声学超表面的非对称声分束特性研究

非对称声分束超表面是由人工微单元结构按照特定序列构建的二维平面结构,可将垂直入射的声波分成两束传播方向和分束比自由调控的透射波,在声功能器件设计及声通信领域具有广泛的应用前景。本文系统研究了一种实现非对称声分束的设计理论和实现方法,基于局域声功率守恒条件研究了声分束器的设计理论、阻抗矩阵分布、法向声强分布、声压场分布等。利用遗传算法对四串联共振腔结构进行参数优化实现了声分束器所需的阻抗矩阵分布,声压场分布表明声波入射到声分束器后在入射侧激发出两列传播方向相反且幅值和衰减系数均相同的表面波,实现了入射侧与透射侧的局域声功率相互匹配。声波经过声分束器后被分为两束透射波,两束透射波的折射角和透射系数与理论值十分吻合,证明了设计理论及实现方法的正确性和可行性。本文的研究工作可以为新型非对称声分束结构设计提供理论参考、设计方法和技术支持,并促进其在工程领域的实际应用。     

Pure annihilation decay of strange beauty meson into two charm heavy mesons

In this study, the heavy to heavy decay of \begin{document}$ B^0_s\rightarrow D^{*+}D^- $\end{document} is evaluated through the factorization approach by using the final state interaction as an effective correction. Under the factorization approach, this decay mode occurs only through the annihilation process, so a small amount is produced. Feynman's rules state that six meson pairs can be assumed for the intermediate states before the final meson pairs are produced. By taking into account the effects of twelve final state interaction diagrams in the calculations, a significant correction is obtained. These effects correct the value of the branching ratio obtained by the pure factorization approach from \begin{document}$ (2.41\pm1.37)\times10^{-5} $\end{document} to \begin{document}$ (8.27\pm2.23)\times10^{-5} $\end{document}. The value obtained for the branching ratio of the \begin{document}$ B^0_s\rightarrow D^{*+}D^- $\end{document} decay is consistent with the experimental results.     

Moderate Deviation for the Rightmost Position in a Branching Brownian Motion

We study the moderate deviation probability of the position of the rightmost particle in a branching Brownian motion and obtain its moderate deviation function. Firstly, Chauvin and Rouault studied the large deviation probability for the rightmost position in a branching Brownian motion. Recently, Derrida and Shiconsidered lower deviation for the same model. By contrast, Our main result is more extensive.     

数学建模对高中生构建数学底层思维的作用及其教学实施建议

数学底层思维即用数学的眼光观察世界、用数学的思维分析世界以及用数学的语言表达世界,是人们面对自然和社会中纷繁多样的现象和问题时,所展现的自发的、不依赖监督的、融汇数学学科核心素养的思维方式.作为国家高中新课程标准中数学六大核心素养之一的数学建模,是培养学生数学底层思维的良好载体,对人才培养和社会发展均起到良好的促进作用.本文主要阐述了数学建模对高中生构建数学底层思维的作用,并结合教学实例给出教学实施建议.     

基于电化学老化衰退模型的锂离子动力电池外特性

当前锂离子动力电池电化学模型存在模型复杂、建模难度大、计算效率低、老化评估效果差的问题,本文提出一种考虑电池衰退老化的机理模型(ADME).本文首先通过有限差分法对伪二维(P2D)电化学模型进行离散降阶处理,得到简化伪二维(SP2D)模型.在SP2D模型的基础上,基于阴阳两极发生的副反应导致的衰退老化现象,提出一种考虑电池衰退老化的机理模型.其次,使用多变量偏差补偿最小二乘法实现模型参数辨识.最后通过动力电池衰退老化性能循环实验,对比分析了恒流、脉冲工况下SP2D模型和ADME模型的终端电压输出.结果表明:ADME模型较为简单、计算效率和估算精度高,可以有效评估电池容量老化衰退,得到理想的锂离子动力电池外特性曲线.     

Finite element computations of viscoelastic two-phase flows using local projection stabilization

A three-field local projection stabilized (LPS) finite element method is developed for computations of a three-dimensional axisymmetric buoyancy driven liquid drop rising in a liquid column where one of the liquid is viscoelastic. The two-phase flow is described by the time-dependent incompressible Navier-Stokes equations, whereas the viscoelasticity is modeled by the Giesekus constitutive equation in a time-dependent domain. The arbitrary Lagrangian-Eulerian (ALE) formulation with finite elements is used to solve the governing equations in the time-dependent domain. Interface-resolved moving meshes in ALE allows to incorporate the interfacial tension force and jumps in the material parameters accurately. A one-level LPS based on an enriched approximation space and a discontinuous projection space is used to stabilize the numerical scheme. A comprehensive numerical investigation is performed for a Newtonian drop rising in a viscoelastic fluid column and a viscoelastic drop rising in a Newtonian fluid column. The influence of the viscosity ratio, Newtonian solvent ratio, Giesekus mobility factor, and the Eötvös number on the drop dynamics are analyzed. The numerical study shows that beyond a critical Capillary number, a Newtonian drop rising in a viscoelastic fluid column experiences an extended trailing edge with a cusp-like shape and also exhibits a negative wake phenomena. However, a viscoelastic drop rising in a Newtonian fluid column develops an indentation around the rear stagnation point with a dimpled shape.     

Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

基于改进格林元的压裂水平井动态分析方法

以建立高效的动态分析方法为出发点，以边单元作为求解点，改进传统的格林元方法，减少未知数和求解矩阵维度；并提出基于改进格林元的加密网格加密方法，保证考虑复杂裂缝网络的压裂水平井动态模拟的早期精度.退化模型与半解析解、数值模拟结果进行对比，验证本文基于加密网格的改进格林元方法的准确性和动态分析的高效性.最后进行动态响应的敏感性分析，结果表明：①格林元方法是一种高精度的动态模拟方法，将求解节点设置在网格的边上可以提高压裂水平井动态模拟的速度；②改进格林元方法的加密基于叠加原理，不需要通过插值近似，其求解精度高.在相同加密网格条件下，基于本文改进格林元方法的加密效果比有限差分加密效果更佳；③复杂裂缝导流能力、改造区渗透率提高倍数、改造区大小等参数对压裂水平井动态特征影响较大，在动态分析和参数反演时，应着重考虑这些因素的影响.     

The coupled-cluster formalism – a mathematical perspective

ABSTRACT

The Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle.