in spheroid coordinates has been explored, the previously developed models are applicable only to particles that are small with respect to the incident wavelength and have little practical use. The major challenge encountered by the previous effort is numerical instability of spheroidal harmonic functions. This project will seek to achieve numerical stability of spheroidal harmonic functions by using advanced algorithms, such as expressing spheroidal functions in terms of the Wigner-d function. The key to computing spheroidal functions is to find eigenvalues of corresponding spheroidal equations. The radial and angular spheroidal equations are of the Sturm-Liouville type. The eigenvalues will be calculated by the invariant-imbedding method, which is expected to be numerically stable and accurate. Thus, the spheroidal functions are expected to be accurate even with extreme parameters. The overarching goal of this project is to develop a numerically stable capability for accurately computing the optical properties of a spheroid beyond the currently applicable particle size and aspect ratio ranges of other existing computational capabilities, such as the discrete dipole approximation method (DDA), the finite-difference time domain (FDTD) method, the extended boundary condition method (EBCM), and the invariant imbedding T-matrix method (IITM).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.

尘埃气溶胶通过部分吸收和反映传入的阳光和大气和表面发出的热能来影响全球气候。灰尘颗粒的光学特性对于减少尘埃气溶胶在气候系统中作用的不确定性至关重要，因此对于预测未来气候至关重要。灰尘颗粒光学性能也是从太空传播和基于地面的遥感观测值来推断尘埃气溶胶特性的基础。灰尘颗粒几乎完全非球。已经广泛证明，与球体模型相比，球形粒子形状模型代表了一个量子飞跃，用于计算非球体的光学性质。目前，只能针对球体计算小型粒子的光学性质。迫切需要具有确切且可靠的计算能力，以计算球形数学的前进性能的光学特性，电磁散射理论的进步以及现代的计算机技术和计算机编码技术，该项目旨在开发一个新颖的程序来开发一个新的程序，以计算一个小粒子的光学特性。因为许多细菌，微型齿，海洋颗粒和固定尘埃颗粒具有大致的球形形状，因此该项目的结果还将在气候科学（部分在气候系统中的辐射能量预算），远程敏感性，工业，生物选择，大洋洲光学，大洋天文学，平面物，其他气氛，其他气氛，其他风格，以及其他气氛，其他风格，以及其他大气层，其他风格，其他。因为该项目着重于一个主要的未解决的跨学科问题，并且由于面临重大挑战，尤其是从计算电磁学和数学的角度来看，因此该项目是探索性但潜在的变革性的，即“高风险 - 高收益”。除科​​学优点外，该项目还包含一个教育组成部分，以培训上述跨学科领域的早期研究人员。该项目旨在解决球形坐标中球形的光散射。尽管已经探索了通过在球体坐标中分离变量的方法来求解电磁波方程，但先前开发的模型仅适用于相对于入射波长很小的粒子，几乎没有实际使用。以前的努力遇到的主要挑战是球形谐波函数的数值不稳定性。该项目将寻求通过使用高级算法（例如根据Wigner-D函数表达球形函数）来实现球形谐波函数的数值稳定性。计算球形函数的关键是找到相应的球形方程的特征值。径向和角球形方程是Sturm-Liouville类型的。特征值将通过不变式的方法来计算，该方法有望单独稳定且准确。这是，即使使用极端参数，球形函数也有望准确。 The overarching goal of this project is to develop a numerically stable capability for accurately computing the optical properties of a sphere beyond the currently applicable particle size and aspect ratio ranges of other existing computational capabilities, such as the discrete dipole approximation method (DDA), the finite-difference time domain (FDTD) method, the extended boundary condition method (EBCM), and the invariant imbedding T-matrix method （IITM）。该奖项反映了NSF的法定使命，并通过使用基金会的知识分子优点和更广泛的影响评估标准来评估，被认为是珍贵的支持。