Modern Physics Letters B

In a recent paper we had defined the dimension of a complex network in terms of the scaling property of the volume. The question assumes significance because the dependence of system behavior on dimension is an important topic in statistical mechanics. Hence we consider the definition in more detail, and we propose a more widely applicable definition in this work. This definition has good mathematical properties, and it is based on the definition of a zeta function for complex networks.

A heteroepitaxial growth model of the ZnO film on sapphire(0001) is calculated by using a plane wave ultrasoft pseudo-potential method based on the density functional theory. A strong chemical adsorption on the sapphire(0001) is observed. It is found that interfacial atoms have different diffusivity at 400°C, 600°C and 800°C. The temperature has a decisive effect on the surface and interface structures of ZnO/α-Al₂O₃(0001) and on the growth mode of ZnO thin films. In the whole process of the adsorption and growth of ZnO, the diffusivity of O atoms is higher than that of Zn, and the interlayer diffusion has an important impact on growth of the thin films. There are two growth modes of ZnO on sapphire(0001), which is further demonstrated by theoretical calculation. It can be observed from the calculation that the vacancies of Zn where the atomic layer is near to the α-Al₂O₃(0001) surface is more than that of O atoms.

In order to increase greatly the calculation accuracy and the computation speed for complex electromagnetic fields in modern physics, a new finite element method, which has the high computation accuracy, fast computation speed and less computer storage requirements, is presented in this paper. The new method with a high-order finite element without internal nodes is introduced to compute and analyze some complex electromagnetic fields in the electron accelerators. In this paper, the complex electromagnetic field in an electromagnetic device has been calculated successfully by the finite elements, and the electromagnetic properties of the electromagnetic device under the specific work condition is analyzed and evaluated. Good agreement is found between the computed values and the experimental values.

A new loop algebra containing four arbitrary constants is presented, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper, which can be reduced to a computing formula of constant γ in the trace identity. As application, two new Liouville integrable hierarchy and Hamiltonian structures are derived.

Zinc thiourea chloride (ZTC) crystals were crystallized by slow evaporation technique. The lattice parameters of the grown crystals were determined by angle dispersive X-ray powder diffraction technique (XRD) and the structure was confirmed. High pressure electrical resistivity study was carried out on this crystal and the results are reported here.

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The relaxation of the transverse magnetization of the protons attached to polymeric chains and pseudo-solid echoes were observed for molten polyizobutyl and for polyizobutyl-C₇D₈ solutions by NMR method, in a large temperature domain. The analysis of the shape of the pseudo-solid echoes leads to the possibility of evaluating the function that characterizes the contribution of the fluctuation of the entanglements to the relaxation of the transverse magnetization. The modification of this function is associated to the perturbation of the superposition property of the relaxation curves and induces changes of the properties of the pseudo-solid echoes.