Band 66, Heft 5

In this research work a time-dependent partial differential equation which has several important applications in science and engineering is investigated and a method is proposed to find its solution. In the current paper, the homotopy analysis method (HAM) is developed to solve the eikonal equation. The homotopy analysis method is one of the most effective methods to obtain series solution. HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of a series solution. Furthermore, this method does not require any discretization, linearization or small perturbation and therefore reduces the numerical computation a lot. Some test problems are given to demonstrate the validity and applicability of the presented technique.

When a circular jet of liquid strikes a sphere normal to the tangent plane at a point, a liquid film is formed on the surface of the sphere. This is a new problem. The flow in the liquid film is studied by means of boundary layer theory for laminar flow. The governing equations are Prandtl’s momentum boundary layer equation and the continuity equation. To solve the problem completely a conserved quantity is required as well as boundary conditions. The conserved quantity for the film of liquid on the sphere is derived with the help of a conserved vector. Two conservation laws for the system have been obtained by Naeem and Naz (Int. J. Nonlin. Sci. 7, 149 (2009)), and one of these is used to derive the conserved quantity for the liquid film. A stream function is introduced which reduces the system to a single third-order partial differential equation. The group invariant solution for this partial differential equation is constructed by considering a linear combination of its Lie point symmetries. The velocity profile of the liquid film on the sphere is investigated.

August 12, 2010 The homotopy perturbation method is used to find an approximate analytic solution of the problem involving a space-time fractional diffusion equation with a moving boundary. This mathematical technique is used to solve the problem which performs extremely well in terms of efficiency and simplicity. Numerical solutions of the problem reveal that only a few iterations are needed to obtain accurate approximate analytical solutions. The results obtained are presented graphically.

In this paper two different methods are presented to approximate the solution of the Black-Scholes equation for valuation of barrier option. These techniques can be applied directly for all types of differential equations, homogeneous or inhomogeneous. The use of these methods provides the solution of the problem in a closed form while the mesh point techniques provide the approximation at mesh points only. Also, the two schemes need less computational work in comparison with the traditional methods. These techniques can be employed for problems with initial condition. In this paper we use the variational iteration and homotopy perturbation methods for solving the Black-Scholes equation with terminal condition. Numerical results are compared with theoretical solutions in order to confirm the validity of the presented procedures.

We derive the symmetry group by the standard Lie symmetry method and prove it constitutes to the Kac-Moody-Virasoro algebra. Then we construct the conservation laws corresponding to the Kac- Moody-Virasoro symmetry algebra up to second-order group invariants

The double-diffusive convection in a compressible couple-stress fluid layer heated and soluted from below through porous medium is considered in the presence of a uniform vertical magnetic field. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the compressibility, stable solute gradient, magnetic field, and couple-stress postpone the onset of convection whereas medium permeability hastens the onset of convection. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient and magnetic field introduce oscillatory modes in the system, which were non-existent in their absence. A condition for the system to be stable is obtained by using the Rayleigh-Ritz inequality. The sufficient conditions for the non-existence of overstability are also obtained.

Transversal magnetoresistance is calculated for numerous metal cases on the basis of simple electron theory. Any metal can be represented by a single band of states having a closed Fermi surface which is assumed to be similar in shape to a sphere. In an external electromagnetic field the electron transport seems to be regulated by two kinds of relaxation times. The first one is due to the electric field, and its size is not appreciably influenced by that field. On the other hand, electron motion in the magnetic field is associated with a relaxation time that is strongly dependent on the strength of that field. Both time parameters combine to an effective relaxation time according to Matthiessen’s rule. A good agreement between experiment and theory is obtained for Li, Cu, Ag, Au and Pd, Pt metals.

Steady state boundary layer equations of an upper convected Maxwell fluid with magnetohydrodynamic (MHD) flow are considered. The strength of the magnetic field is assumed to be variable with respect to the location. Using Lie group theory, group classification of the equations with respect to the variable magnetic field is performed. General boundary conditions including stretching sheet and injection are taken. Restrictions imposed by the boundary conditions on the symmetries are discussed. Special functional forms of boundary conditions for which similarity solutions may exist are derived. Using the symmetries, similarity solutions are presented for the case of constant strength magnetic field. Stretching sheet solutions with or without injection are presented. Effects of physical parameters on the solutions are depicted.

By Lochak (theory) and Urutskoev (experiment) the hypothesis has been suggested that during electric discharges in water (fluids) light magnetic monopoles can be created which according to Lochak should be considered as a kind of excited neutrinos. Based on a quantum field theoretic development of de Broglie’s and Heisenberg’s fusion ideas and the results of preceding papers a transparent proof is given that such magnetic monopoles can occur during discharges. In the theoretical description these circumstances are formulated within the scope of an extended (effective) Standard Model and the monopoles with vanishing electric charge arise from neutrinos whose states are modified by the symmetry breaking caused by the discharge. In the introduction some technical implications are referred to. The article is divided into two parts.

The energy band structure and its characteristics of a two-dimensional metallic photonic crystal with square lattice structure have been studied by using the finite-difference time-domain (FDTD) algorithm. In order to determine the band structure accurately, the spatial distribution of the eigenfunction has been analyzed. By comparing the distribution of different wave vectors and of different energy band eigenmodes, an effective method to determine the band structure was found, which has been verified by the simulation results.

The density ρ, and viscosity η of 0.00, 0.05, 0.10, 0.15, and 0.20 mol kg −1 glycine (Gly), dlalanine (Ala), dl-serine (Ser), and dl-valine (Val) have been measured in 0.002 mol kg−1 aqueous sodium dodecyl sulphate (SDS) at 298.15, 303.15, 308.15, and 313.15 K. These data have been used to calculate the apparent molar volume φ v , infinite dilution apparent molar volume φ v °, and the standard partial molar volumes of transfer φ v ° (tr), of the amino acids from water to the aqueous SDS solutions. Falkenhagen coefficient A, Jones-Dole coefficient B, free energies of activation per mole of solvent (aqueous SDS) Δμ1°*, and per mole solute (amino acids) Δμ 2 °*, also enthalpy ΔH* and entropy ΔS* of activation of viscous flow were evaluated using viscosity data. The molar refraction R D was calculated by using experimental values of the refractive index n D of the systems. The results have been interpreted in terms of ion-ion, ion-polar and hydrophobic-hydrophobic group interactions. The volume of the transfer data suggest that ion-ion intertactions are predominant.

An ab initio method based on the density functional theory has been employed to investigate the behaviours of the bimetallic Ag 2 -doped silicon clusters at a size of n = 1 - 11. The possible geometrical configurations, growth-pattern behaviours, stabilities, energy gaps, and electronic properties are presented and discussed. The optimized geometries reveal that the silicon atom surface-capped and silver atom substituted 3D structures are dominant growth patterns. The calculated averaged binding energy, fragmentation energy, and the second-order difference of energy manifest that the most stable structures of Ag 2 Si n (n = 1 - 11) clusters are Ag 2 Si 2 and Ag 2 Si 5 isomers, which is in qualitative agreement with the AgSin clusters. In addition, the gap between highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) exhibits that the Ag 2 Si 3 and Ag 2 Si 5 isomers have dramatically enhanced chemical stability. Natural population analysis shows that the charge-transfer phenomena are coincidence with the AgSi n clusters but different from Mo 2 Si n systems. Furthermore, the dipole moments of stable Ag 2 Si n (n = 1 - 11) display a pronounced odd-even oscillation with the number of silicon atoms.

M ≥ 7 strong earthquakes have had an obvious commensurability and orderliness in Xinjiang, China, and its neighbourhood region since 1800. The main orderly values are 30a×k (k = 1,2, 3), 11 ~ 12a, 41 ~ 43a, and 18 ~ 19a. According to the informative forecasting theory of Wen-BoWeng and complex networks technology, we try to explore the practical methods for strong earthquake prediction with Chinese characteristics, and conceive the informational orderly network structure of M ≥ 7 strong earthquakes. Based on this, Yutian M7.3 strong earthquake was successful predicted in 2008. Meanwhile, the next strong earthquake with magnitude 7 or so will happen around 2014 - 2015 in this region. The results shows that strong earthquakes could be predicted. This method has an unique effect for mid-and-long term prediction of strong earthquakes.

The equilibrium geometries, relative stabilities, and electronic properties of Li n Cl (n = 1 - 7) clusters were investigated within the density functional theory (DFT). The lowest energy structures reveal that the impurity chlorine atom prefers the apex position with the coordination number two except the Li 6 Cl. From dissociation energy, second-order energy differences, and the energy gaps between highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO), Li n Cl (n=1;3; 5) clusters are more stable within the studied cluster range. The binding energy per atom decreases as the cluster size increases, hence the clusters become more reactive when doped with the chlorine atom.