Nonlinear Dynamics of Solids and Networks

该奖项支持理论凝聚态物理学的综合研究，教育和推广活动。该研究计划的目标是开发新的集成建模问题，涉及相互作用网络的非线性动力学。这些问题出现在材料的机械性能中，从断裂和摩擦到起皱的膜。这项研究工作还将试图将这种方法扩展到医学和生物学的另一个学科边界。该项目将研究在网络由易感人群组成的流行病中疾病传播的问题。以非线性动力学为工作模式的问题跨越了许多领域。有一些共同的主题，例如使用统计物理学和标度定律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可以推广到许多系统。 在这项研究中，具体的问题包括：（i）橡胶的断裂，特别是介观性质和宏观现象之间的联系，（ii）静摩擦动力学。(iii)在大电场和电流存在下的原子尺度摩擦。(iv)膜的几何学与度量。(v)网络上的流行病通过这些不同的调查，需要对非线性科学的基本理解的概括正在出现。这项研究有非常强的教育承诺，再加上它。除了准备研究生和博士后研究人员在学术或工业研究和发展的职业生涯，通过非线性科学的主题已经成为课程的一部分，基于研究小组的专业知识，所以这是很多学生都能够体验到的。在大学之外，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。非技术总结：该奖项支持理论凝聚态物理学的综合研究，教育和推广活动，中心是非线性动力学。非线性动力学涵盖了从宇宙的奇异理论到真实的生活中事物失效的实际问题。本研究中采用的一个例子是预测弹性材料何时停止拉伸（结束线性状态）和开始破裂（进入非线性动力学状态）。 在真实的意义上，聚合物断裂的一个问题可能导致非线性动力系统理论的根本性进步，并有助于防止垃圾袋破裂。该研究计划的目标是开发新的集成建模问题，涉及相互作用网络的非线性动力学。这些问题出现在材料的机械性能超过正常极限时。这项研究工作还将试图将这种方法扩展到医学和生物学的另一个学科边界。该项目将处理有关流行病中疾病传播的问题。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，可能有助于预测流行病。这项研究的第一个教育效益在于参与研究的研究生，他们的工作是博士学位的基础。 论文但是，该研究项目的主要研究者也参与了其他支持K-12教师推广和专业发展的努力。因此，在这项研究中遇到的材料被用于创建教师准备的材料，并提供有趣的主题，PI可以在推广活动中使用到广大公众。调查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.