PIRE: Percolative and Disordered Systems: A U.S.- Brazil-Netherlands Based International Collaboration

该项目涉及概率论和统计物理重叠领域的国际研究和教育合作：无序系统、渗流和Schramm-Loewner进化（SLEs）。参与机构包括纽约大学Courant数学科学研究所、巴西巴西国立应用科学研究所Matemática和阿姆斯特丹信息科学中心。来自其他科研机构的教师、博士后和学生也参与了该项目的网络和活动（如夏季和冬季学校）。该项目涉及随机空间过程，包括无序系统，如自旋玻璃和随机行走陷阱和随机环境，其中宏观现象自然地表达为微观事件渗透空间（或时空）的路径。尺度概念和方法在分析这类过程及其相变和临界行为的本质中起着重要作用。近年来，在渗流及其尺度限制、自旋玻璃和无序随机漫步等方面取得了一些重大进展，PI、联合PI和主要国际合作者都是其中的主要参与者。该项目涉及的问题包括分析现实（即短程）模型中自旋玻璃转变的渗透特征，以及近临界渗透和二维及多维无序随机游走的缩放限制。这些和相关的挑战性问题已经成熟，可以结合美国和国外参与者的各种专业知识进行协作攻击。此外，本项目为渗透和无序系统开发的新技术可以应用于各种领域，包括通信、材料科学、神经科学、理论计算机科学和石油工程。该项目重点培养来自不同背景的美国学生、博士后和教师，从事国际教育和研究合作。piire博士后和博士前研究员预计将在国外度过至少一个学期，由一名国际合作者和一名Courant教职员工共同指导。鼓励其他学生和博士后通过短期访问和参加季节性学校进行国际合作。2008年1月，拉丁美洲的冬季（北半球）学校在智利的圣地亚哥开学；2008年6月，一所一年一度的欧洲暑期学校在意大利佛罗伦萨的纽约大学校园开课。该项目的一个主要目标是为美国、拉丁美洲和欧洲之间的教师、博士后和学生之间的自我维持合作模式建立一个制度基础。目前正在联系各基金会和工业界提供支助，以便将从该方案项目中获得的经验转化为教育和研究方面国际合作的自我维持模式。该项目由国际科学与工程办公室（OISE）和数学科学部（DMS）共同资助。

This PIRE project involves international research and education collaboration in overlapping areas of probability theory and statistical physics: disordered systems, percolation, and Schramm-Loewner evolutions (SLEs). Participating institutions include the Courant Institute of Mathematical Sciences of New York University, the Instituto Nacional de Matemática Pura e Aplicada of Rio de Janeiro, and the Centrum voor Wiskunde en Informatica of Amsterdam. Faculty, postdocs and students from other scientific institutions are also involved in the networks and activities (such as summer and winter schools) of this PIRE project.The project concerns random spatial processes, including disordered systems such as spin glasses and random walks with traps and in random environments, in which macroscopic phenomena are naturally expressed in terms of paths of microscopic events that percolate through space (or space-time). Scaling concepts and methods play an important role in the analysis of such processes and in the nature of their phase transitions and critical behavior. The PI, co-PIs and key international collaborators have been prime participants in some of the major progress in recent years on percolation and its scaling limits, as well as on spin glasses and disordered random walks. Among the issues addressed in this project are analyses of the percolation signature of the spin glass transition in realistic (i.e., short-range) models and of scaling limits for near-critical percolation and disordered random walks in two and more dimensions. These and related challenging problems are ripe for a collaborative attack combining the diverse expertise of the participants from the U.S. and abroad. Moreover, the new techniques being developed in this project for percolative and disordered systems can be applied in a variety of fields, including communication, materials science, neural science, theoretical computer science and petroleum engineering.This project focuses on training U.S. students, postdoctoral fellows and faculty from various backgrounds in international education and research collaboration. PIRE postdoctoral and predoctoral fellows are expected to spend at least one semester abroad with collaborative joint mentoring by one of the international collaborators together with a Courant faculty member. Other students and postdocs will be encouraged to collaborate internationally via shorter visits and by participating in seasonal schools. A yearly winter (in the Northern hemisphere) school in Latin America starts January, 2008 in Santiago, Chile; a yearly summer school in Europe starts June, 2008 at the NYU campus in Florence, Italy. A major goal of this project is to create an institutional basis for a self-sustaining model of enhanced collaboration at faculty, postdoctoral and student levels between the U.S., Latin America and Europe. Contacts are being made for support from foundations and industry to turn the experience developed from this PIRE project into a self-sustaining model for international collaboration in education and research. This PIRE project is funded by the Office of International Science and Engineering (OISE) with co-funding from the Division of Mathematical Sciences (DMS).