Some mathematical aspects of Anderson localization: boundary effect,multimodality, and bifurcation

Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary conditions using a probabilistic approach, and further investigate some mathematical aspects of Anderson localization that are rarely discussed before. First, we observe that under the Neumann boundary condition, the low energy quantum states are localized on the boundary of the domain with high probability. We provide a detailed explanation of this phenomenon using the concept of extended subregions and obtain an analytical expression of this probability in the one-dimensional case. Second, we find that the quantum states may be localized in multiple different subregions with high probability in the one-dimensional case and we derive an explicit expression of this probability for various boundary conditions. Finally, we examine a bifurcation phenomenon of the localization subregion as the strength of disorder varies. The critical threshold of bifurcation is analytically computed based on a toy model and the dependence of the critical threshold on model parameters is analyzed.     

纳秒脉冲放电紫外光纤阵列检测与定位方法

峰化电容作为电磁脉冲模拟器中用于陡化脉冲输出的关键部件,在实际工程应用中易发生沿面放电和击穿现象,采用光电检测系统可对绝缘沿面放电现象进行有效分析。针对峰化电容器沿面放电监测的技术难题,研制了一套绝缘沿面放电过程光电检测系统,对绝缘沿面放电现象进行光电检测。首先提出了绝缘介质沿面放电过程光电探测系统的设计方案;其次,对系统的时延性能进行了评价;最后,完成了绝缘介质沿面放电过程定位实验,验证了光电探测系统的可行性。实验表明,该系统能够实现对放电区域的有效定位。     

Pure single line oscillation of HF lasers in fine atmospheric window

Applied Physics B - A correction to this paper has been published: https://doi.org/10.1007/s00340-021-07611-y     

LIBS对钛合金焊缝中成分的原位统计分布分析表征

钛合金凭借其强度高、耐蚀性好、耐热性高等特点已经被广泛应用于航天、海洋、生物医药等诸多领域,其中Ti-6Al-4V（TC4）合金的耐热性、强度、塑性、韧性、成形性、可焊性、耐蚀性和生物相容性均较好,已成为钛合金工业中的王牌合金。钛合金在激光焊接时,加入表面活性剂可以增加焊缝熔深、提高焊接效率、改善焊缝微观组织的不均匀性,但是可能会改变熔合区和焊缝区中元素含量及其分布状态,从而可能会对材料的性能产生一定的影响。运用LIBS分析技术对TC4钛合金焊接试样表面进行面扫描同步获得多元素成分信息,同时结合原位统计分布分析方法（OPA）,实现了对钛合金母材、熔合区、焊缝成分及其分布状态的快速表征,为活性剂的选择和焊接后钛合金的材料性能提供一种新的评价手段。选取了两个使用不同活性剂进行焊接的TC4钛合金薄板试样,选取焊缝纵切面方向作为分析面,采用320目的氧化铝砂纸进行表面处理,利用LIBSOPA系统进行成分分布统计表征。首先,对激发光斑和剥蚀条件进行条件优化,最终选择200 μm的激发光斑、10个预剥蚀脉冲10个剥蚀脉冲进行实验,并建立了钛合金中C,Al,V,Fe,Si和Ti六个元素的校准曲线（其中Si元素主要来自活性剂）;然后对钛合金焊接样品进行了区域扫描,并对元素含量和分布状态进行了统计表征。同时,在钛合金焊接样品的不同部位进行分区取样,采用高频红外法分析C元素含量,并与LIBSOPA结果进行比对,两种测试方法结果吻合。元素Al,V,Fe,Si和Ti分布结果与微束X荧光光谱法对应性较好。运用LIBSOPA 技术实现了对钛合金母材、熔合区、焊缝中多元素的成分分布表征,为快速判定钛合金焊缝中成分及分布状态提供了全新的评价表征手段。     

复杂网络上的意见动力学对谣言传播的影响

通过在SIR(susceptible-infected-recovered)模型中引入抑制者对谣言的辟谣机制研究了在线社交网络上的意见动力学对谣言传播的影响.在这一模型中,节点可以与自身的邻居组成1个群,传播者可以通过该群传播信息,抑制者也可以在此群中对信息发表意见进行辟谣.辟谣机制在降低未知者对于谣言的接受概率的同时也可以促使传播者向抑制者转变.本文采用ER(Erd?s-Rényi)随机网络、无标度网络以及真实的社交网络研究了抑制者的沉默概率对于谣言传播范围的影响.首先发现,谣言传播的过程以传播者的峰值为界可以分为两个阶段,即谣言自由传播的前期以及抑制者和传播者互相制衡的后期;其次,谣言的传播会随着抑制者的沉默概率的增大而突然暴发.在谣言暴发阈值之下,沉默概率的增大不会导致谣言传播范围显著增大,这是由于未知者在感知到谣言并转变为传播者后又迅速转变为抑制者;而当沉默概率达到谣言暴发阈值时,抑制者将不能控制传播者对谣言的传播从而导致抑制者的降低和谣言的暴发;最后,无标度上的谣言自由传播的前期阶段比随机网络持续的时间更短,从而使无标度上的谣言更难以暴发.本文的模型综合考虑了意见动力学和谣言传播的相互作用,更加真实地模拟了真实世界社交网络中的谣言传播过程.为谣言传播的控制和干预提供了一些有用的思路和见解.     

Intelligent Fault Diagnosis of Rolling-Element Bearings Using a Self-Adaptive Hierarchical Multiscale Fuzzy Entropy

The fuzzy-entropy-based complexity metric approach has achieved fruitful results in bearing fault diagnosis. However, traditional hierarchical fuzzy entropy (HFE) and multiscale fuzzy entropy (MFE) only excavate bearing fault information on different levels or scales, but do not consider bearing fault information on both multiple layers and multiple scales at the same time, thus easily resulting in incomplete fault information extraction and low-rise identification accuracy. Besides, the key parameters of most existing entropy-based complexity metric methods are selected based on specialist experience, which indicates that they lack self-adaptation. To address these problems, this paper proposes a new intelligent bearing fault diagnosis method based on self-adaptive hierarchical multiscale fuzzy entropy. On the one hand, by integrating the merits of HFE and MFE, a novel complexity metric method, named hierarchical multiscale fuzzy entropy (HMFE), is presented to extract a multidimensional feature matrix of the original bearing vibration signal, where the important parameters of HMFE are automatically determined by using the bird swarm algorithm (BSA). On the other hand, a nonlinear feature matrix classifier with strong robustness, known as support matrix machine (SMM), is introduced for learning the discriminant fault information directly from the extracted multidimensional feature matrix and automatically identifying different bearing health conditions. Two experimental results on bearing fault diagnosis show that the proposed method can obtain average identification accuracies of 99.92% and 99.83%, respectively, which are higher those of several representative entropies reported by this paper. Moreover, in the two experiments, the standard deviations of identification accuracy of the proposed method were, respectively, 0.1687 and 0.2705, which are also greater than those of the comparison methods mentioned in this paper. The effectiveness and superiority of the proposed method are verified by the experimental results.     

A Study on Consumers’ Visual Image Evaluation of Wrist Wearables

This study aimed to investigate consumers’ visual image evaluation of wrist wearables based on Kansei engineering. A total of 8 representative samples were screened from 99 samples using the multidimensional scaling (MDS) method. Five groups of adjectives were identified to allow participants to express their visual impressions of wrist wearable devices through a questionnaire survey and factor analysis. The evaluation of eight samples using the five groups of adjectives was analyzed utilizing the triangle fuzzy theory. The results showed a relatively different evaluation of the eight samples in the groups of “fashionable and individual” and “rational and decent”, but little distinction in the groups of “practical and durable”, “modern and smart” and “convenient and multiple”. Furthermore, wrist wearables with a shape close to a traditional watch dial (round), with a bezel and mechanical buttons (moderate complexity) and asymmetric forms received a higher evaluation. The acceptance of square- and elliptical-shaped wrist wearables was relatively low. Among the square- and rectangular-shaped wrist wearables, the greater the curvature of the chamfer, the higher the acceptance. Apparent contrast between the color of the screen and the casing had good acceptance. The influence of display size on consumer evaluations was relatively small. Similar results were obtained in the evaluation of preferences and willingness to purchase. The results of this study objectively and effectively reflect consumers’ evaluation and potential demand for the visual images of wrist wearables and provide a reference for designers and industry professionals.     

Enhanced Slime Mould Algorithm for Multilevel Thresholding Image Segmentation Using Entropy Measures

Image segmentation is a fundamental but essential step in image processing because it dramatically influences posterior image analysis. Multilevel thresholding image segmentation is one of the most popular image segmentation techniques, and many researchers have used meta-heuristic optimization algorithms (MAs) to determine the threshold values. However, MAs have some defects; for example, they are prone to stagnate in local optimal and slow convergence speed. This paper proposes an enhanced slime mould algorithm for global optimization and multilevel thresholding image segmentation, namely ESMA. First, the Levy flight method is used to improve the exploration ability of SMA. Second, quasi opposition-based learning is introduced to enhance the exploitation ability and balance the exploration and exploitation. Then, the superiority of the proposed work ESMA is confirmed concerning the 23 benchmark functions. Afterward, the ESMA is applied in multilevel thresholding image segmentation using minimum cross-entropy as the fitness function. We select eight greyscale images as the benchmark images for testing and compare them with the other classical and state-of-the-art algorithms. Meanwhile, the experimental metrics include the average fitness (mean), standard deviation (Std), peak signal to noise ratio (PSNR), structure similarity index (SSIM), feature similarity index (FSIM), and Wilcoxon rank-sum test, which is utilized to evaluate the quality of segmentation. Experimental results demonstrated that ESMA is superior to other algorithms and can provide higher segmentation accuracy.     

用信号处理技术及传播理论还原雷声频谱

以往关于雷声的研究都限于观测点雷声频域范围的探讨, 由于噪音和衰减因素的影响, 观测点的雷声频谱有很大失真. 针对在兰州地区观测的一次雷暴过程中的雷声信号, 利用数字信号处理技术,由观测点处的雷声音频信号得到频率谱,并对雷声频谱进行噪音分析; 然后结合声音在大气中传播的衰减理论, 分析了不同大气环境对声吸收的影响, 并推算出了声源附近的雷声频率谱. 关键词： 雷声频谱 信号处理 传播理论 峰值频率     

水中目标回波亮点统计特征研究

礁石和海洋动物引起的混响是主动声纳最严重的干扰, 如何区分礁石、鱼群和水中目标一直是制约主动声纳识别技术的难点问题. 针对礁石与目标回波难以区分的问题, 从特征识别的应用角度, 研究水中复杂目标全方位回波亮点特征的有效表征和应用方式, 基于目标回波亮点模型, 提出拷贝相关器输出的目标散射函数估计方法, 给出对目标回波亮点相对关系进行定量分析的目标回波特征统计表征方式, 并基于湖上实验提取了物理机理明确的目标回波亮点统计特征, 使得目标时间-角度谱中所蕴含的目标特征信息能够很直接地转化为主动声纳易于应用的目标特征. 关键词： 水中目标 回波亮点 统计特征