Volume 74, Issue 6

In this paper, the homotopy perturbation method (HPM) is applied to the coupled set of Schrödinger–Poisson (SP) equations in inversion layer problem for obtaining the approximate analytical solution. Inversion layer of n-type is considered, and the electric quantum limit is assumed. By introducing some dimensionless quantities, the SP system has been turned into one which can be solved along the infinite interval. After some appropriate transformations, the infinite interval has been reduced to finite one (0,1)$(0,1)$, and recurrence series of the HPM approximate solutions of the coupled SP system have been obtained. The existence and convergence of obtained HPM approximate solutions have been formally proved. Moreover, these solutions show relative simple mathematical form, as well as high degree of accuracy what is desirable for semiconductor device modelling.

Hückel molecular orbital (HMO) quantities, viz., electron densities, charge densities, bond orders, free valences, total π-electron energies and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO–LUMO) or band gaps of {X,Y}-cyclacene graphs under next-nearest-neighbour ( nnn ) approximations are expressed in analytical forms within a certain range of nnn approximation parameter ( m ). The critical values of m for {X,Y}-cyclacenes with varying X (=C, N, B) and Y (=C, N, B) are calculated. For {X,X}-cyclacenes with a π-electron on each atom, all HMO quantities except total π-electron energies for a given value of m are found to be independent of X. The cyclic dimer (CD) is constructed in obtaining the eigenvalues corresponding to the singular points of the density of states (DOS) of such {X,Y}-cyclacene. Although the HOMO–LUMO gap of the CD differs from that of the cyclacene with a large number of repeating units (i.e. n ⟶ ∞) but becomes the same for m = 0. The analytical expressions can be used for facile computer programming in obtaining the HMO quantities. Such nnn interaction approximations actually release, to some extent, the strain that results in due to the geometrical structures of such cyclacenes, which is evident from the plots of strain energy per segment vs. contribution of such interactions on the total π-electron energy, where the slopes decrease with an increase in m. The vertical absorption energy difference for singlet-triplet states bears excellent linear correlation with the HOMO–LUMO gaps for a certain m value ( m = 0.3) in the case of an even n, but for an odd n, such energy difference remains invariant.

The collision of dressed dust acoustic solitons (DDASs) and the analytical higher-order phase shift are studied in a dusty plasma system that contains cold negative and positive dusty fluids and Maxwellian distributed for ions as well as electrons. The extended Poincaré–Lighthill–Kuo method is applied in order to obtain the nonlinear Korteweg–de Vries and phase shift equations, which admit the variation in soliton profiles and trajectories, respectively. Influences of the higher-order correction and the plasma fluid parameters such as charged dust grains concentration, negative-to-positive dust grain mass ratio, ion-to-negative dust grain number density ratio, and ion-to-electron temperature ratio on the characteristics of DDASs and their phase shifts are discussed. The comparisons between first- and higher-order contributions in rarefactive and compressive profiles are also taken into account. Furthermore, the present consideration may be utilised to mesosphere and magnetosphere.

Propagation of nonlinear and supernonlinear positron-acoustic periodic waves is examined in an electron-positron-ion plasma composed of static positive ions, mobile cold positrons, and q -nonextensive electrons and hot positrons. Employing the phase plane theory of planar dynamical systems, all qualitatively different phase portraits that include nonlinear positron-acoustic homoclinic orbit, nonlinear positron-acoustic periodic orbit, supernonlinear positron-acoustic homoclinic orbit, and supernonlinear positron-acoustic periodic orbit are demonstrated subjected to the parameters q,μ1,μ2,σ1,σ2$q,{\mu_{1}},{\mu_{2}},{\sigma_{1}},{\sigma_{2}}$, and V . The nonlinear and supernonlinear positron-acoustic periodic wave solutions are reported for different situations through numerical computations. It is observed that the nonextensive parameter ( q ) acts as a controlling parameter in the dynamic motion of nonlinear and supernonlinear positron-acoustic periodic waves. The dynamic motions for the positron-acoustic traveling waves with the influence of an extrinsic periodic force are investigated through distinct qualitative approaches, such as phase portrait analysis, sensitivity analysis, time series analysis, and Poincaré section. The results of this paper may be applicable in understanding nonlinear, supernonlinear positron-acoustic periodic waves, and their chaotic motion in space plasma environments.

Consideration is given to steady, fully developed mixed electro-osmotic/pressure-driven flow of Newtonian fluid in an eccentric microannulus. The governing Poisson–Boltzmann and momentum equations are solved numerically in bipolar coordinates. It is shown that for a fixed aspect ratio, fully eccentric channels sustain the maximum average viscosity (i.e. flow rate) under the same dimensionless pressure gradient and electro kinetic radius. For the Debye–Hückel approximation (linearised Poisson–Boltzmann equation), we show that closed-form analytical solution can be derived for velocity field. Finally, the effect of the electrokinetic radius, pressure gradient, and eccentricity on the flow field was investigated in detail.

In this article, we revisit the question of analysing the efficiencies of partially entangled states in three-qubit classes under real conditions. Our results show some interesting observations regarding the efficiencies and correlations of partially entangled states. Surprisingly, we find that the efficiencies of many three-qubit partially entangled states exceed that of maximally entangled three-qubit states under real noisy conditions and applications of weak measurements. Our analysis, therefore, suggests that the efficiencies of partially entangled states are much more robust to noise than those of maximally entangled states at least for the GHZ (Greenberger–Horne–Zeilinger) class states, for certain protocols; i.e. less correlations in the initially prepared state may also lead to better efficiency and hence one need not always consider starting with a maximally entangled state with maximum correlations between the qubits. For a set of partially entangled states, we find that the efficiency is optimal, independent of the decoherence and state parameters, if the value of weak measurement parameter is very large. For other values of the weak measurement parameter, the robustness of the states depends on the decoherence and state parameters. Moreover, we further show that one can achieve higher efficiencies in a protocol by using non-optimal weak measurement strengths instead of optimal weak measurement strengths.

The non-reciprocal transmission properties of transverse electric (TE) mode waves are investigated for two asymmetric, complex photonic crystals composed of magnetic gyrotropic and normal media. Three pairs of non-reciprocal transmission peaks in three different bandgaps for forward and backward waves occur because of optical Tamm states (OTSs) at the interface between the photonic crystals. Numerical results indicate that the non-reciprocal transmission properties are influenced by the incident angles, gyrotropic permeability, and number of layers of the photonic crystals. The asymmetric structure with multiple non-reciprocal transmission peaks at a certain incident angle can provide promising opportunities for the design of multichannel isolators.

The structural, mechanical and vibrational properties of Ru 2 TiZ (Z = Si, Ge, Sn) Full Heusler Alloys (FHAs) are computed using PBE-GGA as an exchange-correlation functional in Kohn–Sham equations. The calculated lattice constants of these alloys in L 2 1 phase deviate from experimental values upto 0.85 % which shows a good agreement between the model and the experiments. These lattice constants are then used to compute the second order elastic constants C 11 , C 12 and C 44 with Wien2k-code. Elastic moduli and mechanical parameters are also calculated by these three independent elastic constants. Mechanical parameters Pugh’s and Poisson’s ratio indicate non-brittle nature of these alloys. Furthermore, the Debye temperature where the collective vibrations shift to an independent thermal vibration, longitudinal and transverse sound velocities, melting temperatures, and thermal conductivities are also obtained to investigate the phonon modes of oscillation. These phonon modes confirm the stability of these alloys as there exists no imaginary phonon frequency in the phonon-dispersion curves.