Volume 67, Issue 5

This investigation reports the boundary layer flow and heat transfer characteristics in a couple stress fluid flow over a continuos moving surface with a parallel free stream. The effects of heat generation in the presence of convective boundary conditions are also investigated. Series solutions for the velocity and temperature distributions are obtained by the homotopy analysis method (HAM). Convergence of obtained series solutions are analyzed. The results are obtained and discussed through graphs for physical parameters of interest.

We study the percolation in the hierarchical lattice of order N where the probability of connection between two nodes separated by a distance k is of the form min{αβ -k ,1},α ≥ 0 and β > 0. We focus on the vertex degrees of the resulting percolation graph and on whether there exists an infinite component. For fixed β, we show that the critical percolation value α c (β) is non-trivial, i.e., α c (β) ∊ (0;∞), if and only if β ∊ (N,N 2 ).

The homotopy analysis method (HAM) is applied to solve a nonlinear ordinary differential equation describing certain phase transition problem in solids. Both bifurcation conditions and analytical solutions are obtained simultaneously for the Euler-Lagrange equation of the martensitic transformation. HAM is capable of providing an analytical expression for the bifurcation condition to judge the occurrence of the phase transition, while other numerical techniques have difficulties in bifurcation analysis. The convergence of the analytical solutions on the one hand can be adjusted by the auxiliary parameter and on the other hand is always obtainable for all relevant physical parameters satisfying the bifurcation condition.

The combined effects of thermal radiation absorption and magnetic field on an unsteady chemically reacting convective flow past an impulsively started vertical plate is studied in the presence of a constant wall heat flux. Boundary layer equations are derived and the resulting approximate nonlinear partial differential equations are solved numerically using a semi-discretization finite difference technique. A parametric study of all parameters involved is conducted, and a representative set of numerical results for the velocity, temperature, and concentration profiles as well as the skin-friction parameter and Sherwood number are illustrated graphically to show typical trends of the solutions. Further validation with previous works is carried out and an excellent agreement is achieved.

In this research, the Laplace-Adomian decomposition method (LADM) is applied for the analytical and numerical treatment of the nonlinear differential equation that describes a magnetohydrodynamic (MHD) flow under slip condition over a permeable stretching surface. The technique is well applied to approximate the similarity solutions of the problem for some typical values of model parameters. The obtained series solutions by the LADM are combined with the Pad´e approximation to improve the accuracy and enlarge the convergence domain of the obtained results. Through tables and figures, the efficiency of the presented method is illustrated.

In the present paper, we have focused our attention to highlight the study of a non-Newtonian nanofluid between coaxial cylinders with variable viscosity. The governing equations of the non- Newtonian fluid with variable viscosity along with energy and nanoparticles are given. The coupled nonlinear differential equations are solved analytically with the help of the homotopy analysis method (HAM). The convergence of the solution is discussed through h -curves. The physical features of pertinent parameters are discussed by plotting graphs.

The main idea of the present article is to introduce a new computational technique, explicitly, the modified Laplace Pad´e decomposition method (MLPDM) which is a recipe of Laplace transformation, decomposition technique, and rational polynomial to offer new solution mechanism of magnetohydrodynamics (MHD) flow of an steady viscous, incompressible nonlinear stretching sheet. A good harmony among the attained solution and the exact solution has been verified.

This paper aims to construct a general formulation for the d -dimensional orthogonal functions and their derivative and product matrices. These matrices together with the Tau method are utilized to reduce the solution of partial differential equations (PDEs) to the solution of a system of algebraic equations. The proposed method is applied to solve homogeneous and inhomogeneous two-dimensional parabolic equations. Also, the mentioned method is employed to find the solution of the coupled Burgers equation. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

The effect of a uniform vertical magnetic field on thermosolutal convection in a layer of an electrically conducting couple-stress fluid heated and soluted from below is considered. For the case of stationary convection, the stable solute gradient, magnetic field, and couple-stress parameter have stabilizing effect on the system. It is also observed that a stable solute gradient and a magnetic field introduce oscillatory modes in the system, but in the absence of a stable solute gradient and a magnetic field, oscillatory modes are not allowed and the principle of exchange of stabilities is valid.

The majority logic criterion is applicable in the evaluation process of substitution boxes used in the advanced encryption standard (AES). The performance of modified or advanced substitution boxes is predicted by processing the results of statistical analysis by the majority logic criteria. In this paper, we use the majority logic criteria to analyze some popular and prevailing substitution boxes used in encryption processes. In particular, the majority logic criterion is applied to AES, affine power affine (APA), Gray, Lui J, residue prime, S 8 AES, Skipjack, and Xyi substitution boxes. The majority logic criterion is further extended into a generalized majority logic criterion which has a broader spectrum of analyzing the effectiveness of substitution boxes in image encryption applications. The integral components of the statistical analyses used for the generalized majority logic criterion are derived from results of entropy analysis, contrast analysis, correlation analysis, homogeneity analysis, energy analysis, and mean of absolute deviation (MAD) analysis.

The geometrical structures, stabilities, and electronic properties of Ga n Li ( n = 1 - 13) clusters were investigated within the density functional theory (DFT). The impurity lithium atom enhances the stability of Ga n Li ( n = 1 - 13) clusters, especially Ga n Li ( n = 9 - 13) compared to Ga n ( n = 9 - 14), that is at either apex position or side position. The dissociation energy, second-order energy differences, and the energy gaps between highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) indicate that the Ga 7 Li, Ga 9 Li, and Ga 11 Li clusters are more stable within the studied cluster range. Moreover, the variation of the average bond length of Ga-Li is due to the surface effect, and the binding strength increases resulting from the increase of charge amount.

A Coulomb dissociation model is presented for molecular nanoparticles, e.g. nanoclusters consisting of identical atoms or small molecules. These nanoparticles graze with velocities less than the Bohr velocity (10 8 cm=s) along an organic surface at atomic distances. The surface molecules contain IR-antennas, which consist of periodically located identical diatomic valence bonds with significant dipole momenta, e.g. hydrocarbon chains like (CH 2 ) n . Here, we analyse the Coulomb interaction of these surface molecules with grazing nanoparticles, which do not contain any IR-antennas, e.g. fullerene molecules. Provided that the grazing velocity is in the range of 10 5 - 10 7 cm=s and the minimum distance of the grazing nanoparticles to the surface is approximately 2 Å , the IR-antennas of the interacting surface molecules will collect vibrational energy quanta, the so-called excimols. The number of excimols accumulated during the interaction time of at least 1 ps increases with the number of dipoles in the IR-antennas. Excimol energy can be transmitted back to the grazing nanoparticle by a ps-photon flux, which is estimated intense enough to induce multi-ionization of nanoparticle constituents. The resulting charges inside the nanoparticles cause high Coulomb repulsion forces, which will be able to promptly dissociate them.

63 Cu nuclear magnetic resonance (NMR) and viscosity studies of 0:064M CuClO 4 solutions have been reported in binary mixtures of acetonitrile (AN) with pyridine (Py) and 2, 3, and 4-picolines (2,3,4-Pic) at 298 K using a Bruker 500 MHz NMR spectrometer and an Ubbelohde viscometer, respectively. Chemical shift d and linewidth D for the 63 Cu signals have been recorded referenced to a 0:064M CuClO 4 solution in anhydrous AN. The copper quadrupole coupling constants ( e 2 Qq = h ) have been calculated in all cases. The variation of the d and e 2 Qq = h values as a function of mol fraction of the co-solvent show that all these bases interact with Cu + more strongly than AN. They replace AN from the Cu + complexed with AN in the form [Cu(AN) 4 ] + and form a mixed complex of the type [Cu(AN) 4 -x(S)x] + ( x =1 - 4) where S stands for the base. At relatively high mole fraction of the co-solvents, the mixed solvated complex gradually changes to a more symmetrical complex of the type [Cu(S) 4 ] + which remains stable in the solution. The solvating effect of 2-Pic and 4-Pic is observed to be stronger than that of Py and 3-Pic.

China is one of the countries which have the most earthquake disasters in the world. A total of 23 M ≥ 8 earthquakes occurred in Mainland China from 1303 to 2010. The seismic activity of M ≥ 8 earthquakes has had an obvious self-organized orderliness. The main ordered values are 252~258 a, 108~112 a, 94~98 a, 44~47 a, 24~25 a, 16~19 a, and 11~14 a. According to the information forecasting theory of Wen-Bo Weng and combining ordered analysis with complex network technology, we build an informational ordered network structure of M ≥ 8 great earthquakes in Mainland China and try to explore the practical method for M ≥ 8 great earthquake prediction with Chinese characteristics. In this paper, we have summarized the prediction research on two great earthquakes (the 2001 Kunlunshan M 8.1 and the 2008 Wenchuan M 8.0 earthquake) during the beginning of the 21st century in western Mainland China. At last, with the method of ordered network structure, we present a new prediction opinion: the future M ≥ 8 great earthquakes will happen in 2026 and 2065 pre and post in Mainland China. The results show that a M ≥ 8 great earthquake could be predicted and the network feature is the formation mechanism of great earthquakes. The ordered network method has a unique effect on moderate term and long term prediction for M ≥ 8 great earthquakes.