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.

粉尘气溶胶通过部分吸收和反射入射的阳光以及大气和地表发出的热能来影响全球气候。尘埃颗粒的光学特性对于减少目前关于尘埃气溶胶在气候系统中的作用的认识的不确定性至关重要，因此对于预测未来气候也很重要。尘埃粒子的光学特性也是从星载和地面遥感观测推断尘埃气溶胶特征的基础。灰尘颗粒几乎都是非球形的。已经广泛证明，与球形模型相比，球形颗粒形状模型在计算非球形颗粒的光学特性方面代表了巨大的飞跃。目前，只能计算球体从小到大颗粒的光学特性。迫切需要拥有精确且强大的计算能力来计算球状粒子的光学特性。利用计算数学的进步、电磁散射理论的进步以及现代计算机技术和计算机编码技术，该项目旨在开发一种新颖的程序来计算从小到大粒径范围内球体粒子的光学特性。由于许多细菌、微草、海洋颗粒和星际尘埃颗粒具有近似球形的形状，该项目的成果还将在气候科学（特别是气候系统中的辐射能量收支）、遥感、工业、生物光学、海洋光学、天体物理学、行星科学以及大气科学以外的其他领域得到广泛的应用。由于该项目关注的是一个尚未解决的重大跨学科问题，并且由于面临重大挑战，特别是从计算电磁学和数学的角度来看，该项目是探索性的，但具有潜在的变革性，即“高风险-高回报”。除了其科学价值外，该项目还包含教育内容，旨在培训上述跨学科领域的早期职业研究人员。该项目旨在解决球体坐标中球体的光散射问题。尽管已经探索了通过椭球体坐标中的变量分离方法求解电磁波方程，但先前开发的模型仅适用于相对于入射波长较小的粒子，几乎没有实际用途。先前的努力遇到的主要挑战是球谐函数的数值不稳定性。该项目将寻求通过使用先进的算法来实现球谐函数的数值稳定性，例如用 Wigner-d 函数来表达球函数。计算球体函数的关键是找到相应球体方程的特征值。径向和角球体方程属于 Sturm-Liouville 类型。特征值将通过不变嵌入方法计算，预计该方法在数值上稳定且准确。因此，即使参数极端，球体函数也有望准确。该项目的总体目标是开发一种数值稳定的能力，用于精确计算球体的光学特性，超出其他现有计算能力当前适用的粒径和纵横比范围，例如离散偶极近似法（DDA）、时域有限差分法（FDTD）、扩展边界条件法（EBCM）和不变嵌入T矩阵法 (IITM)。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。