Nonlinear Dynamics of Solids and Networks

技术综述：该奖项支持理论凝聚态物理的综合研究、教育和推广活动。这项研究的目标是开发涉及相互作用网络的非线性动力学问题的新的集成建模。这些问题出现在材料的机械性能上，从断裂和摩擦到起皱的薄膜。这项研究还将尝试将这种方法跨越另一门学科的界限扩展到医学和生物学。该项目将处理有关疾病在流行病中传播的问题，在流行病中，网络由易感人群组成。以非线性动力学为工作模式的问题涉及多个领域。有一些共同的主题，比如使用统计物理和标度定律来对复杂的非线性动力系统进行详细的预测。研究是针对具体问题进行的，但由此产生的理论突破往往适用于许多制度。在这项研究中，具体的问题包括：(I)橡胶的断裂，特别是介观性质与宏观现象之间的联系，(Ii)静摩擦动力学。(3)在大电场和大电流存在的情况下，原子尺度上的摩擦。(Iv)带度量的膜几何。(V)网络上的流行病。通过这样不同的调查，对非线性科学的基本理解所需的概括正在形成。这项研究具有非常强大的教育承诺。除了为研究生和博士后研究人员在学术或工业研发领域的职业生涯做准备外，基于课题组的专业知识，非线性科学主题已成为课程的一部分，因此它是许多学生能够体验到的。除了大学之外，PU还参与了一个强大的K-12教学推广计划，将K-12教师与大学研究人员联系起来，作为K-12教师专业发展的一部分。非技术概述：该奖项支持理论凝聚态物理与中心在非线性动力学方面的综合研究、教育和推广活动。非线性动力学涵盖了从奇异的宇宙理论到现实生活中事物失败的实际问题。这项研究中采用的一个例子是预测弹性材料何时停止拉伸(结束线性区域)并开始破裂(进入非线性动力学区域)。在非常真实的意义上，聚合物断裂中的一个问题可以导致非线性动力系统理论的根本进步，并有助于防止垃圾袋破裂。这项研究的目标是开发涉及相互作用网络的非线性动力学问题的新的集成建模。这些问题出现在超出正常极限的材料的机械性能上。这项研究还将尝试将这种方法跨越另一门学科的界限扩展到医学和生物学。该项目将处理有关流行病中疾病传播的问题。对聚合物网络破裂的研究提供了理论工具，当网络由易感个体组成时，这些工具可能有助于预测流行病。这项研究的第一个教育好处在于参与研究的研究生，对他们来说，这项工作是博士论文的基础。但是，这项研究项目的首席调查员还参与了支持K-12教师外展和专业发展的其他努力。因此，这项研究中遇到的材料被用来为教师准备编写材料，并提供有趣的主题，供国际宣传社在向广大公众宣传活动中使用。研究人员的活动还包括更新凝聚态物理学的研究生教科书，并指导一个国家认可的教师培训计划。

TECHNICAL SUMMARY:This award supports integrated research, education and outreach activities in theoretical condensed matter physics. The goal of this research program is to develop new integrated modeling of problems involving nonlinear dynamics of interacting networks. These problems arise in the mechanical properties of materials ranging from fracture and friction to wrinkled membranes. This research effort will also attempt to extend this approach across another disciplinary boundary into medicine and biology. The project will take up problems concerning diseases propagation in epidemics where the networks consists of the population of susceptible individuals. The problems where nonlinear dynamics is the operational mode span many fields. there are common themes such as the use of statistical physics and scaling laws to make detailed predictions about complicated nonlinear dynamical systems. Research is carried out on specific problem, but resulting theoretical breakthroughs are often generalizable to many system. In this research, specific problems include: (i) The fracture of rubber, particularly connections between mesoscopic properties and macroscopic phenomena, (ii) Dynamics of static friction. (iii) Friction at the atomic scale in the presence of large electrical fields and currents. (iv) Geometries of membranes with metrics. (v) Epidemics on networks. Through such diverse investigations, the generalizations needed for a fundamental understanding of nonlinear science are emerging.This research has very strong educational commitments coupled to it. In addition to preparing graduate students and postdoctoral researchers for careers in academic or industrial research and development, by the topic of nonlinear science has become part of the curriculum based on the expertise of the research group, so it is something many students are able to experience. Beyond the university, there PU is engages in a strong K-12 teaching outreach program that connects K-12 teachers to university researchers as part of K-12 teacher professional development.NON-TECHNICAL SUMMARY:This award supports integrated research, education and outreach activities in theoretical condensed matter physics with the central these on nonlinear dynamics. Nonlinear dynamics spans the range from exotic theories of the cosmos to the practical matters of when things fail in real life. One example taken up in this research is prediction of when elastic material cease to stretch (end the linear regime) and begin to rupture (enter the regime of nonlinear dynamics). In a very real sense, the one problem in polymer fracture could result in both fundamental advance in the theory of nonlinear dynamical systems and help keep garbage bags from breaking. The goal of this research program is to develop new integrated modeling of problems involving nonlinear dynamics of interacting networks. These problems arise in the mechanical properties of materials pushed beyond normal limits. This research effort will also attempt to extend this approach across another disciplinary boundary into medicine and biology. The project will take up problems concerning diseases propagation in epidemics. The studies of rupture in networks of polymers provides theoretical tools that may help make predictions about epidemics when networks consists of the population of susceptible individuals. The first educational benefit of this research resides with the graduate students who participate in the research and for whom the work is the foundation for the Ph.D. dissertation. But, the principle investigator of this research project is also involved in other efforts supporting outreach and professional development for K-12 teachers. As a consequence, the material encountered in this research is employed in creating materials for teacher preparation, and in supplying interesting topics the PI can use in outreach activities to the broad public. Activities of the investigator also include updating a graduate textbook in condensed matter physics and directing a nationally recognized program for preparation of teachers.