Volume 67, Issue 10-11

Under investigation in this paper is a variable-coefficient coupled Gross-Pitaevskii (GP) system, which is associated with the studies on atomic matter waves. Through the Painlev´e analysis, we obtain the constraint on the variable coefficients, under which the system is integrable. The bilinear form and multi-soliton solutions are derived with the Hirota bilinear method and symbolic computation. We found that: (i) in the elastic collisions, an external potential can change the propagation of the soliton, and thus the density of the matter wave in the two-species Bose-Einstein condensate (BEC); (ii) in the shape-changing collision, the solitons can exchange energy among different species, leading to the change of soliton amplitudes.We also present the collisions among three solitons of atomic matter waves.

Earthquake disasters occurred very frequently in China. As a result, to evaluate the losses has important social value and economic effect. This paper focuses on the assessment of economic losses of earthquake disasters which is divided into two parts: direct economic loss and indirect economic loss. First, the Kolmogorov-Smirnov (KS) test is used to determine the distribution of the earthquake losses per year in China, fitting the frequency of earthquake that happened per month in China. Second, the grey clustering method and principal component analysis (PCA) are applied, respectively, for direct economic loss rating and indirect economic loss rating. Finally, the economic loss generated by the earthquakes which happened from 2006 to 2009 in China is evaluated, and eight earthquakes are rated based on the comprehensive economic loss.

In this work, the coupled Higgs field equation is studied. The extended Jacobi elliptic function expansion methods are efficiently employed to construct the exact periodic solutions of this model. As a result, many exact travelling wave solutions are obtained which include new shock wave solutions or kink-shaped soliton solutions, solitary wave solutions or bell-shaped soliton solutions, and combined solitary wave solutions are formally obtained.

In this paper, we discuss the quasi-ordering of hexagonal systems with respective to the coefficients of their Clar covering polynomials (also known as Zhang-Zhang polynomials). The last six minimal catacondensed hexagonal systems and the hexagonal chains with the maximum Clar covering polynomial are determined. Furthermore, the smallest pair of incomparable catacondensed hexagonal systems is given.

Based on the quantum master equation which describes the dynamical evolution of a two-level atom interacting with one mode of the quantized photon field in a cavity, we have investigated the systemic dissipative and decoherence properties by use of the development algebraic dynamic method for the automatic and non-automatic condition. Furthermore, using the exact solution of the quantum master equation, we have investigated the asymptotic behaviours of the system.

The Killingbeck potential consisting of the harmonic oscillator plus Cornell potential, ar 2 +br −c/r, is of great interest in particle physics. The solution of the Dirac equation with the Killingbeck potential is studied in the presence of the pseudospin (p-spin) symmetry within the context of quasiexact solutions. Two special cases of the harmonic oscillator and Coulomb potential are also discussed.

Magnetohydrodynamic free convection flow of an incompressible viscous fluid past an infinite vertical oscillating plate with uniform heat flux in a porous medium is studied. Exact dimensionless solutions of momentum and energy equations, under Boussinesq approximation, are obtained using Laplace transforms. They satisfy all imposed initial and boundary conditions and reduce to known solutions from the literature as special cases. Finally, the influence of different parameters like thermal radiation parameter, Grashof number, Prandtl number, and time on velocity, temperature, and skin friction is shown by graphs.

Two-dimensional self-similar azimuthons are introduced and investigated analytically and numerically in nonlocal nonlinear media with space-dependent diffractive, gain (attenuation) coefficient based on the similarity transformation and variational approach.We demonstrate that the azimuthons of critical power in the strongly nonlocal limit are more stable than the ones with lower nonlocality. Remarkably, these self-similar azimuthons have the azimuthal angle modulated by the distributed diffractive coefficient, apart from the beam width and intensity changing self-similarly.

Transport properties of poly(3-hexylthiophene) (P3HT), and of its blend with [6,6]-phenyl C61- butyric acid methylester (PCBM), were studied by analysing temperature dependent current-voltage characteristics of spin cast thin films sandwiched between aluminium electrodes in a metal-insulator- metal (MIM) configuration. It was found that in Al/P3HT/Al devices, the current is limited by space charge that accumulates near the hole injecting electrode due to the poor bulk transport properties of P3HT. At low temperatures and high applied electric fields the current density obeys a power law of the form J _ Vm, characteristic of space charge limited current (SCLC) in the presence of exponentially distributed traps within the band gap. These traps are filled by charge that is injected by quantum mechanical tunnelling, which is adequately described by the Fowler-Nordheim (FN) theory. By calculating the majority charge carrier mobility in Al/P3HT/Al and Al/P3HT:PCBM/Al devices from the Ohmic, SCLC, and FN tunnelling fits at different temperatures, we have obtained that the charge carrier mobility in P3HT is two orders smaller than the electron mobility in the P3HT:PCBM blend at room temperature, but comparable at low temperatures. This information is important in determining the origin of open circuit voltage and short circuit current limit in solar cells that employ this blend as the active layer.

Under investigation in this paper is the dissipative Zabolotskaya-Khokhlov equation from nonlinear acoustics. Through extending a symbolic computation algorithm, namely, the (G'/G)-expansion method, a new type of exact solution with variable separation is constructed for the equation. The solution is more general because two arbitrary functions are involved with regard to the time variable. Some novel time solitons are observed by appropriately choosing the arbitrary functions at special cases.

We study finite-dimensional product Hilbert spaces, coupled spin systems, entanglement, and energy level crossing. The Hamilton operators are based on the Pauli group.We show that swapping the interacting term can lead from unentangled eigenstates to entangled eigenstates and from an energy spectrum with energy level crossing to avoided energy level crossing.

In this paper, the soliton solutions and the corresponding conservation laws of a few nonlinear wave equations will be obtained. The Hunter-Saxton equation, the improved Korteweg-de Vries equation, and other such equations will be considered. The Lie symmetry approach will be utilized to extract the conserved densities of these equations. The soliton solutions will be used to obtain the conserved quantities of these equations.

In this paper, based on the homotopy analysis method (HAM), a new powerful algorithm is used for the solution of the nonlinear reaction-diffusion equation. The algorithm presents the procedure of constructing a set of base functions and gives the high-order deformation equation in a simple form. Different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of the solution series by introducing an auxiliary parameter h. The solutions of the problem of presence and absence of absorbent term and external force for different particular cases are presented graphically.

In this paper, a three-dimensional, unsteady state non-Newtonian fluid flow in a pipe-shaped artery of viscoelastic blood is considered in the presence of emotion-induced pressure gradient. The results have been expressed in terms of radial profiles of both axial velocity and viscosity and were presented numerically by using the shooting technique coupled with the Newtonian method and the Boubaker polynomials expansion scheme. The effects of some parameters on the dynamics are analyzed.

Time-differential perturbed angular correlation (TDPAC) studies in hafnium metal (~5%Zr) have been carried out at different temperatures. It is found that hafnium metal on heating at 873 K continuously for two days in air, transforms partially and abruptly to HfO 2 while no component of oxide has been observed for heating up to 773 K and during initial heating at 873 K for 1 day. This result is strikingly different to that expected from the Arrhenius theory. Also, a strong nuclear relaxation effect has been observed at 873 K due to rapid fluctuation of hafnium atoms in hexagonal closepacked (hcp) hafnium. At this temperature, ~ 5% probe nuclei experience static perturbation due to monoclinic HfO 2 , ~ 50% experience fluctuating interaction, and ~ 5% produce static defect configuration of hcp hafnium. With lowering of temperature, defect configurations of hafnium increase at the cost of fluctuating interaction. An almost total fluctuating interaction observed in hcp hafnium at a temperature much lower than its melting point is another interesting phenomenon.

Unsteady two-dimensional flow of a Maxwell fluid over a stretching surface in a porous medium subjected to suction/blowing is investigated. The upper-convected Maxwell fluid model is used to characterize the non-Newtonian fluid behaviour. With the help of similarity transformations, the boundary layer equation corresponding to the momentum equation is transformed to an ordinary one and then solved numerically by the shooting method. The flow characteristics for different values of the governing parameters are analyzed and discussed in detail. The fluid velocity initially decreases with increasing unsteadiness parameter. Also, it is found that the fluid velocity decreases with increasing permeability parameter. The effect of increasing values of the Maxwell parameter is to suppress the velocity field. Due to suction, the fluid velocity is found to decrease in the boundary layer region.

This paper investigates the effect of radiative heat transfer to oscillatory hydromagnetic non- Newtonian couple stress fluid flow through a porous channel with non-uniform wall temperature due to periodic heat input at the heated wall. Based on some simplifying assumptions, the dimensionless partial differential equations are transformed into a set of ordinary differential equations and then solved using the Adomian decomposition method. The effects of the flow parameters on temperature and velocity profiles are shown graphically and discussed.