一类节点结构互异的复杂网络的混沌同步

提出了一种实现节点结构互异的复杂网络的混沌同步方法.以异结构混沌系统作为节点构造复杂网络,基于Lyapunov稳定性定理确定了复杂网络中连接节点的耦合函数的形式.以Rssler系统、Coullet系统以及Lorenz系统作为网络节点构成的复杂网络为例,仿真模拟发现,整个复杂网络存在稳定的混沌同步现象.此方法不但可以实现任意混沌系统作为节点的网络混沌同步,而且网络节点数对整个复杂网络同步的稳定性也无影响,因而,具有一定的普适性. 关键词： 混沌同步 复杂网络 异结构 Lyapunov稳定性定理     

A new information dimension of complex networks

The fractal and self-similarity properties are revealed in many complex networks. The classical information dimension is an important method to study fractal and self-similarity properties of planar networks. However, it is not practical for real complex networks. In this Letter, a new information dimension of complex networks is proposed. The nodes number in each box is considered by using the box-covering algorithm of complex networks. The proposed method is applied to calculate the fractal dimensions of some real networks. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks.     

The effect of bromine substitution on the charge-transfer emission of the complex of phenanthrene and tetracyanobenzene

The absorption spectra of the charge-transfer complexes of sym-tetracyanobenzene (TCNB) with phenanthrene, 9-bromophenanthrene, and 9,10-dibromophenanthrene are measured in chloroform solutions at room temperature. The total emission and phosphorescence spectra of the donors and the complexes are measured at 77 K in rigid glasses. The phosphorescence decay lifetimes are determined for phenanthrene, TCNB, and for the phenanthrene-TCNB complex, and a decrease in the phenanthrene-TCNB complex lifetime relative to the lifetimes of the two components is observed. The luminescence spectra of the complexes exhibit both a red shift and a lack of structure as compared with the donor spectra. The results are interpreted, in agreement with the results of Iwata et al. for the phenanthrene-TCNB complex (1), as an indication that there is a considerable degree of charge-transfer character in the lowest triplet state (T₁). Bromine substitution leads to a decrease in the energy of the phenanthrene triplet state. As a result, the energy gap between the donor molecule triplet state and the complex charge-transfer triplet state decreases from phenanthrene, to 9-bromophenanthrene, to 9,10-dibromophenanthrene. The results suggest that the proximity of these two triplet states in 9,10-dibromophenanthrene and its charge-transfer complex leads to some local donor triplet state character in the emitting complex triplet state.     

Complex resonance at periodic excitation of an oscillator

Periodic excitation of an oscillator by an external signal close to an exponential one with a complex frequency at the main part of the period is analyzed. The characteristics of a stabilized excitation regime are determined, as are its features when approaching the complex resonance, when the complex frequency of an external signal at the main part of the period is compared with the complex eigenfrequency of the oscillator. A criterion of closeness to the complex resonance is suggested. Estimations of the allowed level of intensity, when nonlinear distortions of the oscillator response are insignificant, are presented.     

Quantum field theoretical description of unstable behavior of a Bose-Einstein condensate with a highly quantized vortex in a harmonic potential

The Bogoliubov-de Gennes equations are used for a number of theoretical works to describe quantum and thermal fluctuations of trapped Bose-Einstein condensates. We consider the case in which the condensate has a highly quantized vortex. It is known that these equations have complex eigenvalues in this case. We give the complete set including a pair of complex modes whose eigenvalues are complex conjugates to each other. The expansion of the quantum fields which represent neutral atoms in terms of the complete set brings the operators associated with the complex modes, which are simply neither bosonic nor fermionic ones. The eigenstate of the Hamiltonian is given. Introducing the notion of the physical states, we discuss the instability of the condensates in the context of Kubo’s linear response theory.     

Configurations of high-frequency ultrasonics complex vibration systems for packaging in microelectronics

Ultrasonic high-frequency complex vibrations are effective for various ultrasonic high-power applications. Three types of ultrasonic complex vibration system with a welding tip vibrating elliptical to circular locus for packaging in microelectronics were studied. The complex vibration sources are using (1) a longitudinal-torsional vibration converter with diagonal slits that is driven only by a longitudinal vibration source, (2) a complex transverse vibration rod with several stepped parts that is driven by two longitudinal vibration source crossed at a right angle and (3) a longitudinal vibration circular disk and three longitudinal transducers that are installed at the circumference of the disk.     

复Ginzburg-Landau方程时空混沌的网络同步与参量辨识

研究了参量未知的时空混沌系统构成复杂网络的同步与参量辨识问题. 设计的参量辨识律可以有效地辨识复杂网络中所有节点时空混沌系统中的未知参量. 基于稳定性定理, 通过构造适当的Lyapunov函数, 确定了网络完全同步的条件. 以参量未知的一维复Ginzburg-Landau方程作为网络节点为例, 通过仿真模拟检验了参量辨识律以及同步方法的有效性.     

Theory of hydrogen-related metastability in disordered silicon

Density functional electronic structure calculations are employed to examine hydrogen for a variety of configurations in silicon. A novel complex is found for hydrogen in amorphous silicon. The complex involves the breaking of a weak silicon bond to form two Si-H bonds with both hydrogens in between the original silicon atoms. This complex provides a microscopic model for new metastable complexes observed in amorphous silicon. Mechanisms for hydrogen-related metastability are discussed for amorphous and polycrystalline silicon.     

Complex relativity and real solutions II: Classification of complex bivectors and metric classes

This paper continues the examination of real metrics and their properties from the viewpoint of complex relativity as initiated by McIntosh and Hickman [1]. Tetrads of real metrics can be formally complexified by complex coordinate transformations and tetrad rotations and their properties investigated from the viewpoint of complex relativity. First, complex bivectors are examined and classified, partly by using the fundamental quadric surface of a metric in projective complex 3-space P³-an elegant but not well-known method of investigating the null structure of a metric. A generalization of the Mariot-Robinson theorem from real relativity is then given and related to various canonical forms of complex bivectors. The second part of the paper discusses four classes of complex metrics. Real metrics of the first class are ones with a null congruence whose wave surfaces have equal curvature. The second class, a subcase of the first one, is the main one; it contains integrable double Kerr-Schild metrics. Different, but equivalent, definitions of such metrics are given from various viewpoints. Two other subcasses are also discussed. The nonexpanding typs-D vacuum metric is considered and it is shown how complex transformations may be made to write it (and subcases) in double (or single) Kerr-Schild form.     

Lie and Noether symmetries of systems of complex ordinary differential equations and their split systems

The Lie and Noether point symmetry analyses of a kth-order system of m complex ordinary differential equations (ODEs) with m dependent variables are performed. The decomposition of complex symmetries of the given system of complex ODEs yields Lie- and Noether-like operators. The system of complex ODEs can be split into 2m coupled real partial differential equations (PDEs) and 2m Cauchy–Riemann (CR) equations. The classical approach is invoked to compute the symmetries of the 4m real PDEs and these are compared with the decomposed Lie- and Noether-like operators of the system of complex ODEs. It is shown that, in general, the Lie- and Noether-like operators of the system of complex ODEs and the symmetries of the decomposed system of real PDEs are not the same. A similar analysis is carried out for restricted systems of complex ODEs that split into 2m coupled real ODEs. We summarize our findings on restricted complex ODEs in two propositions.     

GGA+U方法研究ZnO孪晶界对V_(Zn)-N_O-H复合体对p型导电性的影响

采用基于密度泛函理论的广义梯度近似平面波赝势方法,探究四种ZnO-Σ7(1230)孪晶界中V_(Zn)-N_O-H复合体的电子结构和p型导电机理.计算结果表明,在ZnO-Σ7(1230)孪晶界中,N掺杂后会与锌空位(V_(Zn))、氢填隙(Hi)等点缺陷结合,进而形成V_(Zn)-N_O-H复合体,并出现在孪晶中的晶格应变集中区.此外,四种孪晶界中孪晶GB7a有利于V_(Zn)-N_O-H离化能降低,从而使其表现出浅受主特征.分析显示特殊的孪晶结构导致了氮替位(N_O)与近邻的O原子间距离缩短,阴离子之间发生相互作用,导致禁带中的空带能级下降,降低了电子跃迁所需能量.这一结果也说明GB7a孪晶界中的V_(Zn)-N_O-H可能成为N掺杂ZnO材料的p型导电的来源之一.     

Comparison between the dispersion curves calculated in complex frequency and the minima of the reflection coefficients for an embedded layer

Analytical solutions of Lamb functions for symmetric and antisymmetric elastodynamic modes propagating within a solid layer embedded in an infinite medium are presented. Alternative theoretical analyses of such modes are performed, first in terms of the usual approach of harmonic heterogeneous plane waves (real frequency and complex slowness) and then in terms of transient homogeneous plane waves (complex frequency and real slowness). An example structure of a 0.1-mm-thick "alpha case" (an oxygen-rich phase of titanium that is relatively stiff) plate embedded in titanium is used for the study. A large difference between the usual dispersion curves calculated in real frequency and complex slowness and those calculated in complex frequency and real slowness is shown. Thus the choice between a spatial and a temporal parameter to describe the imaginary part of the guided waves is shown to be significant. The minima and the zeros of the longitudinal and shear plane-wave reflection coefficients are calculated and are compared with the dispersion curves. It is found that they do not match with the dispersion curves for complex slowness, but they do agree quite well with the dispersion curves for complex frequency. This implies that the complex frequency approach is better suited for the comparison of the modal properties with near-field reflection measurements.     

Computerization of experiments on interaction of microwave electromagnetic radiation with heterogeneous liquids

A method for computerization of experiments on the interaction of microwave electromagnetic radiation and heterogeneous liquids is implemented as a measurement software complex that is integrated in the laboratory setup. The complex allows computerized measurements of various parameters of interaction of electromagnetic waves and material substances, control of the setup, and off-line processing of experimental data. The proposed computerized experimental procedures are superior to conventional manual procedures owing to faster and simpler measurements and analysis. The advantages of the proposed complex are demonstrated in experiments with known substances and artificial colloids and emulsions that contain magnetite nanoparticles.     

基于Kramers-Kronig关系建立金属太赫兹色散模型

提出了一种基于测量反射率谱、使用Kramers-Kronig(KK)关系建立金属太赫兹色散模型的方法.结合合金铝和合金铜4—40 THz的测量反射率谱,通过反射系数振幅和相位的KK关系,采用高频端指数外推,低频端常数外推的方法,反演金属复折射率.以KK反演的复折射率作为实验值,以拟合复折射率和实验值误差最小为准则,使用遗传优化算法,拟合了合金铝和合金铜的Drude色散参数(等离子频率和碰撞频率).基于优化的Drude模型计算了0.1—40 THz材料的复折射率,与椭偏仪的实测结果符合,验证了模型的准确性.该方法理论与实验相互验证,以测量的复折射率作为实验定标,将远红外频段的色散信息拓展到太赫兹频域,确定了太赫兹频段金属的微观物理参数,提供了太赫兹频段色散和散射机理的研究依据.     

Phase diagram of epidemic spreading — unimodal vs. bimodal probability distributions

Disease spreading on complex networks is studied in SIR model. Simulations on empirical complex networks reveal two specific regimes of disease spreading: local containment and epidemic outbreak. The variables measuring the extent of disease spreading are in general characterized by a bimodal probability distribution. Phase diagrams of disease spreading for empirical complex networks are introduced. A theoretical model of disease spreading on m-ary tree is investigated both analytically and in simulations. It is shown that the model reproduces qualitative features of phase diagrams of disease spreading observed in empirical complex networks. The role of tree-like structure of complex networks in disease spreading is discussed.     

Energy-momentum complex of gravitational field in the Palatini formalism

It is shown that Murphy's energy-momentum complex of the gravitational field, derived from the Hilbert Lagrangian by use of the Palatini formalism, is identical to the complex derived from the same Lagrangian in a standard way by Mitskievic. The explicitly tensorial formulation of conservation laws in general relativity is eflectively used and some properties of the complex in question are discussed in connection with Murphy's article.     

Characteristics of large capacity ultrasonic complex vibration sources with stepped complex transverse vibration rods

Configurations of large capacity ultrasonic complex vibration sources with multiple longitudinal transducers are proposed and studied. The ultrasonic complex vibration systems are effective and essential for new applications in various industries. The complex vibration source of 27 kHz consists of a complex transverse rod with a welding tip (aluminum alloy, stainless steel and titanium alloy), a complex vibration rod with a flange and stepped part for holding the system, a circular longitudinal vibration disk (aluminum alloy) and six bolt-clamped Langevin type PLT transducers. Three transducer pairs are driven simultaneously using three driving systems at phase difference 120 degrees, and almost circular vibration locus is obtained.     

Solution of dispersion relations for planar waveguides in the case of complex roots

A method for calculating the complex roots of a nonlinear equation is described whereby the solution of the problem is reduced to quadratures. Applications of the method to the investigation of dispersion relations for various open waveguide structures with a complex dielectric permittivity are discussed. The possibilities of the prismatic excitation of modes corresponding to the roots of the dispersion relations on different Riemann sheets are analyzed. Solutions are obtained for the inverse problems of reconstructing complex mode propagation constants and determining the parameters of films that guide waveguide and leaky modes. The solution is based on processing of the angular dependence of the reflection coefficient in a prismatic excitation scheme. Zh. Tekh. Fiz. 68, 88–95 (April 1998)     

Complex relativity and real solutions. I: Introduction

This is the first of a series of papers on complex spaces and their use in complex relativity. The basic aim is to develop the theory of complex relativity but only insofar as it helps in obtaining, and understanding, real solutions of Einstein's vacuum equations as slices of complex solutions. In this first paper, specific aims of the whole series are first presented. The basic equations and key entities, which are used later, are presented. The basic relativistic language used is that of Newman and Penrose. Included is a discussion of a number of important properties which arise in the development of the basic equations and key concepts, these properties being mainly ones which are not apparent in standard real formulations.     

Exponential synchronization of complex networks with Markovian jump and mixed delays

In this Letter, we investigate the exponential synchronization problem for an array of N linearly coupled complex networks with Markovian jump and mixed time-delays. The complex network consists of m modes and the network switches from one mode to another according to a Markovian chain with known transition probability. The mixed time-delays are composed of discrete and distributed delays, both of which are mode-dependent. The nonlinearities imbedded with the complex networks are assumed to satisfy the sector condition that is more general than the commonly used Lipschitz condition. By making use of the Kronecker product and the stochastic analysis tool, we propose a novel Lyapunov–Krasovskii functional suitable for handling distributed delays and then show that the addressed synchronization problem is solvable if a set of linear matrix inequalities (LMIs) are feasible. Therefore, a unified LMI approach is developed to establish sufficient conditions for the coupled complex network to be globally exponentially synchronized in the mean square. Note that the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required. A simulation example is provided to demonstrate the usefulness of the main results obtained.