Volume 68, Issue 5

In this article, we applied the variational iteration method along with a Padé approximation (VIM-Padé) to obtain the analytical approximate solution for the motion of a spherical particle in a plane Couette flow. We studied the effects of different flow parameters on the velocity field. It is examined that the present analytical technique is extremely efficient and easy to apply for such a problem.

The geometric structures, stabilities, electronic and magnetic properties of silicon doped silver clusters Ag n Si (n = 1 - 9) have been systematically investigated by using meta-generalized gradient approximation (meta-GGA) exchange correlation Tao-Perdew-Staroverov-Scuseria (TPSS) functional. Due to the sp 3 hybridization, the lowest energy structures of doped clusters favour the threedimensional structure. The silicon atom prefers to be located at the surface of the host silver clusters. The isomers that correspond to high coordination numbers of the Si-Ag bonds are found to be more stable. By analyzing the relative stabilities, the results show that the quadrangular bipyramid Ag 4 Si structure is the most stable geometry for the Ag n Si clusters. Meanwhile, the fragmentation energies, second-order difference of energies, difference of highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO gaps), and total magnetic moments exhibit pronounced even-odd alternations. The largest hardness difference (2:24 eV) exists between the clusters Ag 4 Si and Ag 5 , which illustrates that the corresponding Ag 4 Si cluster has dramatically enhanced chemical stability.

The g factors and the hyperfine structure constants for the octahedral interstitial Mn 2+ and Cr + impurities in silicon are theoretically studied using the perturbation formulas of these parameters for an octahedral 3d 5 cluster. In the calculations, both the crystal-field and charge transfer contributions are taken into account in a uniform way, and the related molecular orbital coefficients are quantitatively determined from the cluster approach. The theoretical g factors and the hyperfine structure constants are in good agreement with the experimental data. The charge transfer contribution to the g-shift (≈g-g s , where g s ≈ 2:0023 is the spin only value) is opposite (positive) in sign and about 51% - 116% in magnitude as compared with the crystal-field one for Mn 2+ and Cr + , respectively. Nevertheless, the charge transfer contribution to the hyperfine structure constant has the same sign and about 12% - 19% that of the crystal-field one. Importance of the charge transfer contribution shows the order Cr + < Mn 2+ due to increase of the impurity valence state in the same host, especially for the g factor.

In this paper, we consider a coupled system of Petrovsky equations in a bounded domain with clamped boundary conditions. Due to several physical considerations, a linear damping which is distributed everywhere in the domain under consideration appears only in the first equation whereas no damping term is applied to the second one (this is indirect damping). Many studies show that the solution of this kind of system has a polynomial rate of decay as time tends to infinity, but does not have exponential decay. For four different ranges of initial energy, we show here the blow-up of solutions and give the lifespan estimates by improving the method of Wu (Electron. J. Diff. Equ. 105, 1 (2009)) and Li et al. (Nonlin. Anal. 74, 1523 (2011)). From the applications point of view, our results may provide some qualitative analysis and intuition for the researchers in other fields such as engineering and mechanics when they study the concrete models of Petrovsky type.

With the help of the symbolic computation system Maple, the mapping approach, and a linear variable separation method, a new exact solution of the (3+1)-dimensional generalized shallow water wave (GSWW) system is derived. Based on the obtained solitary wave solution, some novel soliton excitations are investigated.

An analytical nonlinear buckling model where the rod is assumed to be an inextensible column and prismatic is studied. The dimensionless parameters reduce the constitutive equation to a nonlinear ordinary differential equation which is solved using the Adomian decomposition method (ADM) through Green’s function technique. The nonlinear terms can be easily handled by the use of Adomian polynomials. The ADM technique allows us to obtain an approximate solution in a series form. Results are presented graphically to study the efficiency and accuracy of the method. To the author’s knowledge, the current paper represents a new approach to the solution of the buckling of the rod problem. The fact that ADM solves nonlinear problems without using perturbations and small parameters can be judged as a lucid benefit of this technique over the other methods

Molecular orbital calculations were performed to estimate the 18 O/ 16 O and D/H isotopic reduced partition function ratios (rpfrs) of water molecules around magnesium and calcium ions. As model for water molecules in the ith hydration sphere of the cation in aqueous solutions containing that cation, we considered water molecules in the ith hydration sphere that were surrounded by water molecules in the (i+1)th hydration sphere in clusters, M2+(H 2 O)n (M = Mg or Ca; n up to 100). The calculations indicated that the decreasing order of the 18 O preference over 16 O in the primary hydration sphere is Mg 2+ > Ca 2+ > bulk water. That is, water molecules in the primary hydration spheres of the Mg 2+ and Ca 2+ ions are expected to be enriched in the heavier isotope of oxygen relative to water molecules in bulk, and the degree of the enrichment is larger for the Mg 2+ ion than for the Ca 2+ ion. No such preference was observed for hydrogen isotopes in any hydration sphere or for oxygen isotopes in the secondary and outer hydration spheres.

The the Jiangsu-South Yellow Sea region is one of the key seismic monitoring defence areas in the eastern part of China. Since 1846, M ≥ 6 strong earthquakes have showed an obvious commensurability and orderliness in this region. The main orderly values are 74∼75 a, 57∼58 a, 11∼12 a, and 5∼6 a, wherein 74∼75 a and 57∼58 a with an outstanding predictive role. According to the information prediction theory of Wen-Bo Weng, we conceived the M ≥ 6 strong earthquake ordered network structure in the South Yellow Sea and the whole region. Based on this, we analyzed and discussed the variation of seismicity in detail and also made a trend prediction of M ≥ 6 strong earthquakes in the future. The results showed that since 1998 it has entered into a new quiet episode which may continue until about 2042; and the first M ≥ 6 strong earthquake in the next active episode will probably occur in 2053 pre and post, with the location likely in the sea area of the South Yellow Sea; also, the second and the third ones or strong earthquake swarm in the future will probably occur in 2058 and 2070 pre and post.

A mathematical model is developed to examine the effects of an induced magnetic field on the peristaltic flow in a curved channel. The non-Newtonian pseudoplastic fluid model is used to depict the combined elastic and viscous properties. The analysis has been carried out in the wave frame of reference, long wavelength and low Reynolds scheme are implemented. A series solution is obtained through perturbation analysis. Results for stream function, pressure gradient, magnetic force function, induced magnetic field, and current density are constructed. The effects of significant parameters on the flow quantities are sketched and discussed.

As an extension to the functional variable separation approach, the approximate functional variable separation approach is proposed, and it is applied to study the quasi-linear diffusion equations with weak source. A complete classification of these perturbed equations which admit approximate functional separable solutions is obtained. As a result, the corresponding approximate functional separable solutions to the resulting perturbed equations are derived via examples.

Hybrid nanostructures are interesting materials for numerous applications in chemistry, physics, and biology, due to their novel properties and multiple functionalities. Here, we present a synthesis of metal-semiconductor hybrid nanostructures composed of nontoxic I-III-VI semiconductor nanoparticles and gold. Copper indium sulfide selenide (CuInSSe) nanocrystals with zinc blende structure and trigonal pyramidal shape, capped with dodecanethiol, serve as an original semiconductor part of a new hybrid nanostructure. Metallic gold nanocrystals selectively grow onto vertexes of these CuInSSe pyramids. The hybrid nanostructures were studied by transmission electron microscopy, energy dispersive X-ray analysis, X-ray diffraction, and UV-Vis-absorption spectroscopy, which allowed us conclusions about their growth mechanism. Hybrid nanocrystals are generated by replacement of a sacrificial domain in the CuInSSe part. At the same time, small selenium nanocrystals form that stay attached to the remaining CuInSSe/Au particles. Additionally, we compare the synthesis and properties of CuInSSe-based hybrid nanostructures with those of copper indium disulfide (CuInS 2 ). CuInS 2 /Au nanostructures grow by a different mechanism (surface growth) and do not show any selectivity.