US-Mexico Cooperative Research: Statistical Mechanics of Chemical Kinetics and Random Systems

该奖项将支持波士顿大学的西德尼·雷德纳教授与墨西哥库尔纳瓦卡国立自治大学的弗朗索瓦·A·莱夫拉兹教授的研究合作。研究人员打算以现代统计力学的方法为基础，研究广泛的动力学和动力学现象。这项研究的一个主要目的是从总体上阐明涨落在简单扩散控制反应中的作用，以及在可逆和不可逆化学反应中的慢弛豫现象。此外，研究人员将寻求更好地理解系统的多重分形性背后的基本物理规律，如随机电阻网络和随机系统下的一类物理过程，这些随机系统包括流体动力弥散和过滤。了解扩散控制反应的动力学是一个重要的基础科学问题，有着广泛的应用，如凝聚体中的捕获和松弛过程，聚集和凝胶化过程，以及化学反应器工程。应用现代和强大的工具，如标度和重整化群，应该会对这些过程产生进一步的见解。随机系统的研究是一个较新的研究领域，无序的影响导致了各种新的物理现象，同时也提出了一些基本和持久的问题。墨西哥方面将在扩散和聚集过程领域提供强大的背景知识，而美国方面将带来统计力学和随机系统研究方面的专业知识。

This award will support Professor Sidney Redner of Boston University in a research collaboration with Professor Francois A. Leyvraz of the National Autonomous University in Cuernavaca, Mexico. The investigators intend to study a wide-range of kinetic and dynamic phenomena, based on approaches using modern statistical mechanics. A major goal of the research is to elucidate, in general terms, the role of fluctuations in simple diffusion-controlled reactions, as well as slow relaxation phenomena in both reversible and irreversible chemical reactions. In addition, the researchers will seek a better understanding of the fundamental physical laws underlying multi-fractality for systems such as the random resistor network and a class of physical processes under random systems that encompass hydrodynamic dispersion and filtration. Understanding the kinetics of diffusion-controlled reactions is an important basic science problem with a wide variety of applications, such as trapping and relaxation processes in condensed-matter, aggregation and gelation processes, and chemical reactor engineering. Application of modern and powerful tools, such as scaling and the renormalization group, should yield further insights into these processes. The study of random system is a much more recent area of research, the effects of disorder giving rise to a variety of new physical phenomena, as well as posing fundamental and enduring questions. The Mexican side will contribute a strong background in the area of diffusion and aggregation processes while the U.S. side brings to the collaboration expertise with statistical mechanics and the study of random systems.