Volume 67, Issue 1-2

The present paper deals with a thermal instability problem in a viscoelastic fluid saturating an anisotropic porous medium under gravity modulation. To find the gravity modulation effect, the gravity field is considered in two parts: a constant part and an externally imposed time-dependent periodic part. The time-dependent part of the gravity field, which can be realized by shaking the fluid, has been represented by a sinusoidal function. Using Hill’s equation and the Floquet theory, the convective threshold has been obtained. It is found that gravity modulation can significantly affect the stability limits of the system. Further, we find that there is a competition between the synchronous and subharmonic modes of convection at the onset of instability. Effects of various parameters on the onset of instability have also been discussed.

This paper presents the cross focusing of two high power lasers by taking off-axial contributions of the laser beams in a collisionless plasma. Due to relativistic and ponderomotive nonlinearities the two laser beams affect the dynamics of each other and cross focusing takes place. The expressions for the laser beam intensities by using the eikonal method are derived. The contributions of the r 2 and r 4 terms are incorporated. By expanding the eikonal and the other relevant quantities up to the fourth power of r, the solution of the pump laser beam is obtained within the extended paraxial ray approximation. Filamentary structures of the laser beams are observed due to the relativistic and the ponderomotive nonlinearity. The focusing of the laser beams is shown to become fast in the extended paraxial region. Using the laser beam and the plasma parameters, appropriate for beat wave processes, the filaments of the laser beams are studied and the relevance of these results to beat wave processes is pointed out.

The travelling-wave solution of the Volterra lattice has been constructed by the optimal homotopy analysis method. The optimal method used here contains three auxiliary convergence-control parameters to adjust and control the convergence region of the solution. By minimizing the averaged residual error, the optimal convergence-control parameters can be obtained, which give much better approximations than those given by the usual homotopy analysis method. The obtained results show that the optimal homotopy analysis method is also very efficient for differential-difference equations.

Based on the use of the Hirota bilinear method and the Riemann theta function, we develop in this paper a constructive method for obtaining explicit quasi-periodic wave solutions of a new integrable generalized differential-difference equation. Analysis on the asymptotic property of the quasiperiodic wave solutions is given, and it is shown that the quasi-periodic wave solutions converge to the soliton solutions under certain conditions.

Chemical preparation techniques have proved in the past unsuitable for the synthesis of linear chain conductors which are said to exhibit anomalously large electrical conductivities via moving charge density waves (CDWs) which are depinned from the underlying linear ionic lattice and move in a direct current (DC) electric field nearly unattenuated. We present a novel technique which uses only purely physical processes to fabricate linear chain conductors which seem to meet all claims laid by the CDW mechanism of conductivity in its ideal form. A spark engraves in an originally low-conducting nonlinear silver-based material, driven far from equilibrium beyond some critical power input, a discharge pattern, inside the branches of which chains of Ag+-ions run which form a high-conducting current path, along which CDWs may propagate nearly unattenuated. The material obtained exhibits an electrical conductivity which is by four orders of magnitude higher than the conductivity of metallic silver. A simple model is presented to explain this high conductivity and some related phenomena associated with electrical conduction via a moving CDW

Under investigation in this paper is the vector Hirota (VH) equation which governs the simultaneous propagation of multiple interacting femtosecond pulses in a certain type of coupled optical waveguides. By the Nth iterated Darboux transformation starting from the zero potential, the VH equation is found to admit the bright N-soliton solutions in terms of the multi-component Wronskian. Asymptotic formulae of the bright N-soliton solutions are derived for any given set of spectral parameters, which allows us to directly analyze the collision dynamics of VH solitons. Via symbolic computation, some collision properties possessed by the two- and three-soliton solutions are revealed from four aspects: the asymptotic patterns of the colliding solitons, parametric conditions for the amplitude-preserving collisions, phase shifts induced by the vector-soliton collisions, and soliton state changes described by the generalized linear fractional transformations.

The change of magnetoresistance in dependence on the strength of the magnetic induction is examined theoretically for several heterostructures taken as examples. Different temperatures of the examined samples, concentrations of the electron or hole carriers, and band structure properties are then involved. A general result is that a linear increase of magnetoresistance as a function of the magnetic induction should be obtained for all samples. This finds its counterpart in the behaviour of the experimental data. The ratios of the theoretical slopes of increase to the experimental ones range between 0.1 and 11, but the average ratio amounts to less than 1.8.

In this work, we study the dynamic properties (equilibrium points, local and global stability, chaos and bifurcation) of the predator-prey discontinuous dynamical system. The existence and uniqueness of uniformly Lyapunov stable solution will be proved

A common property of many, though not all, massive real-world networks, including the World- Wide Web, the Internet, and social networks, is that the connectivity of the various nodes follows a scale-free distribution, P(k) ∞ k -α , with typical scaling exponent 2≤α≤3. In this letter, we prove that the Erdős-Ŕenyi random graph with unbounded expected degrees has a scale-free behaviour with scaling exponent 1=2 in a neighbourhood of expected degree hki. This interesting phenomenon shows a discrepancy from the Erdős-Ŕenyi random graph with bounded expected degree, which has a bell shaped connectivity distribution, peaking at 〈k〉, and decaying exponentially for large k.

The unsteady two-dimensional boundary layer flow past a shrinking sheet in a non-Newtonian power-law fluid is investigated. The governing partial differential equations are transformed into a nonlinear ordinary differential equation using a similarity transformation before being solved numerically by the Runge-Kutta-Fehlberg method and the NAG Fortran library subroutine DO2HAF with shooting technique. The results obtained by both methods are in good agreement. It is found that dual solutions exist for a certain range of the unsteadiness parameter and the suction parameter. Moreover, by increasing the power-law index n, the skin friction coefficient is enhanced.

This article reports the flow of a Casson fluid in the region of stagnation-point towards a stretching sheet. The characteristics of heat transfer with viscous dissipation are also analyzed. The partial differential equations representing the flow and heat transfer of the Casson fluid are reduced to ordinary differential equations through suitable transformations. The flow is therefore governed by the Casson fluid parameter β, the ratio of the free stream velocity to the velocity of the stretching sheet a=c, the Prandtl number Pr, and the Eckert number Ec. The analytic solutions in the whole spatial domain have been computed by the homotopy analysis method (HAM). The dimensionless expressions for the skin friction coefficient and the local Nusselt number have been calculated and discussed.

In this paper, we consider the dynamics of Klein-Gordon and Dirac oscillators in (2+1) dimensions with noncommutativity of the spatial coordinates using the supersymmetric path integral formalism. The propagator is calculated and the energy eigenvalues with their corresponding eigenfunctions are deduced.

We have reported a relativistic multiconfiguration Dirac-Fock (MCDF) study on low-lying level structures of protactinium IV (Z =91) and uranium V (Z =92) ions. Excitation energies and electric dipole (E1) transition parameters (wavelengths, oscillator strengths, and transition rates) for these low-lying levels have been given. We have also investigated the influence of the transverse Breit and quantum electrodynamic (QED) contributions besides correlation effects on the level structure. A comparison has been made with a few available data for these ions in the literature.

The local meta-GGA (generalized gradient approximation) exchange correlation density functional (TPSS) with relativistic effective core potential was employed to systematically investigate the geometric structures, stabilities, and electronic properties of bimetallic Au 2 Si n (n = 1 - 8) clusters. The optimized geometries show that the most stable isomers have a three-dimensional structure except for Au 2 Si 1,3 clusters. The doped gold atoms prefer to occupy the surface site in the Au 2 Si n clusters. Here, the averaged atomic binding energies and fragmentation energies show that the Au 2 Si 5 isomer is the most stable among the Au 2 Si n (n = 1 - 8) clusters. A pronounced even-odd alternation is found in the energy difference between the highest occupied and the lowest unoccupied molecular orbital (HOMO-LUMO gaps), especially, the Au 2 Si 5 cluster has the largest HOMO-LUMO gap of 2.06 eV. Moreover, the reverse even-odd alternation rule to the average polarizability per atom versus the charges transfer was found. A transition point appears at n = 5.