NSF-BSF: Global Correlation in complex structures

非技术摘要：材料无序在天然材料和人造材料中普遍存在。因此，重要的是要了解无序对电子、电信、环境传感、生物医学成像和资源勘探等不同领域中不同类型波的流动的影响。该研究小组试图发现控制无序材料中波流动的共同原理，基于整个材料的波散射。这项研究计划探索如何创造一种状态，在这种状态下，传输消失，传输对材料的变化变得极其敏感。研究小组还探索了含有金属元素的样品中微波辐射的极端散射，这可能会打开极端捕获波的新方法。从实验和理论分析两个方面探讨了利用微波辐射在散射介质中传输进行信息处理的可行性。多样化的研究项目为高中生、本科生和研究生提供了从事波浪流动的理论、模拟、统计分析和实验的机会，作为解决强烈基础和应用兴趣问题的国际团队的一部分。技术概述：该研究小组对无序系统中波的全局关联的基本方面进行了关联的实验、计算和理论研究，在激发工程、光学计算、成像和传感方面具有潜在的应用前景。复杂系统中波的许多最耐人寻味、最具挑战性和潜在有用的方面来自于该场的全球相关性。这种相关性管理链接入射场和出射场的传输矩阵的统计。研究小组探索了传输矩阵的奇点，即介质和传输零点的共振。本研究(1)研究了传输零点在复频率平面上随样本变化的演化；(2)研究了随机样本间传输本征道的轴向速度的相关性及其对随机系统中激发能量的影响；(3)研究了某些随机系统中态密度消失的特征和来源；(4)探索了含有金属元素的系统中传输的本质；(5)通过散射样本的传输矩阵研究了随机映射中的降维问题；以及，(6)探索微波辐射在传输本征信道背景下通过散射介质传播的随机投影。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Non-technical Abstract:Material disorder is pervasive in natural and fabricated materials. It is therefore important to understand the impact of disorder on the flow of different types of waves in diverse fields of endeavor including electronics, telecommunications, environmental sensing, bio-medical imaging, and resource exploration. The research team seeks to discover common principles governing the flow of waves in disordered materials based on wave scattering in the entirety of a material. This research program explores how to create a state in which transmission vanishes and transmission becomes extremely sensitive to changes in a material. The research team also explores extreme scattering of microwave radiation in samples with metallic elements, which may open up new approaches to the extreme trapping of waves. The feasibility of harnessing the transmission of microwave radiation in scattering media for information processing are explored in experiments and theoretical analysis. The diverse research projects provide high school, undergraduate and graduate students the opportunity to engage with theory, simulations, statistical analysis, and experiments of the flow of waves as part of an international team tackling problems of intense fundamental and applied interest. Technical Summary:The research team carries out linked experimental, computational and theoretical studies of fundamental aspects of global correlation of waves in disordered systems with potential applications in excitation engineering, optical computation, imaging, and sensing. Many of the most intriguing, challenging, and potentially useful aspects of waves in complex systems arise from global correlation of the field. Such correlation governs the statistics of the transmission matrix which links the incident and outgoing fields. The research team explores the singularities of the transmission matrix, which are the resonances of the medium and the transmission zeros. This research (1) studies the evolution of transmission zeros in the complex frequency plane as samples are changed, (2) explores the correlation of the axial velocity of transmission eigenchannels across random samples and its impact upon the energy excited within random systems, (3) investigates the characteristics and source of the vanishing of the density of states within certain random systems, (4) explores the nature of propagation in systems with metallic elements, (5) investigates dimensionality reduction in random mappings via the transmission matrix of scattering samples, and, (6) explores random projections of microwave radiation propagating through scattering media in the context of transmission eigenchannels.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.