Behaviors of Systems with Many Interacting Components

这个程序关注的是具有多个自由度的系统的行为-无限大或渐近大。在这种情况下，所有组成部分的详细行为基本上是一个毫无意义的概念，人们寻找的是（a）系统作为一个整体的集体行为或（B）单个组成部分行为的统计描述。在可行的情况下，PI对各种系统的分析将体现这两种描述。这些研究将使用四种相互关联的方法，从凝聚态问题的解释。这些是（i）经典自旋粒子系统，（ii）量子自旋系统，（iii）相互作用粒子模型和（iv）集群模型/图形表示。将审查所有四类问题。具体的例子包括量子，经典和连续流体系统中的不连续相变，由于无序介质中的不均匀性和临界二维系统的方法，其连续共形不变的限制，中断和增强的运输。PI与场论和凝聚态物理领域的物理学家以及来自各个分支学科的数学家保持着广泛的联系。大多数情况下，PI带来了必要的数学，以引起对物理系统的增强理解。有时，对特定系统的物理洞察力会影响相关的数学领域。一种从20世纪60年代末开始流行的哲学是普遍性-大规模和/或长期的集体行为不依赖于模型的细节。因此，虽然该提案的主要科学目标倾向于物理科学的进步，但这些研究直接导致对具有补充应用的模型的考虑。特别是：（1）研究生物系统和拥挤的人类群体中的集体群集行为，并进一步应用于监视和收集情报。(2)研究犯罪行为，并应用于住宅抢劫发生率统计中的热点形成和敌对街头帮派的敌意互惠。(3)研究信息在大规模网络中的传播和流动。这项研究涵盖了各个层面广泛的应用研究机会。该计划将需要许多合作者的协助和加州大学洛杉矶分校的设施的广泛使用。PI与来自各种文化背景的本科生，研究生，博士后和高级研究人员合作，男女都有充分的代表性。

This program concerns the behavior of systems with many degrees of freedom - either infinite or asymptotically large. Under these circumstances, the detailed behavior of all the constituents is essentially a meaningless concept and one looks for (a) collective behavior of the system as a whole or (b) a statistical description of the behavior of an individual component. The analyses of various systems pursued by the PI will, whenever feasible, embody both descriptions. The studies will use four interrelated methods from depictions of condensed matter problems. These are (i) Classical Spin & Particle Systems, (ii) Quantum Spin Systems, (iii) Interacting Particle Models and (iv) Cluster Models/Graphical Representations. Problems from all four categories will be examined. Specific instances include discontinuous phase transitions in quantum, classical and continuum fluid systems, the disruptions and enhancements of transport due to inhomogeneities in disordered media and the approach of critical 2D systems to their continuum conformal invariant limits. The PI maintains extensive contact with physicists in the areas of field theory and condensed matter physics as well as mathematicians from various subdisciplines. Most often the PI brings to bear the necessary mathematics in order to elicit enhanced understanding of a physical system. On occasion, physical insight for a particular system can influence the associated areas of mathematics.Broader Impact. A philosophy which became prevalent beginning in the late 1960s is that of universality - largescale and/or longtime collective behaviors do not depend on the details of the model. Hence, while the primary scientific goals of this proposal lean towards the advancement of the physical sciences, these investigations lead directly to considerations of models with supplemental applications. In particular: (1) Studies of collective swarming behavior in biological systems and in crowded human aggregations with further applications to surveillance and gathering of intelligence. (2) Studies of criminal behavior with applications to hotspot formation in the statistical occurrences of residential burglaries and to hostility reciprocations of rival street gangs. (3) Studies of the dissemination and flow of information in large scale networks. This research encompasses an extensive array of applications research opportunities at every level. The program will require the assistance of many collaborators and extensive use of the facilities at UCLA. The PI has collaborated with undergraduate, graduate, postdoctoral, and senior level coresearchers from a variety of cultural backgrounds with both genders adequately represented.