Volume 71, Issue 8

In the current work, the electromagnetic (EM) scattering from infinite perfectly conducting cylinders with arbitrary cross sections in both transverse magnetic (TM) and transverse electric (TE) modes is numerically investigated. The problems of TE and TM EM scattering can be mathematically modelled via the magnetic field integral equation (MFIE) and the electric field integral equation (EFIE), respectively. An efficient technique is performed to approximate the solution of these surface integral equations. In the proposed numerical method, compactly supported radial basis functions (RBFs) are employed as the basis functions. The radial and compactly supported properties of these basis functions substantially reduce the computational cost and improve the efficiency of the method. To show the accuracy of the proposed technique, it has been applied to solve three interesting test problems. Moreover, the method is well used to compute the electric current density and also the radar cross section (RCS) for some practical scatterers with different cross section geometries. The reported numerical results through the tables and figures demonstrate the efficiency and accuracy of the proposed technique.

This article presents a fuzzy dynamic reliable sampled-data control design for nonlinear Markovian jump systems, where the nonlinear plant is represented by a Takagi–Sugeno fuzzy model and the transition probability matrix for Markov process is permitted to be partially known. In addition, a generalised as well as more practical consideration of the real-world actuator fault model which consists of both linear and nonlinear fault terms is proposed to the above-addressed system. Then, based on the construction of an appropriate Lyapunov–Krasovskii functional and the employment of convex combination technique together with free-weighting matrices method, some sufficient conditions that promising the robust stochastic stability of system under consideration and the existence of the proposed controller are derived in terms of linear matrix inequalities, which can be easily solved by any of the available standard numerical softwares. Finally, a numerical example is provided to illustrate the validity of the proposed methodology.

In this article, we applied the method of multiple scales for Korteweg–de Vries (KdV) type equations and we derived nonlinear Schrödinger (NLS) type equations. So we get a relation between KdV type equations and NLS type equations. In addition, exact solutions were found for KdV type equations. The (G′G)$\left( {{{G'} \over G}} \right)$-expansion methods and the (G′G, 1G)$\left( {{{G'} \over G},{\rm{ }}{1 \over G}} \right)$-expansion methods were proposed to establish new exact solutions for KdV type differential equations. We obtained periodic and hyperbolic function solutions for these equations. These methods are very effective for getting travelling wave solutions of nonlinear evolution equations (NEEs).

In this article, the nonlinear dynamic characteristics of oil-in-water emulsions under the addition of surfactant were experimentally investigated. Firstly, based on the vertical upward oil–water two-phase flow experiment in 20 mm inner diameter (ID) testing pipe, dynamic response signals of oil-in-water emulsions were recorded using vertical multiple electrode array (VMEA) sensor. Afterwards, the recurrence plot (RP) algorithm and multi-scale weighted complexity entropy causality plane (MS-WCECP) were employed to analyse the nonlinear characteristics of the signals. The results show that the certainty is decreasing and the randomness is increasing with the increment of surfactant concentration. This article provides a novel method for revealing the nonlinear dynamic characteristics, complexity, and randomness of oil-in-water emulsions with experimental measurement signals.

Oxide solubility in chloride melts depends on temperature and composition of molten solvent. The solubility of barium oxide in the solvents with barium chloride content is essentially higher than that in molten alkali chlorides. Spectral data demonstrate the existence of oxychloride ionic groupings in such melts. This work presents the results of the BaO solubility in two molten BaCl 2 –NaCl systems with different barium chloride content. The received data together with earlier published results revealed the main regularities of BaO solubility in molten BaO–BaCl 2 –MCl systems.

From the known Lax pair of the Korteweg–de Vries (KdV) equation, the Lie symmetry group method is successfully applied to find exact invariant solutions for the KdV equation with nonlocal symmetries by introducing two suitable auxiliary variables. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to the hyperbolic and Jacobi elliptic functions are derived. Figures show the physical interaction between the cnoidal waves and a solitary wave.

The Lie symmetry analysis is applied to study the Ablowitz–Kaup–Newell–Segur (AKNS) system of water wave model. The AKNS system can be obtained from a dispersive-wave system via a variable transformation. Lie point symmetries and corresponding point transformations are determined. The optimal system of one-dimensional subalgebras is presented. On the basis of the optimal system, the similarity reductions and the invariant solutions are obtained. Some conservation laws are derived using the multipliers. In addition, the AKNS system is quasi self-adjoint. The conservation laws associated with the symmetries are also constructed.

In this manuscript, the ultrashort soliton pulse propagation through nonlinear tunneling in cubic quintic media is investigated. The effect of chirping on propagation characteristics of the soliton pulse is analytically investigated using similarity transformation. In particular, we investigate the propagation dynamics of ultrashort soliton pulse through dispersion barrier for both chirp and chirp-free soliton. By investigating the obtained soliton solution, we found that chirping has strong influence on soliton dynamics such as pulse compression with amplification. These two important dynamics of chirped soliton in cubic quintic media open new possibilities to improve the solitonic communication system. Moreover, we surprisingly observe that a dispersion well is formed for the chirped case whereas a barrier is formed for the chirp-free case, which has certain applications in the construction of logic gate devices to achieve ultrafast switching.

Lattice dynamics, structural phase transition, and the thermodynamic properties of barium titanate (BaTiO 3 ) are investigated by using first-principles calculations within the density functional theory (DFT). It is found that the GGA-WC exchange-correlation functional can produce better results. The imaginary frequencies that indicate structural instability are observed for the cubic, tetragonal, and orthorhombic phases of BaTiO 3 and no imaginary frequencies emerge in the rhombohedral phase. By examining the partial phonon density of states (PDOSs), we find that the main contribution to the imaginary frequencies is the distortions of the perovskite cage (Ti-O). On the basis of the site-symmetry consideration and group theory, we give the comparative phonon symmetry analysis in four phases, which is useful to analyze the role of different atomic displacements in the vibrational modes of different symmetry. The calculated optical phonon frequencies at Γ point for the four phases are in good agreement with other theoretical and experimental data. The pressure-induced phase transition of BaTiO 3 among four phases and the thermodynamic properties of BaTiO 3 in rhombohedral phase have been investigated within the quasi-harmonic approximation (QHA). The sequence of the pressure-induced phase transition is rhombohedral→orthorhombic→tetragonal→cubic, and the corresponding transition pressure is 5.17, 5.92, 6.65 GPa, respectively. At zero pressure, the thermal expansion coefficient α V , heat capacity C V , Grüneisen parameter γ , and bulk modulus B of the rhombohedral phase BaTiO 3 are estimated from 0 K to 200 K.

The spin Hamiltonian parameters and local structures are theoretically studied for Cu 2+ -doped alkaline earth lead zinc phosphate (RPPZ, R=Mg, Ca, Sr, and Ba) glasses based on the high-order perturbation calculations for a tetragonally elongated octahedral 3d 9 cluster. The relative elongation ratios are found to be ρ ≈3.2%, 4.4%, 4.6%, and 3.3% for R=Mg, Ca, Sr, and Ba, respectively, because of the Jahn-Teller effect. The whole decreasing crystal-field strength Dq and orbital reduction factor k from Mg to Sr are ascribed to the weakening electrostatic coulombic interactions and the increasing probability of productivity of nonbridge oxygen (and hence increasing Cu 2+ –O 2− electron cloud admixtures) under PbO addition, respectively, with increasing alkali earth ionic radius. The anomalies (the largest Dq and the next highest k among the systems) for R=Ba are attributed to the cross linkage of this large cation in the network. The overall increasing order (Mg≤Ba<Ca<Sr) of ρ is largely due to the decreasing crystal-field strength Dq and hence the decreasing force constant of the Cu 2+ –O 2− bonds. The present studies would be helpful to understand local structures and the influences on the optical properties of RPPZ glasses containing copper dopants.