四维杂化弦

利用十维N-S玻色弦和四维费米弦杂化,我们给出了四维杂化弦.其内部规范对称群为[SU(2)]⁶.它的基态包含有四维时空的超引力多重态及四维超杨-Mills规范多重态.四维杂化弦具有超对称、无快子态及洛仑兹不变等特性.     

分形维数和分形凝聚

在自然界中存在着许多研究对象,它们具有标度不变的性质.所谓标度不变性是指,当我们用不同倍数的照相机拍摄这个研究对象时,不管放大倍数如何改变,我们看到的相片都是相似的(从统计意义上说),而且从相片上也无法判断所用相机的倍数.天上的云团、地上的海岸线以及灰尘微粒的凝聚集团等均属于这一类研究对象.这种结构的物体在几何性质上具有重要的特征,即可以用一个有效的空间维数来表示,这个维数可以不是一个整数,而是一个可以连续变化的数,称为豪斯道夫维数.我们首先介绍豪斯道夫维数的概念. 一、豪斯道夫维数[1-4] 长期来人们对空间维数只…     

悬线式二维碰撞实验

提出用长摆线单摆实现在准水平面内的无摩擦运动,用摄像头记录二维碰撞过程,设计了检验二维碰撞中动量守恒和机械能守恒的教学实验.     

三明治结构量子阱的维数

讨论了无限深和有限深量子阱电子系统的维数.在无限深量子阱中,随着阱宽由大减小到零,量子阱的维数由3单调减小到2;有限深量子阱中,在阱宽较大或阱宽趋于零时,量子阱电子系统的维数都趋近于3,随着阱宽的减小,量子阱的维数呈现出先减小后增大的情况,存在一个维数极小值.     

求解二维Euler方程有限单元边插值的降维重构算法

数值求解二维Euler方程的有限体积法（如k-exact，WENO重构、紧致重构等），无一例外地要进行耗时的网格单元上的二维重构.然而这些二维重构最后仅用于确定网格单元边界上高斯积分点处的解值，单元上二维重构似乎并非必需的.因此，文章提出用网格边上的一维重构来取代有限体积法中网格单元上的二维重构，分别在一致矩形网格和非结构三角形网格上发展了基于网格边重构的求解二维Euler方程的新方法，称为降维重构算法.数值算例表明该算法可以计算有强激波的无黏流动问题，且有较高的计算效率.      

二维准晶的声子及其熔化性质

本文研究具有五次对称性的二维Penrose 准晶的声子及其熔化性质.我们找到了一个相似变换矩阵, 利用它成功地对动力学矩阵进行约化.这约化一方面大大地减少了计算量, 另一方面通过它可解析地得出振动模中有2/3是双重简并的, 而余下的1/ 3 是非简并的结论.利用原子均方位移判据, 我们研究了二维Penrose 准晶格的熔化性质, 得出边界较内部先熔化, 原子间相互作用大的系统不易熔化等合理结论。 关键词：     

低维半导体偏振光探测器研究进展

偏振光探测在遥感成像、环境监测、医疗检测和军事设备等领域都具有很好的应用价值,目前已经有一系列偏振探测和成像产品.随着信息器件进一步小型化、集成化,基于新型低维材料的偏振光探测器可以直接利用材料本征的各向异性对偏振光进行感知,在未来偏振光探测领域有很好的应用前景.很多二维/一维半导体材料,例如:黑磷, ReS_2, GaTe, GeSe, GeAs及ZrS_3等,都具有较强的本征面内各向异性,可以用于高性能偏振光探测器.基于此类低维半导体材料设计的不同结构类型的偏振光探测器已经覆盖了紫外、可见以及红外等多个波段.本文总结了近年来相关领域的研究进展和我们课题组的一些工作.     

广义布洛赫条件下二维晶格的磁交换作用

二维磁性材料是近几年新兴的研究领域,该材料在开发自旋电子器件等领域具备良好的应用潜能.为了了解二维磁性材料的磁性质,明确体系内各近邻磁性原子间的磁相互作用非常重要.第一性原理为各近邻磁交换参数的计算奠定了基础.目前各近邻参数的第一性原理计算常用的是能量映射法,但这种方法存在一定的缺陷.本文通过广义布洛赫条件推导了3种常见二维磁性结构的海森伯作用与Dzyaloshinskii-Moriya (DM)相互作用的自旋螺旋色散关系,这3种结构为四方结构,元胞包含一个磁性原子的六角结构,元胞包含两个磁性原子的六角结构.为了将本文推导的自旋螺旋色散关系应用于实际,我们通过第一性原理计算了一些材料的海森伯和DM作用的交换参数,这些材料分别是MnB,VSe₂,MnSTe,Cr₂I₃Cl₃.其中,MnSTe和Cr₂I3Cl₃都属于二维Janus材料,磁性原子层的上下层对称性破缺,整个体系存在DM相互作用.     

二维相关光谱探测荧光能量转移现象

以EuCl₃和NdCl₃混合水溶液为研究对象,按正交浓度序列以浓度为外部扰动构建紫外可见-荧光二维相关光谱。在混合溶液的二维相关光谱中,观察到了Eu3+的荧光发射谱峰与Nd^{3+的吸收谱峰之间存在交叉峰。交叉峰的出现表明Eu3+和Nd3+的荧光发射与吸收之间存在能量传递。二维相关光谱中交叉峰的产生并非由于溶剂水分子与溶质(Eu3+或Nd3+)之间相互作用;若以单一溶质的EuCl₃和NdCl₃的水溶液构造模拟的“混合溶液”的拟合光谱构建二维紫外可见-荧光相关光谱,由于Eu3+和Nd3+在空间上相互分离,无相互作用发生,交叉峰并不存在。二维相关光谱的交叉峰可为从光谱学角度探测复杂体系能量传递及其相关机制提供一条新思路。}     

n维经典非理想气体的物态方程与热力学函数

求出了n维经典非理想气体的物态方程和热力学函数.由London理论得出了维数n(n<6)不同时的经典非理想气体的物态方程形式基本一样,且与能谱关系无关的结论;当维数n≥6时,如果仍用London理论,巨配分函数发散,此时物态方程及热力学函数将无意义.事实上只要使用刚性球模型,无论是否使用London理论,总存在一个维数n,当维数大于n时巨配分函数发散.     

Correlation Dimension

In many situations, both deterministic and probabilistic, one can develop further the study of the multifractal structure of a dynamical system, particularly when there exist strange attractors. Multifractal refers to a notion of size emphasizing the variations of the weigth of the measure. In such schemes, one has to compute a free energy function associated to some sequence of partitions. We relate the free energy function, associated to a sequence of uniform partitions of exponentially decreasing diameters, and the correlation dimension which refers to a quantity that is the most accessible in numerical computations. Finally we discuss of two assumptions for the existence of free energy functions.     

Dimension on discrete spaces

In this paper we develop some combinatorial models for continuous spaces. We study the approximations of continuous spaces by graphs, molecular spaces, and coordinate matrices. We define the dimension on a discrete space by means of axioms based on an obvious geometrical background. This work presents some discrete models ofn-dimensional Euclidean spaces,n-dimensional spheres, a torus, and a projective plane. It explains how to construct new discrete spaces and describes in this connection several three-dimensional closed surfaces with some topological singularities. It also analyzes the topology of (3+1)-space-time. We are also discussing the question by R. Sorkin about how to derive the system of simplicial complexes from a system of open coverings of a topological space.     

基于量纲分析的建模研究

在量纲分析理论的基础上,结合工程实际问题研究了量纲分析建模的基本思路和方法.     

Hausdorff Dimension in Stochastic Dispersion

We consider the evolution of a connected set in Euclidean space carried by a periodic incompressible stochastic flow. While for almost every realization of the random flow at time t most of the particles are at a distance of order away from the origin, there is an uncountable set of measure zero of points, which escape to infinity at the linear rate. In this paper we prove that this set of linear escape points has full Hausdorff dimension.     

Dimension estimates and physiological data

Dimension estimates for data from physiological systems are notoriously difficult since the data are far from ideal in the sense of deterministic dynamical systems. Possible pitfalls and necessary precautions are pointed out and a recipe is given which is viable for those researchers who want to use the Grassberger-Procaccia algorithm but who are not familiar with the vast existing literature on dimension estimates. The relevance of dimension estimates for the characterization of physiological data is discussed, where both the cases of finding and not finding a low dimension are considered. (c) 1995 American Institute of Physics.     

Double Semions in Arbitrary Dimension

We present a generalization of the double semion topological quantum field theory to higher dimensions, as a theory of \({d-1}\) dimensional surfaces in a d dimensional ambient space. We construct a local Hamiltonian that is a sum of commuting projectors and analyze the excitations and the ground state degeneracy. Defining a consistent set of local rules requires the sign structure of the ground state wavefunction to depend not just on the number of disconnected surfaces, but also upon their higher Betti numbers through the semicharacteristic. For odd d the theory is related to the toric code by a local unitary transformation, but for even d the dimension of the space of zero energy ground states is in general different from the toric code and for even \({d > 2}\) it is also in general different from that of the twisted \({Z_2}\) Dijkgraaf–Witten model.