Does the eigenratio λ2/λN represent the synchronizability of a complex network?

In the study of complex networks,it is commonly believed that the eigenratio λ2/λ N of the Laplacian matrix of a network represents the network synchronizability,especially for symmetric networks.This paper gives two counterexamples to show that this is not true for the case where the network has a disconnected synchronized region.Consequently,a simple answer is presented to the question of when the eigenratio λ2/λ N does represent the network synchronizability.     

Does the eigenratio synchronizability of λ2/λN represent the a complex network？

In the study of complex networks, it is commonly believed that the eigenratio λ2/λN of the Laplacian matrix of a network represents the network synchronizability, especially for symmetric networks. This paper gives two counterexamples to show that this is not true for the case where the network has a disconnected synchronized region. Consequently, a simple answer is presented to the question of when the eigenratio λ2/λN does represent the network synchronizability.     

Are networks with more edges easier to synchronize,or not？

In this paper, the relationship between network synchronizability and the edge-addition of its associated graph is investigated. First, it is shown that adding one edge to a cycle definitely decreases the network synchronizability. Then, since sometimes the synchronizability can be enhanced by changing the network structure, the question of whether the networks with more edges are easier to synchronize is addressed. Based on a subgraph and complementary graph method, it is shown by examples that the answer is negative even if the network structure is arbitrarily optimized. This reveals that generally there are redundant edges in a network, which not only make no contributions to synchronization but actually may reduce the synchronizability. Moreover, a simple example shows that the node betweenness centrality is not always a good indicator for the network synchronizability. Finally, some more examples are presented to illustrate how the network synchronizability varies following the addition of edges, where all the examples show that the network synchronizability globally increases but locally fluctuates as the number of added edges increases.     

Undetermination of the synchronizability and relation between network betweenness centrality

Betweenness centrality is taken as a sensible indicator of the synchronizability of complex networks. To test whether betweenness centrality is a proper measure of the synchronizability in specific realizations of random networks, this paper adds edges to the networks and then evaluates the changes of betweenness centrality and network synchronizability. It finds that the two quantities vary independently.     

Undetermination of the relation between network synchronizability and betweenness centrality

Betweenness centrality is taken as a sensible indicator of the synchronizability of complex networks. To test whether betweenness centrality is a proper measure of the synchronizability in specific realizations of random networks,this paper adds edges to the networks and then evaluates the changes of betweenness centrality and network synchronizability. It finds that the two quantities vary independently.     

Synchronization speed of identical oscillators on community networks

Synchronizability of complex oscillators networks has attracted much research interest in recent years. In contrast, in this paper we investigate numerically the synchronization speed, rather than the synchronizability or synchronization stability, of identical oscillators on complex networks with communities. A new weighted community network model is employed here, in which the community strength could be tunable by one parameter δ. The results showed that the synchronization speed of identical oscillators on community networks could reach a maximal value when δ is around 0.1. We argue that this is induced by the competition between the community partition and the scale-free property of the networks. Moreover, we have given the corresponding analysis through the second least eigenvalue λ₂ of the Laplacian matrix of the network which supports the previous result that the synchronization speed is determined by the value of λ₂.     

Step instability of the In_0.2Ga_0.8As （001） surface during annealing

Anisotropic evolution of the step edges on the compressive-strained In0.2Ga0.8 As/GaAs(001) surface has been investigated by scanning tunneling microscopy (STM). The experiments suggest that step edges are indeed sinuous and protrude somewhere a little way along the [110] direction, which is different from the classical waviness predicted by the theoretical model. We consider that the monatomic step edges undergo a morphological instability induced by the anisotropic diffusion of adatoms on the terrace during annealing, and we improve a kinetic model of step edge based on the classical Burton–Cabrera–Frank (BCF) model in order to determine the normal velocity of step enlargement. The results show that the normal velocity is proportional to the arc length of the peninsula, which is consistent with the first result of our kinetic model. Additionally, a significant phenomenon is an excess elongation along the [110] direction at the top of the peninsula with a higher aspect ratio, which is attributed to the restriction of diffusion lengths.     

Two Novel Methods to Enhance Network Synchronizability

In this paper, we propose two methods to enhance the synchronizability of a class of complex networks which do not hold the positive correlation between betweenness centrality （BC） and degree of a node, and observe other topology characteristics of the network affected by the methods. Numerical simulations show that both methods can effectively enhance the synchronizability of this kind of networks. Furthermore, we show that the maximal BC of all edges is an important factor to affect the network synchronizability, although it is not the unique factor.     

Enhancing synchronizability by rewiring networks

<正>According to different forms of synchronized region,complex networks are divided into typeⅠ(unbounded synchronization region) and typeⅡ(bounded synchronization region) networks.This paper presents a rewiring algorithm to enhance the synchronizability of typeⅠand typeⅡnetworks.By utilizing the algorithm for an unweighted and undirected network,a better synchronizability of network with the same number of nodes and edges can be obtained. Numerical simulations on several different network models are used to support the proposed procedure.The relationship between different topological properties of the networks and the number of rewirings are shown.It finds that the final optimized network is independent of the initial network,and becomes homogeneous.In addition the optimized networks have similar structural properties in the sense of degree,and node and edge betweenness centralities.However,they do not have similar cluster coefficients for typeⅡnetworks.The research may be useful for designing more synchronizable networks and understanding the synchronization behaviour of networks.     

A density functional theory study on the adsorption of CO and O₂ on Cu-terminated Cu₂O（111） surface

The adsorptions of CO and O2 molecules individually on the stoichiometric Cu-terminated Cu2O(111) surface are investigated by first-principles calculations on the basis of the density functional theory.The calculated results indicate that the CO molecule preferably coordinates to the Cu2 site through its C atom with an adsorption energy of -1.69 eV,whereas the O2 molecule is most stably adsorbed in a tilt type with one O atom coordinating to the Cu2 site and the other O atom coordinating to the Cu1 site,and has an adsorption energy of -1.97 eV.From the analysis of density of states,it is observed that Cu 3d transfers electrons to 2π orbital of the CO molecule and the highest occupied 5σ orbital of the CO molecule transfers electrons to the substrate.The sharp band of Cu 4s is delocalized when compared to that before the CO molecule adsorption,and overlaps substantially with bands of the adsorbed CO molecule.There is a broadening of the 2π orbital of the O2 molecule because of its overlapping with the Cu 3d orbital,indicating that strong 3d-2π interactions are involved in the chemisorption of the O2 molecule on the surface.     

The doping effects of BiFe_1-xCo_xO₃（x=0.0-0.8） in layered perovskite Bi₄Ti₃O₁₂ ceramics

Bi5Fe1-xCoxTi3O15(x = 0.0, 0.2, 0.4, 0.5, 0.6, and 0.8) multiferroic ceramics are synthesized in two steps using the solid state reaction technique. X-ray diffraction patterns show that the samples have four-layer Aurivillius phases. At room temperature (RT), the samples each present a remarkable coexistence of ferromagnetism (FM) and ferroelectricity (FE). The remnant polarization (2P r ) reaches its greatest value of 14 μC/cm 2 at x = 0.6. Remnant magnetization (2M r ) first increases and then decreases, and the greatest 2M r is 7.8 menu/g when x = 0.5. The magnetic properties for x = 0.4 are similar to those for x = 0.6, indicating that the magnetic properties originate mainly from the coupling between Fe 3+ and Co 3+ ions, rather than from their own magnetic moments.     

Predictions of pressure-induced structural transition,mechanical and thermodynamic properties of α-and β-Si₃N₄ ceramics:ab initio and quasi-harmonic Debye modeling

The plane-wave pseudo-potential method within the framework of ab initio technique is used to investigate the structural and elastic properties of α-and β-Si3N4.The ground-state parameters accord quite well with the experimental data.Our calculation reveals that α-Si3N4 can retain its stability to at least 40 GPa when compressed at 300 K.The α→β phase transformation would not occur in a pressure range of 0-40 GPa and a temperature range of 0-300 K.Actually,the α→β transition occurs at 1600 K and 7.98 GPa.For α-and β-Si3N4,the c axes are slightly more incompressible than the a axes.We conclude that β-Si3N4 is a hard material and ductile in nature.On the other hand,β-Si3N4 is also found to be an ionic material and can retain its mechanical stability in a pressure range of 0-10 GPa.Besides,the thermodynamic properties such as entropy,heat capacity,and Debye temperature of α-and β-Si3N4 are determined at various temperatures and pressures.Significant features in these properties are observed at high temperature.The calculated results are in good agreement with available experimental data and previous theoretical values.Many fundamental solid-state properties are reported at high pressure and high temperature.Therefore,our results may provide useful information for theoretical and experimental investigations of the Si3N4 polymorphs.     

The crystal structures and physical properties of the solid solution compound Ba₅Y_8-xMn₄O_21-1.5x（x = 0,1）

New oxometallides with the formula Ba5Y8 xMn4O21 1.5x(x = 0,1) are prepared through an atmospherecontrolled solid-state reaction.Two single-phase samples with Ba/Y/Mn atomic ratios 5/8/4(Y8) and 5/7/4(Y7) are obtained.The crystal structures and the physical properties of the compounds are investigated by X-ray powder diffraction,magnetization,conductivity,and dielectricity measurements.The Ba5Y8 xMn4O21 1.5x compound is demonstrated to be a Y-deficient solid solution.The solid solution compound Ba5Y8 xMn4O21 1.5x crystallizes into tetragonal symmetry with the space group I4/m.Detailed structure analysis by Rietveld refinement of the X-ray powder diffraction data reveals that the Y vacancies occur preferentially at the Y(2) site.Thermal magnetization measurements indicate the presence of antiferromagnetic interaction between Mn ions in the compounds,and temperature-dependent resistivity measurements show that insulator-semiconductor transitions occur around 175 K and 170 K for the Y8 and Y7 samples,respectively.Strong frequency dependences of the dielectric constant are observed above ～175 K for the two compounds.     

Synchronization of coupled logistic maps on random community networks

The collective synchronization of a system of coupled logistic maps on random community networks is investigated. It is found that the synchronizability of the community network is affected by two factors when the size of the network and the number of connections are fixed. One is the number of communities denoted by the parameter rn, and the other is the ratio σ of the connection probability p of each pair of nodes within each community to the connection probability q of each pair of nodes among different communities. Theoretical analysis and numerical results indicate that larger rn and smaller σ are the key to the enhancement of network synchronizability. We also testify synchronous properties of the system by analysing the largest Lyapunov exponents of the system.     

Structural analysis and crystal-field calculations of Nd³⁺ in Gd_x Lu_1-x TaO₄（x = 0.85） polycrytalline

The crystal structural parameters of Nd 3+-doped rare earth orthotantalate Gd x Lu 1 x TaO 4(x = 0.85) are determined by applying the Rietveld refinement to its X-ray diffraction,and its emission and excitation spectra at 77 K are analysed.The relativistic model of ab initio self-consistent DV-Xα method,which is applied to the cluster NdO 8 in Gd x Lu 1 x TaO 4,and the effective Hamiltonian model are used to investigate its spin-orbit and crystal-field parameters.The free-ions and crystal-field parameters are fitted to the experimental energy levels at 77 K with a root-mean-square deviation of 14.92 cm 1.According to the crystal-field calculations,96 levels of Nd 3+ are assigned.Finally,the fitting results of free-ions and crystal-field parameters are compared with those already reported for Nd 3+:YAlO 3.The results indicate that the free-ion parameters are similar to those of the Nd3+ in Gdx Lu1-x TaO4 and YAlO 3 hosts,and the crystal-field interaction of Nd3+ in Gdx Lu1-x TaO4 is stronger than that in YAlO 3.     

Average Range and Network Synchronizability

The influence of structural properties of a network on the network synchronizability is studied by introducing a new concept of average range of edges. For both small-world and scale-free networks, the effect of average range on the synchronizability of networks with bounded or unbounded synchronization regions is illustrated through numerical simulations. The relations between average range, range distribution, average distance, and maximum betweenness are also explored, revealing the effects of these factors on the network synchronizability of the small-world and scale-free networks, respectively.     

Pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions

This paper studies pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions. To study a state-feedback pinning-controlled network with N nodes, it first converts the controlled network to an extended network of N+1 nodes without controls. It is shown that the controlled synchronizability of the given network is determined by the real part of the smallest nonzero eigenvalue of the coupling matrix of its extended network when the synchronized region is unbounded; but it is determined by the ratio of the real parts of the largest and the smallest nonzero eigenvalues of the coupling matrix when the synchronized region is bounded. Both theoretical analysis and numerical simulation show that the portion of controlled nodes has no critical values when the synchronized region is unbounded, but it has a critical value when the synchronized region is bounded. In the former case, therefore, it is possible to control the network to achieve synchronization by pinning only one node. In the latter case, the network can achieve controlled synchronization only when the portion of controlled nodes is larger than the critical value.     

The analytical potential energy function of flue gas SO₂（X¹A₁）

The equilibrium structure of flue gas SO 2 is optimized using the density functional theory (DFT)/ B3P86 method and CC-PV5Z basis. The result shows that it has a bent (C2V ,X1A1) ground state structure with an angle of 119.1184 . The vibronic frequencies and the force constants are also calculated. Based on the principles of atomic and molecular reaction statics (AMRS), the possible electronic states and reasonable dissociation limits for the ground state of SO2 molecule are determined. The potential functions of SO and O2 are fitted by the modified Murrell–Sorbie+c6 (M-S+c6) potential function and the fitted parameters, the force constants and the spectroscopic constants are obtained, which are all close to the experimental values. The analytic potential energy function of the SO2 (X1A1) molecule is derived using the many-body expansion theory. The contour lines are constructed, which show the static properties of SO2 (X1A1), such as the equilibrium structure, the lowest energies, the most possible reaction channel, etc.     

Synchronization between Different Networks

Synchronization between two networks with different topology structures and different dynamical behaviours is studied. These two different networks are driving and responding networks, respectively. Under the preconditions that the driving network gets synchronization, we give the conditions for the responding network to be synchronized to the same dynamics as the driving network with the help of the open-plus-closed-loop method. Then a example is given to verify the validity of the theoretical results.     

Investigation of the free volume and ionic conducting mechanism of poly（ethylene oxide）-LiClO₄ polymeric electrolyte by positron annihilating lifetime spectroscopy

The positron annihilation lifetime and ionic conductivity are each measured as a function of organophilic rectorite(OREC) content and temperature in a range from 160 K to 300 K.According to the variation of ortho-positronium(o-Ps) lifetime with temperature,the glassy transition temperature is determined.The continuous maximum entropy lifetime(MELT) analysis clearly shows that the OREC and temperature have important effects on o-Ps lifetime and free volume distribution.The experimental results show that the temperature dependence of ionic conductivity obeys the Vogel-Tammann-Fulcher(VTF) and Williams-Landel-Ferry(WLF) equations,implying a free-volume transport mechanism.A linear least-squares procedure is used to evaluate the apparent activation energy related to the ionic transport in the VTF equation and several important parameters in the WLF equation.It is worthwhile to notice that a direct linear relationship between the ionic conductivity and free volume fraction is established using the WLF equation based on the free volume theory for nanocomposite electrolyte,which indicates that the segmental chain migration and ionic migration and diffusion could be explained by the free volume theory.