求解二维多区域声波散射问题的边界元方法

对于多散射区域的声波散射问题的外Neumann边值问题,用单层位势来逼近每个散射域上的散射波,再利用位势理论的跳跃关系将问题转换为第二类边界积分方程组的求解问题,然后用Nystrom方法进行了求解.对多个随机散射区域的声波散射问题,数值例子体现了该求解方法的可行性和准确性.     

The metallic C6S monolayer with high specific capacity for K-ion batteries

K-ion batteries (KIBs) attract considerable attention due to the abundance of K, high-working voltages, and chemical similarity with Li, enabling the utilization of mature Li-ion technology. However, shortage of high-performance anode materials is a critical obstacle for the development of KIBs. Through first-principles swarm-intelligence structural search, we identify a potential anode material, the C₆S monolayer, which provides not only a remarkably high specific capacity of 1546 mAh/g but also a low diffusion barrier of 0.11 eV and a low open-circuit voltage of 0.21 V. Inherent metallicity originates from delocalized π electrons.     

适用于本科教学的BET比表面测定实验

采用自组装的流动吸附仪建立了基于BET吸附原理的快速测定固体比表面积的实验方法(单点法),对同一活性炭样品,在多功能气体吸附系统上进行对照实验(多点法)。实验结果表明,采用流动吸附仪测定比表面积方便易行,数据稳定可靠,实验教学效果良好。本文介绍这一特色实验,期望对从事物理化学实验教学的同行有所助益。     

Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films北大核心CSCD

Based on the equivalent elasticity theory for layered materials, the micro-mechanics equivalent models for single and dual damascene structures were established. The equivalent elastic constant of the patterned structure was introduced, to establish the propagation model for the surface acoustic waves propagating in the layered structure of the patterned film/ substrate, and the theoretical dispersion curves of the surface acoustic waves were calculated with Green’s function and the matrix method. The finite element method was used to calculate 24 numerical examples of damascene structures with different volume ratios, and the results were compared with those of the strain energy method. The results show that, the average relative errors of the equivalent Young’s moduli of the 300 nm-thick dual damascene film and the 100 nm-thick single damascene film are 2.06% and 2.27%, respectively. The research verifies the correctness of the equivalent patterned structure model and the feasibility of the surface acoustic wave method to characterize the mechanical properties of patterned films, and provides a reference for the development of suitable chemico-mechanical polishing technologies for patterned films under low pressure. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

有限元/边界元耦合方法在海洋生物目标强度特性研究的应用*

目标强度特性是海洋生物声学识别与资源量评估的重要依据,其中,基于近似几何体和声阻抗特性的理论模型法是研究海洋生物目标强度的重要手段。由于对几何形态近似处理以及数值求解方法的限制,传统理论模型对声波频率、入射方位以及目标声阻抗、形态尺寸等均有各自不同的适用范围,单一模型难以满足不同种类或同一种类但不同尺寸海洋生物的目标强度求解。本文尝试将逐渐见诸应用的有限元/边界元耦合方法用于海洋生物目标强度特性研究,分别以球形生物、纺锤形鱼类尾明角灯鱼(Ceratoscopelus warmingii)和细长形浮游动物南极大磷虾(Euphausia superba)为例进行仿真计算,并与相适应的经典理论模型进行对比分析。结果表明,对于球形生物,有限元/边界元耦合方法与解析模型的目标强度频响曲线完全吻合;对于纺锤形鱼类,有限元/边界元耦合方法可有效弥补基于模态级数解的形变圆柱体模型在中低频和两端入射时的准确性问题;对于细长形浮游动物,有限元/边界元耦合方法与畸变波玻恩近似模型高度吻合。综上,有限元/边界元耦合方法对多种海洋生物目标强度求解均具有较好的适用性,未来有待进一步结合实验测定进行验证。     

超声辅助电镀的仿真与实验*

为了提高镀层的表面质量,提出了一种超声辅助电镀的方法。超声的空化与搅拌作用可以影响电镀的电沉积过程。设计了合理的换能器结构,并搭建了超声辅助电镀装置。通过对模型进行压电声学场与电镀场耦合仿真分析,结果表明：在硫酸铜电解液,镀铜时间60s,电压300V条件下,进行超声辅助电镀,镀层厚度分布均匀,镀层中部电流密度分布均匀,边缘最大电流密度是未加超声的2倍左右 。基于仿真结果,进行相同的实验测试,结果表明：超声辅助电镀可以提高镀层的均匀性,减少铜颗粒表面的杂质,提高表面的光洁度。阴极样品距离换能器头部位置在60mm左右,镀层质量良好。     

非均匀流体介质内部散射声场重建的逐层计算方法*

入射声波激励下非均匀流体介质内部散射声场的重建方法对超声层析成像具有重要意义。以往采用矩量法求解,但该方法全域离散形成的复数满秩矩阵规模随着分辨率与计算精度的提高而急剧增大,对算力具有很高的要求,一定程度上限制了其在实际中的应用。为克服上述缺陷,本文以逐层离散、逐层计算为核心思想,以声散射基本公式与近场声全息理论为基础,推导出逐层计算非均匀流体介质内部散射声场的理论公式并给出对应的几何离散模型。为验证该方法的可行性,以矩量法为参照,对同样的介质模型进行介质内部声场重构仿真。结果表明,逐层算法不仅可以有效地重建非均匀流体介质内部散射声场,且大幅度减小了求解规模。     

Channel temporal correlation-based optimization method for imperfect underwater acoustic channel state information

The rapid time variations and large channel estimation errors in underwater acoustic (UWA) channels mean that transmitters for adaptive resource allocation quickly become outdated and provide inaccurate channel state information (CSI). This results in poor resource allocation efficiency. To address this issue, this paper proposes an optimization approach for imperfect CSI based on a Gauss–Markov model and the per-subcarrier channel temporal correlation (PSCTC) factor. The proposed scheme is applicable to downlink UWA orthogonal frequency division multiple access systems. The proposed PSCTC factors are measured, and their long-term stability is verified using data recorded in real-world sea tests. Simulation and experimental results show that the optimized CSI effectively mitigates the effects of the temporal variability of UWA channels. It demonstrates that the resource allocation scheme using optimized CSI achieves a higher effective throughput and a lower bit error rate than both imperfect CSI and the CSI predicted by the recursive least-squares (RLS) algorithm.     

Evidence of Strange Attractors in Class C Amplifier with Single Bipolar Transistor: Polynomial and Piecewise-Linear Case

This paper presents and briefly discusses recent observations of dynamics associated with isolated generalized bipolar transistor cells. A mathematical model of this simple system is considered on the highest level of abstraction such that it comprises many different network topologies. The key property of the analyzed structure is its bias point since the transistor is modeled via two-port admittance parameters. A necessary but not sufficient condition for the evolution of autonomous complex behavior is the nonlinear bilateral nature of the transistor with arbitrary reason that causes this effect. It is proved both by numerical analysis and experimental measurement that chaotic motion is miscellaneous, robust, and it is neither numerical artifact nor long transient motion.