Novel Computational Methods for Eigenvalue Problems

This dissertation focuses on novel computational method for eigenvalue problems. In Chapter 1, preliminaries of functional analysis related to eigenvalue problems are presented. Some classical methods for matrix eigenvalue problems are discussed. Several PDE eigenvalue problems are covered. The chapter is concluded with a summary of the contributions. In Chapter 2, a novel recursive contour integral method (RIM) for matrix eigenvalue problem is proposed. This method can effectively find all eigenvalues in a region on the complex plane with no a priori spectrum information. Regions that contain eigenvalues are subdivided and tested recursively until the size of region reaches specified precision. The method is robust, which is demonstrated using various examples. In Chapter 3, we propose an improved version of RIM for non-Hermitian eigenvalue problems, called SIM-M. By incorporating Cayley transformation and Arnoldi’s method, the main computation cost of solving linear systems is reduced significantly. The numerical experiments demonstrate that RIM-M gains significant speed-up over RIM. In Chapter 4, we propose a multilevel spectral indicator method (SIM-M) to address the memory requirement for large sparse matrices. We modify the indicator of RIM-M such that it requires much less memory. Matrices from University of Florida Sparse Matrix Collection are tested, suggesting that a parallel version of SIM-M has the potential to be efficient. In Chapter 5, we develop a novel method to solve the elliptic PDE eigenvalue problem. We construct a multi-wavelet basis with Riesz stability in H1 0 ( ). By incorporating multi-grid discretization scheme and sparse grids, the method retains the optimal convergence rate for the smallest eigenvalue with much less computational cost

Recursive integral method for transmission eigenvalues

Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse problems for target identification and nondestructive testing. The problem is numerically challenging because it is non-selfadjoint and nonlinear. In this paper, we propose a recursive integral method for computing transmission eigenvalues from a finite element discretization of the continuous problem. The method, which overcomes some difficulties of existing methods, is based on eigenprojectors of compact operators. It is self-correcting, can separate nearby eigenvalues, and does not require an initial approximation based on some a priori spectral information. These features make the method well suited for the transmission eigenvalue problem whose spectrum is complicated. Numerical examples show that the method is effective and robust.Comment: 18 pages, 8 figure

A Variational Auto-Encoder Enabled Multi-Band Channel Prediction Scheme for Indoor Localization

Indoor localization is getting increasing demands for various cutting-edged technologies, like Virtual/Augmented reality and smart home. Traditional model-based localization suffers from significant computational overhead, so fingerprint localization is getting increasing attention, which needs lower computation cost after the fingerprint database is built. However, the accuracy of indoor localization is limited by the complicated indoor environment which brings the multipath signal refraction. In this paper, we provided a scheme to improve the accuracy of indoor fingerprint localization from the frequency domain by predicting the channel state information (CSI) values from another transmitting channel and spliced the multi-band information together to get more precise localization results. We tested our proposed scheme on COST 2100 simulation data and real time orthogonal frequency division multiplexing (OFDM) WiFi data collected from an office scenario

Recent advances in ocular graft-versus-host disease

Ocular graft-versus-host-disease (GVHD) remains a significant clinical complication after allogeneic hematopoietic stem cell transplantation. Impaired visual function, pain, and other symptoms severely affect affected individuals’ quality of life. However, the diagnosis of and therapy for ocular GVHD involve a multidisciplinary approach and remain challenging for both hematologists and ophthalmologists, as there are no unified international criteria. Through an exploration of the complex pathogenesis of ocular GVHD, this review comprehensively summarizes the pathogenic mechanism, related tear biomarkers, and clinical characteristics of this disease. Novel therapies based on the mechanisms are also discussed to provide insights into the ocular GVHD treatment

Excitonic Mott insulator in a Bose-Fermi-Hubbard system of moir\'e WS2\rm{WS}_2/WSe2\rm{WSe}_2 heterobilayer

Understanding the Hubbard model is crucial for investigating various quantum many-body states and its fermionic and bosonic versions have been largely realized separately. Recently, transition metal dichalcogenides heterobilayers have emerged as a promising platform for simulating the rich physics of the Hubbard model. In this work, we explore the interplay between fermionic and bosonic populations, using a $\rm{WS}_2$/$\rm{WSe}_2$ heterobilayer device that hosts this hybrid particle density. We independently tune the fermionic and bosonic populations by electronic doping and optical injection of electron-hole pairs, respectively. This enables us to form strongly interacting excitons that are manifested in a large energy gap in the photoluminescence spectrum. The incompressibility of excitons is further corroborated by measuring exciton diffusion, which remains constant upon increasing pumping intensity, as opposed to the expected behavior of a weakly interacting gas of bosons, suggesting the formation of a bosonic Mott insulator. We explain our observations using a two-band model including phase space filling. Our system provides a controllable approach to the exploration of quantum many-body effects in the generalized Bose-Fermi-Hubbard model.Comment: Main text: 7 pages, 5 figures. Supplementary Material: 10 pages, 7 figure

Heteroatom-Induced Molecular Asymmetry Tunes Quantum Interference in Charge Transport through Single-Molecule Junctions

We studied the interplay between quantum interference (QI) and molecular asymmetry in charge transport through a single molecule. Eight compounds with five-membered core rings were synthesized, and their single-molecule conductances were characterized using the mechanically controllable break junction technique. It is found that the symmetric molecules are more conductive than their asymmetric isomers and that there is no statistically significant dependence on the aromaticity of the core. In contrast, we find experimental evidence of destructive QI in five-membered rings, which can be tuned by implanting different heteroatoms into the core ring. Our findings are rationalized by the presence of antiresonance features in the transmission curves calculated using nonequilibrium Green’s functions. This novel mechanism for modulating QI effects in charge transport via tuning of molecular asymmetry will lead to promising applications in the design of single-molecule devices

Transition from tunneling leakage current to molecular tunneling in single-molecule junctions

数十年来，半导体工业一直遵循基于“摩尔定律”所设定的发展蓝图，逐步提升集成电路芯片上晶体管的集成度和运行速度，减小器件尺寸。为探索这一尺寸极限，课题组基于机械可控裂结技术自主开发了具有飞安级电学测量和亚纳米级位移控制灵敏度的科学仪器，在国际上首次获取了一系列具有不同重复单元的寡聚苯乙炔类分子电导随电极间距的演变关系，并发现随着电极间距的缩小，器件电输运由通过分子器件电流占主导逐步转变到由隧穿漏电流占主导。对于本研究中具有最小尺寸的寡聚苯乙炔分子器件，其由于隧穿漏电流所制约的尺寸极限可小至0.66 nm，预示了有机分子器件在未来电子器件小型化方面具有重要的应用潜力。 这一研究工作是在化学化工学院洪文晶教授、萨本栋微纳研究院杨扬助理教授以及英国Durham University的MartinR. Bryce教授共同指导下完成的。能源材料化学协同创新中心iChEM Fellow刘俊扬博士为论文第一作者，博士研究生郑珏婷、李瑞豪和硕士研究生黄晓艳、唐永翔、皮九婵、本科生王飞等参与了研究工作。田中群教授、毛秉伟教授和师佳副教授为论文工作提供了重要指导。【Abstract】The tunneling leakage current will be a major quantum obstacle during miniaturization in the semiconductor industry down to the scale of several nanometers. At this scale, to promote charge transport and overcome the tunneling leakage current between the source and drain terminals, molecular electronic junctions offer opportunities by inserting molecules between these two electrodes. Employing a series of oligo(aryleneethynylene) (OAE) molecules, here we investigate the transition from tunneling leakage current to molecular tunneling in the single-molecule devices using mechanically controllable break junction (MCBJ) technique, and the transition distances of the OAE molecular junctions were determined and even down to 0.66 nm for OAE2 molecular junction, which demonstrates that the intrinsic charge transport properties of a single-molecule device can be outstripped from the tunneling leakage current. Consequently, molecular electronic devices show the potential to push the ultimate limit of miniaturization to the scale of several angstroms.This work was supported by the National Key R&D Program of China (2017YFA0204902). This work was also generously supported by the Young Thousand Talent Project of China, the EC FP7 ITN “MOLESCO” project number 606728, the National Natural Science Foundation of China (nos. 21703188, 21673195, 21503179), and the China Postdoctoral Science Foundation (2017M622060). 该工作获得科技部国家重点研发计划课题（2017YFA0204902），国家自然科学基金委（21673195、21703188、21503179）以及中国博士后科学基金（2017M622060）等项目的资助，也得到了固体表面物理化学国家重点实验室、能源材料化学协同创新中心的支持

Electric-field-induced selective catalysis of single-molecule reaction

随着单分子电学检测技术的迅速发展，分子电子学的研究不再局限于分子电子学器件的构筑及其电学性质的测量，而且扩展到单分子尺度化学反应过程的探索。然而目前相关的研究仍然局限于理论计算方面，在单分子尺度上实时监测和调控化学反应的活性和选择性是化学领域的长期目标和挑战。针对这一挑战，洪文晶教授课题组与程俊教授课题组合作，自主研发了精密科学仪器，将单个有机分子定向连接在两个末端尺寸为原子级的电极之间，解决了化学反应中分子取向控制的问题.理论计算结果证实了定向电场可以有效地稳定化学反应的过渡态，从而降低反应能垒。该研究工作在化学化工学院洪文晶教授、程俊教授、能源材料化学协同创新中心（iChEM）刘俊扬副研究员的共同指导下完成，由硕士研究生黄晓艳、iChEM博士研究生唐淳、博士研究生李洁琼以及兰州大学的陈力川博士作为共同第一作者，化学化工学院师佳副教授、陈招斌高级工程师、夏海平教授和田中群教授，萨本栋微纳研究院杨扬副教授、环境与生态学院白敏冬教授以及兰州大学张浩力教授参与了研究工作的讨论并给予指导，博士后乐家波、博士研究生郑珏婷、张佩（已毕业）、李瑞豪、李晓慧也参与了研究工作。Oriented external electric fields (OEEFs) offer a unique chance to tune catalytic selectivity by orienting the alignment of the electric field along the axis of the activated bond for a specific chemical reaction; however, they remain a key experimental challenge. Here, we experimentally and theoretically investigated the OEEF-induced selective catalysis in a two-step cascade reaction of the Diels-Alder addition followed by an aromatization process. Characterized by the mechanically controllable break junction (MCBJ) technique in the nanogap and confirmed by nuclear magnetic resonance (NMR) in bottles, OEEFs are found to selectively catalyze the aromatization reaction by one order of magnitude owing to the alignment of the electric field on the reaction axis. Meanwhile, the Diels-Alder reaction remained unchanged since its reaction axis is orthogonal to the electric fields. This orientation-selective catalytic effect of OEEFs reveals that chemical reactions can be selectively manipulated through the elegant alignment between the electric fields and the reaction axis.This work was supported by the National Key R&D Program of China (2017YFA0204902), the National Natural Science Foundation of China (21722305, 21703188, 21673195, 21621091, 51733004, 51525303, and 91745103), the China Postdoctoral Science Foundation (2017M622060), and the Young Thousand Talents Project of China. 该工作得到国家自然科学基金委（21722305、21703188、21673195、51733004、51525303、91745103），国家重点研发计划课题（2017YFA0204902），中国博士后面上基金（2017M622060）的资助，以及固体表面物理化学国家重点实验室、醇醚酯化工清洁生产国家工程实验室、能源材料化学协同创新中心的支持