NSF-BSF: Global Correlation in complex structures

非技术摘要：材料无序普遍存在于自然和人造材料中。因此，重要的是要了解的影响，在不同领域的奋进，包括电子，电信，环境传感，生物医学成像和资源勘探的不同类型的波的流动的障碍。该研究小组试图根据材料整体的波散射来发现控制无序材料中波流动的共同原理。该研究计划探索如何创建一个状态，在该状态下，传输消失，传输变得对材料的变化非常敏感。研究小组还探索了微波辐射在含有金属元素的样品中的极端散射，这可能为极端捕获波开辟了新的方法。从实验和理论分析两方面探讨了利用微波辐射在散射介质中的传输进行信息处理的可行性。多样化的研究项目为高中，本科和研究生提供了参与理论，模拟，统计分析和波浪流动实验的机会，作为国际团队解决强烈的基础和应用兴趣问题的一部分。技术摘要：研究团队对无序系统中波的全局相关性的基本方面进行了相关的实验，计算和理论研究，这些研究在激发工程，光学计算，成像和传感方面具有潜在的应用。复杂系统中波的许多最有趣、最具挑战性和潜在有用的方面都来自于该领域的全局相关性。这种相关性决定了连接入射场和输出场的传输矩阵的统计特性。研究小组探索了传输矩阵的奇异性，即介质的谐振和传输零点。本研究（1）研究了复频率平面上传输零点随样本变化的演化规律;（2）探讨了传输本征通道轴向速度在随机样本上的相关性及其对随机系统激发能量的影响;（3）研究了某些随机系统中态密度消失的特征和来源，（4）探索了具有金属元件的系统中的传播的性质，（5）研究了通过散射样本的传输矩阵的随机映射的降维，以及，（六）探索在传输本征信道的背景下通过散射介质传播的微波辐射的随机投影。该奖项反映了NSF的法定使命，并被认为是值得的通过使用基金会的知识价值和更广泛的影响审查标准进行评估，

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.