非轴对称光腔的矩阵光学分析

用矩阵光学理论对一般非轴对称光学谐振腔进行了研究,得出基模本征解。讨论了约束稳定、非约束稳定及准约束稳定的条件。指出这种腔在一般情况下存在双解。所得结果适用于多元件非轴对称光腔,具有普遍性。     

岩石的磁各向异性

各种岩石都不同程度地具有磁各向异性。磁各向异性采用磁化率张量来描述,并用于研究岩石的磁组构。     

Computing surfaces invariant under subdivision

In this paper, we propose a general subdivision algorithm for generating surfaces. The algorithm has as motivation our earlier work on the design of free form curves where similar ideas were investigated. Here we describe some properties of uniform refinement algorithms for surface generation. A detail analysis of their properties will be given later by one of us.     

裂隙岩体渗流参数讨论和渗流场有限元计算与分析

本文综合讨论了裂隙岩体渗流参数的特征,及由裂隙参数确定岩体渗透张量的过程。叙述了将岩体作为连续介质的三维非均质各向异性稳定渗流场有限元计算方法。通过对简单模型的有限元计算分析,讨论了各向异性渗流场的二个特征,即渗透主轴对渗流场的控制意义、以及渗透主轴与边界的关系对渗流场的控制意义。     

Damage Constitutive Equations and its Application to Fiber Reinforced Composites under Transverse Impact

Two continuous field variables, called as continuity tensor and damage variable tensor, are used to describe the anisotropic responses of an elastic-brittle material under transverse impact load. Based on the continuum damage mechanics, anisotropic damage constitutive equations in both full and incremental forms are proposed here. The expressions of effective elastic module tensor, damage variable tensor and damage propagation force tensor are further derived, and the methods for determining the tensors are explained in detail. An example of strain and damage response of a fiber reinforced composite laminated plate under transverse impact load is employed to demonstrate the application of this theory. In the example, the damage variable coupled with geometric large deformation of laminated plate is also considered. The calculating results illustrate the influence of damage on strain field in the impacted laminated plate.     

Neumann原理与分子的转动性质

给出分子惯量张量的并矢式,利用标量场性质得到惯量张量的示性曲面,根据Neumann原理讨论各种点群分子惯量张量示性面的特点,给出分子惯量张量沿不同方向值的分布规律及角动量与角速度共线的方向.     

基于四阶累积张量方法的欠定盲源信号分离

针对瞬时欠定盲源信号分离问题,提出一种四阶累积张量分解算法.首先构建观察信号四阶累积协方差,依据源信号具有相互独立且均值为零的性质,对累积协方差化简并扩展到张量域,得到四阶累积张量.采用分层交替最小二乘算法对四阶累积张量进行非负库克分解,求得非负库克模型的参数,同时获得非负混合矩阵并求其伪逆,最终估计出源信号.选用真实的语音信号和生物信号进行仿真实验,结果表明该方法提高了源信号和非负混合矩阵的估计性能.     

A Resistant Quantum Key Exchange Protocol and Its Corresponding Encryption Scheme

The emergence of quantum computer will threaten the security of existing public-key cryptosystems, including the Diffie Hellman key exchange protocol, encryption scheme and etc, and it makes the study of resistant quantum cryptography very urgent. This motivate us to design a new key exchange protocol and eneryption scheme in this paper. Firstly, some acknowledged mathematical problems was introduced, such as ergodic matrix problem and tensor decomposition problem, the two problems have been proved to NPC hard. From the computational complexity prospective, NPC problems have been considered that there is no polynomial-time quantum algorithm to solve them. From the algebraic structures prospective, non-commutative cryptography has been considered to resist quantum. The matrix and tensor operator we adopted also satisfied with this non-commutative algebraic structures, so they can be used as candidate problems for resisting quantum from perspective of computational complexity theory and algebraic structures. Secondly, a new problem was constructed based on the introduced problems in this paper, then a key exchange protocol and a public key encryption scheme were proposed based on it. Finally the security analysis, efficiency, recommended parameters, performance evaluation and etc. were also been given. The two schemes has the following characteristics, provable security,security bits can be scalable, to achieve high efficiency, quantum resistance, and etc.     

一个抗量子密钥交换协议及其对应的加密方案(英文)

The emergence of quantum computer will threaten the security of existing public-key cryptosystems,including the Diffie Hellman key exchange protocol,encryption scheme and etc,and it makes the study of resistant quantum cryptography very urgent.This motivate us to design a new key exchange protocol and encryption scheme in this paper.Firstly,some acknowledged mathematical problems was introduced,such as ergodic matrix problem and tensor decomposition problem,the two problems have been proved to NPC hard.From the computational complexity prospective,NPC problems have been considered that there is no polynomial-time quantum algorithm to solve them.From the algebraic structures prospective,non-commutative cryptography has been considered to resist quantum.The matrix and tensor operator we adopted also satisfied with this non-commutative algebraic structures,so they can be used as candidate problems for resisting quantum from perspective of computational complexity theory and algebraic structures.Secondly,a new problem was constructed based on the introduced problems in this paper,then a key exchange protocol and a public key encryption scheme were proposed based on it.Finally the security analysis,efficiency,recommended parameters,performance evaluation and etc.were also been given.The two schemes has the following characteristics,provable security,security bits can be scalable,to achieve high efficiency,quantum resistance,and etc.     

Experimental investigation on fracturing process of marble under biaxial compression

In this study, servo-controlled biaxial compression tests were conducted on marble specimens to investigate their failure characteristics and fracturing process. The complete stress–strain curves were obtained, and the three-dimensional (3D) features of the failure surfaces were acquired by 3D laser scanning. Acoustic emission (AE) monitoring and moment tensor (MT) analysis were used in combination to better understand the fracturing mechanism of marble under biaxial compression. It was noted that a type of 3D stepwise cracking behaviour occurred on the fracturing surfaces of the examined specimens. The stress dropped multiple times, and a repeated fracturing mode corresponding to the repeated stress drops in the post-peak regime was observed. Three substages, i.e. stress stabilisation, stress decrease and stress increase, were identified for a single fracturing mode. Then quantitative and statistical analyses of the fracturing process at each substage were discussed. Based on the testing results, it was found that at the stress stabilisation substage, the proportion of mixed-mode fractures increased. At the stress decrease substage, the proportion of mixed-mode fractures decreased, and the tensile or shear fractures increased. At the stress increase substage, the proportion of mixed-mode or tensile fractures decreased, and the shear fractures increased. Finally, a conceptual model for the stepwise crack formation was proposed.