Boundary-Connected Higher Order Weyl Semimetals in a Helix-Shaped Phononic Crystal

The proposal of higher-order topology leads to intriguing wave propagation properties beyond the conventional bulk-boundary principle in condensed matter physics. Theoretical and experimental models have been conducted to reveal exotic higher-order hinge and corner states in lower dimensions. Meanwhile, this concept is extended to semimetals and verified in platforms like acoustic and photonic systems. However, most existing schemes are confined to C_n-symmetric-like frameworks. Here a phononic higher-order Weyl semimetal (HOWSM) is put forward by introductions of artificial gauge flux shape. Distinguished from most existing schemes, the traditional two-dimensional lattice with a vertical screw-extending operation is deformed, which guarantees the emergence of higher-order Weyl points. The invariant index is utilized to measure different phases between non-trivial topological and normal insulators visibly. Simulation results indicate that the structure supports robust hinge wave transmission in a piling sample. This work brings new approaches for constructing HOWSMs and enriches the potential applications in manufacturing high-performance acoustic devices.     

留数定理在拓扑相变中的应用

留数定理是高校物理专业必修课程数学物理方法中的一个重要定理.传统教学中关于该定理的讲授着重于数学公式的推导和数学思想的传达,而对于其在具体物理问题上的应用鲜有涉及.本文以一维Su-Schrieffer-Heeger模型的拓扑相变问题为例,阐明了如何利用留数定理解析得到二阶位移量的表达式并用该物理量表征拓扑相变.在讲授留数定理的教学过程中引入具体物理问题的分析实例,可以使学生更深刻地理解数学定理中的物理内涵.     

Weighted Cebysev-Ostrowski type inequalities

In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new estimates on these types of inequalities.     

基于拓扑描述函数的连续体结构拓扑优化方法

提出了一种利用拓扑描述函数(TDF)作为拓扑设计变量求解连续体结构拓扑优化问题 的新方法. 优化问题的目标函数是结构的整体柔顺性，约束条件为对于可利用材料的体积限 制. 这种方法不仅可以消除拓扑优化中经常出现的棋盘格式等数值不稳定现象，而且能够有 效地抑制传统算法处理此类优化问题时所引发的边界扩散效应. 与其它的基于水平集描述函 数的拓扑优化方法相比，所提出的算法不仅无需求解控制水平集函数演化的双曲守恒方 程，而且合理地考虑了目标函数的拓扑导数信息，因而使得算法的计算效率有了显著的提高.     

Numbering homoclinic points of diffeomorphisms in the plane

In this paper we introduce a numerical conjugacy invariant for planar maps with homoclinic points. This invariant can be estimated based on partial information about the location of compact pieces of the stable and unstable manifolds of the system. The invariant is also related to topological entropy, and we indicate a method by which good bounds on the entropy of a system can be obtained.     

平面膜结构拓扑优化的有无复合体方法

将作者对桁架在应力约束下结构拓扑优化的有无复合体模型发展到平面膜结构在应力、位移约束下结构拓扑优化的建模与求解。同时提出了该模型的有效解法,获得了令人满意的数值结果。本文工作表明独立连续拓扑变量的提出对于结构拓扑优化的研究是有意义的。     

STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH TIME DELAY

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓｔｈｅｄｙｎａｍｉｃｂｅｈａｖｉｏｒｏｆｔｈｅｆｏｌｌｏｗｉｎｇＨｏｐｆｉｅｌｄｎｅｕｒａｌｎｅｔｗｏｒｋｓｍｏｄｅｌｗｉｔｈｔｉｍｅｄｅｌａｙｈａｖｅｂｅｅｎｉｎｖｅｓｔｉｇａｔｅｄｔｈｏｒｏｕｇｈｌｙＣｉ ｘｉ(ｔ) =-ｘｉＲｉ + ∑ｎｊ=1Ｔｉｊｆｊ(ｘｊ(ｔ-τｉｊ) ) +Ｉｉ　　 (ｉ=1 ,2 ,… ,ｎ) ,( 1 )ｗｈｅｒｅＲｉ,ＣｉａｎｄＩｉｒｅｐｒｅｓｅｎｔｒｅｓｉｓｔａｎｃｅ ,ｃａｐａｃｉｔａｎｃｅａｎｄｅｌｅｃｔｒｉｃｃｕｒｒｅｎｔ.Ｒｉ,Ｃｉａｒｅｐａ…     

类升力体外形高超声速粘性绕流拓扑结构分析

采用交替方向隐式分解的隐式NND格式求解全N-S方程模拟“类升力体”外形在高超声速下的大攻角流动,给出了“类升力体”外形表面极限流线随攻角变化的拓扑结构及40°攻角下垂直于体轴的横截面流线拓扑结构。结果表明:类升力体外形三维流场结构十分复杂,攻角从0°～40°变化时,背风面表面极限流线依次由不分离、开式分离向起始于鞍、结点组合的高阶奇点的分离方式转化,翼面横向分离亦随攻角增大而增大;垂直于体轴的横截面流动拓扑结构与文献[2]给出的理论分析一致。     

Infinite-Dimensional Hyperbolic Sets and Spatio-Temporal Chaos in Reaction Diffusion Systems in $${\mathbb{R}^{n}}$$

The paper is devoted to a rigorous construction of a parabolic system of partial differential equations which displays space–time chaotic behavior in its global attractor. The construction starts from a periodic array of identical copies of a temporally chaotic reaction-diffusion system (RDS) on a bounded domain with Dirichlet boundary conditions. We start with the case without coupling where space–time chaos, defined via embedding of multi- dimensional Bernoulli schemes, is easily obtained. We introduce small coupling by replacing the Dirichlet boundary conditions by strong absorption between the active islands. Using hyperbolicity and delicate PDE estimates we prove persistence of the embedded Bernoulli scheme. Furthermore we smoothen the nonlinearity and obtain a RDS which has polynomial interaction terms with space and time-periodic coefficients and which has a hyperbolic invariant set on which the dynamics displays spatio-temporal chaos. Finally we show that such a system can be embedded in a bigger system which is autonomous and homogeneous and still contains space–time chaos. Obviously, hyperbolicity is lost in this step. Research partially supported by the INTAS project Attractors for Equations of Mathematical Physics, by CRDF and by the Alexander von Humboldt–Stiftung.     

BEST APPROXIMATION THEOREM FOR SET-VALUED MAPPINGSWITHOUT CONVEX VELUES AND CONTINUITY

I.Introduction'In1969,KyFanl[Iprovedthefollowingwell-knownresultsonbestapproximation.Theorem1.1LetXbeanonemptycompactconvexsubsetofalocallyconvextopologicalvectorspaceEandf:X~Ebeacontinuousmapping.TheneitherfhasafixedpointinX,orthereexistapointyo6XandacontinuousseminormponEsucllthat0相似文献