Ordering Mechanisms in Dynamical Systems

9412416这笔赠款由材料研究部的材料理论项目和物理部的数学物理活动共同资助。这项理论研究涉及几种不同的机制，这些机制可能在受简单动力学规则支配的系统中产生空间或时间顺序。重点是控制高频系统和时空复杂系统中的混沌，以及慢驱动动力系统中的相干全局振荡和自组织临界关联。近期的目标包括更全面地理解一种使用连续反馈控制混沌的新技术，开发用于检测自然系统中这种类型的控制机制的测试，以及分析显示全球振荡和新形式的自组织临界行为的沙堆的简单模型。这项理论研究属于非线性科学的一般领域，由物理和材料研究部共同支持。这项工作关注的是一类由简单的当地规则管理的问题。这项工作可能会影响单个半导体激光器件的设计，影响用于在此类激光器阵列或约瑟夫森结阵列中诱导相干的反馈机制的设计，以及表征从心脏混沌到颗粒材料中的雪崩等自然动力系统中观察到的不稳定性的更好方法。

9412416 This grant is supported jointly by the Materials Theory Program in the Division of Materials Research and the Mathematical Physics Activity in the Physics Division. The theoretical research concerns several different mechanisms that may play a role in generating spatial or temporal order in systems governed by simple dynamical rules. The emphases are on controlling chaos in high- frequency systems and spatiotemporally complex systems and on coherent global oscillations and self-organized critical correlations in slowly driven dynamical systems. Immediate goals include a more complete understanding of a novel technique for controlling chaos using continuous feedback, the development of tests for detecting this type of control mechanism in natural systems, and the analysis of simple models of sandpiles that exhibit global oscillations and novel forms of self-organized critical behavior. %%% This theoretical research is in the general area of nonlinear science and is jointly supported by the Physics and Materials Research Divisions. The work focuses on a class of problems which are governed by simple local rules. The work may impact the design of individual semiconductor laser devices, the design of feedback mechanisms for inducing coherence in arrays of such lasers or arrays of Josephson junctions, and better methods for characterizing the instabilities observed in natural dynamical systems ranging from cardiac chaos to avalanches in granular materials.