Non-Markovian Diffusion Imaging

在化学测量与成像项目的支持下，以及原子、分子和光学物理实验与理论项目的共同资助下，加州大学洛杉矶分校的布查德教授正在开发研究气体扩散的新方法——气体中分子的随机运动。在这些过程的传统模型中，假设任何给定时刻的快照（状态）与气体中游动的分子之间过去的碰撞无关。然而，如果照片拍得足够快，就有可能探测到分子对最近碰撞的“记忆”，从而研究分子所遇到的表面的性质。布沙尔博士的团队正在开发实验方法和基础理论，以促进对这些碰撞记忆很重要的系统（例如催化剂和肺）的理解。他们使用核磁共振（NMR）光谱学，这是磁共振成像（MRI，一种重要的医学诊断工具）的核心工具，可以避免使用有害的电离辐射，如x射线。从事这项研究的研究生和本科生接受广泛的跨学科培训，并为相关入门化学材料的开发做出贡献，这些材料将免费向公众提供。中性分子稠密气体中的自扩散是非马尔可夫的，必须用带记忆核的朗之万方程来模拟。Bouchard小组已经获得了与广义朗之万描述一致的实验核磁共振波谱结果，正如在Carr-Purcell-Meiboom-Gill （CPMG）实验中意外的核磁共振线宽温度依赖性以及脉冲间隔依赖性所证实的那样。虽然新理论很好地描述了自由自扩散的结果，但边界存在时的扩散行为尚未得到探讨。Bouchard博士目前正在探索具有各种边界的多孔介质中的受限扩散，并基于有界扩散（粘性、反射、杀伤和吸收边界）的随机微积分对基础理论进行了新的扩展。基于核磁共振的新方法可能会为气体动力学理论带来新的启示，通过提供新的工具来提取多孔岩石、土壤或肺部等介质中的孔隙结构和功能信息，从而有利于化学物理学和医学成像。这些工具还显示出对催化反应表面和反应过程中质量传递的表征，以及对超极化气体MRI的更好理解。教育方面的影响将来自于对多名学生的培训和积极参与研究，以及通过该机构网站发布的免费在线教育课程材料的创建。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。

With support from the Chemical Measurement & Imaging program and co-funding from the Atomic, Molecular, and Optical Physics - Experiment and Theory programs, Professor Bouchard at the University of California, Los Angeles is developing new methods to study gaseous diffusion - the random motions of molecules in gases. In traditional models of these processes, a snapshot (state) at any given moment is assumed to be independent of past collisions between molecules swimming in the gas. However, if the picture can be taken quickly enough, it is possible to detect molecules’ "memory" of collisions from the recent past, and thus to investigate the nature of surfaces encountered by the molecules. Dr. Bouchard's group is developing both experimental methods and the underlying theory to advance understanding in systems (e.g., catalysts and lungs) where the memory of these collisions are important. They use nuclear magnetic resonance (NMR) spectroscopy, the tool at the heart of Magnetic Resonance Imaging (MRI, an important medical diagnostic tool) which avoids the use of harmful ionizing radiation like x-rays. Graduate and undergraduate students engaged in this research receive broad interdisciplinary training, and contribute to the development of relevant introductory chemistry materials that will be made freely available to the public. Self-diffusion in a dense gas of neutral molecules is non-Markovian and must be modeled by a Langevin equation with memory kernel. The Bouchard group has obtained experimental NMR spectroscopy results that are consistent with a generalized Langevin description, as confirmed by an unexpected temperature dependence of the NMR linewidth as well as dependence on inter-pulse spacing during Carr-Purcell-Meiboom-Gill (CPMG) experiments. While the new theory describes the results of free self-diffusion well, the diffusion behavior in the presence of boundaries has not yet been explored. Dr. Bouchard is now probing restricted diffusion in porous media possessing various types of boundaries, and developing new extensions of the underlying theory based on the stochastic calculus of bounded diffusions (sticky, reflecting, killing, and absorbing boundaries). The new NMR-based methods may shed new light into the kinetic theory of gases, benefitting chemical physics and medical imaging by offering new tools to extract information about pore structure and function in media such as porous rocks, soils, or lungs. The tools also show promise for both characterization of catalytically reactive surfaces and mass transport during reactions and provision of a better understanding of hyperpolarized gas MRI. Educational impacts will derive from the training and active participation of multiple students in the research as well as the creation of free online educational course materials disseminated via the institution's web site.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.