Simulation of the Wave-Matter Interactions at Extreme Scales

Iowa State University, Ames IA

Investigators

Abstract

This project is devoted to providing reliable models and the state-of-the-art numerical methods for studying the wave-matter interactions at extreme scales as in geometrical optics, kinetic models, and nano optics, with practical applications arising from astrophysics, geosciences, plasma physics, fusion energy sciences, biology, semiconductor technology, material sciences, nano-technology and nano-sciences. For example, the geophysical exploration processes, the wave-plasma interactions in fusion energy sciences, and the fabrication of nano-motors for solar energy conversion. The proposed models and numerical methods are based on knowledge of geometrical optics, physical optics, kinetic theories, nano optics, computational chemistry and scientific computing. Interdisciplinary collaborations will be pursued to extend the practical applications of the proposed methods. The project also involves the integration of research and education in computational mathematics. Graduate and undergraduate students, and members from underrepresented groups will be encouraged to participate in the project to enhance their knowledge and research. The proposed project will further the training and education of students and encourage them to pursue future career in science, technology, engineering and mathematics (STEM). In the project, reliable models and efficient numerical methods will be proposed to simulate the wave-matter interactions at extreme scales: (I) If the size of the matter is much greater than the wavelength, the interactions are equivalent to high frequency wave propagation in inhomogeneous media. The PI will develop asymptotic methods that combine integral representations of the waves and asymptotic high frequency theories (notably geometrical optics). (II) If the size of the matter decreases to meso or micro scale, kinetic models are popularly applied for modeling the interactions. The PI will develop asymptotic methods that utilize the Hopf-Cole transformation of the 6-D probabilistic distribution function. (III) If the size of the matter keeps decreasing to nano or atomic scale, the motion of the matter must be determined quantum mechanically while the wave propagation is determined. The PI will use semi-classical theories as the building block to develop numerically trackable semi-classical models and efficient multi-scale methods. The core ideas consist of the following: For (I), integral representations with Green's functions will serve as the mechanism for wave propagation, geometrical optics approximations will provide the information of Green's functions, and fast multi-level algorithms will be designed to evaluate the oscillatory integrals efficiently with optimal complexities. For (II), the phase function of the Hopf-Cole transformation of the probabilistic distribution function will be approximated as a power series expansion with the expansion terms determined through solutions of equations formulated in 3-D spatial space, and high-order schemes can be designed to solve such equations efficiently. For (III), the wave propagation will be determined classically through Maxwell's equations, Ehrenfest molecular dynamics and time-dependent current density functional theory will be applied to resolve the difficulty of dealing with many-body Schrodinger equations for the matter, and the models will be solvable by well-designed multi-scale solvers.