International Journal of Modern Physics B

In this paper, the auxiliary expansion equation method is applied to compute the analytical wave solutions for (3+1)-dimensional Boussinesq and Kadomtsev–Petviashvili (KP) equations. A simple transformation is carried out to reduce the set of nonlinear partial differential equations (NPDEs) into ODEs. These obtained results hold numerous traveling wave solutions that are of key importance in elucidating some physical circumstance.

Coherence arises from the superposition principle, where it plays a central role in quantum mechanics. In Phys. Rev. Lett. 114, 210401 (2015), it has been shown that the freezing phenomenon of quantum correlations beyond entanglement is intimately related to the freezing of quantum coherence (QC). In this paper, we compare the behavior of entanglement and quantum discord with quantum coherence in two different subsystems (optical and mechanical). We use respectively the entanglement of formation (EoF) and the Gaussian quantum discord (GQD) to quantify entanglement and quantum discord. Under thermal noise and optomechanical coupling effects, we show that EoF, GQD and QC behave in the same way. Remarkably, when entanglement vanishes, GQD and QC remain almost unaffected by thermal noise, keeping nonzero values even for high-temperature, which is in concordance with Phys. Rev. Lett. 114, 210401 (2015). Also, we find that the coherence associated with the optical subsystem is more robust — against thermal noise — than those of the mechanical subsystem. Our results confirm that optomechanical cavities constitute a powerful resource of QC.

Curie temperature (T_C) of the ferromagnetic compound Sr₂FeMoO₆ can be modified by increasing the itinerant electrons at the Fermi level. Nd doping increases the electron density but the charge neutrality should be taken into account. In this work, a series of double perovskites Sr${}_{2-y}$Nd${}_y$Fe${}_{1+x}$Mo${}_{1-x}$O₆ (y=0.0, 0.25, 0.5, 0.75 and 1.0) for both cases, the off-stoichiometric (x=0) and the stoichiometric (x$>$0 with x=y/2) one, were synthesized via solid state route and discussed in detail. A crystalline structure transition was confirmed by X-ray diffraction analysis, showing a change of the lattice parameters and the unit cell volume as a function of Nd doping. It was also found that the nominal valence in Fe is mainly Fe${}^{3+}$ and in Mo is Mo${}^{4+}$. The T_C increases continuously with Nd doping in the stoichiometric case. The increase of the T_C follows a competition with the substitution of Sr${}^{2+}$ ions by Nd${}^{3+}$ ions and the charge neutrality considered in our system.

In this work, the ZnO thin film, the Al-doped ZnO (AZO) thin film (0.98M ZnO, 0.02M Al) and the (Al,Co) co-doped ZnO thin film (AZO:Co) (0.95M ZnO, 0.02M Al, 0.03M Co) were deposited on the glass substrate by the Sol–Gel method. We fabricated a sample of the ZnO thin film, a sample of the AZO thin film and three samples of AZO:Co thin films. The spin-coating was used to deposit thin film on the glass substrate. The ZnO and the AZO thin films were annealed at 450${}^{\circ }$C while three samples of the AZO:Co thin films were annealed at 300${}^{\circ }$C, 450${}^{\circ }$C and 600${}^{\circ }$C in air for 60 min, respectively. In order to prepare three samples of the AZO:Co thin films, we deposited the (Al,Co) co-doped ZnO on the glass substrate for 20 s then all samples were per-heated at 80${}^{\circ }$C for 10 min. we repeated this deposition process five times for each sample. Finally, three samples were annealed at 300${}^{\circ }$C, 450${}^{\circ }$C and 600${}^{\circ }$C in air for 60 min, respectively. The procedure to prepare of the ZnO and AZO thin films was like the AZO:Co thin films except that the annealing temperature was 450${}^{\circ }$C. The structural and optical properties of the thin films were investigated by X-ray diffraction technique, UV-Vis spectrophotometer and Field Emission Scanning Electron Microscopy (FESEM). Results indicated that (Al,Co) co-doping in the ZnO thin film improve the optical transmission while changes in the lattice structure is small with respect to the AZO thin film. Also, the AZO:Co thin film which was annealed at 450${}^{\circ }$C exhibited simultaneously the high thickness and high optical transmission.

Bifurcation analysis of the propagation of femtosecond pulses for the Triki–Biswas (TB) equation in monomode optical fibers is reported for the first time. Bifurcation of phase plots of the dynamical system is dispensed using phase plane analysis through symbolic computation. It is observed that the TB equation supports femtosecond solitary pulse, periodic pulse, superperiodic pulse, kink and anti-kink pulses, which are presented through time series plot numerically. Analytical forms of the femtosecond solitary pulses are obtained. This contribution may be applicable to interpret the dynamical behavior of various femtosecond pulses in monomode optical fibers beyond the Kerr limit.

The structural and electronic transport properties of ${\mathrm{\text{Ga}}}_x{\mathrm{\text{N}}}_y(x+y=5)$ clusters are studied based on density functional theory (DFT). Their most stable structures are proved to be planar by the particle swarm optimization (PSO) algorithm, and have decreasing binding energies with the increasing number of Ga atom in clusters. The electronic transport properties of these clusters connected with two Al(1 0 0) electrodes are calculated by combining nonequilibrium Green’s-function (NEGF) with DFT. Most of them have an equilibrium conductance of above $1.0{\mathrm{\text{G}}}_0$, except for ${\mathrm{\text{G}}}_1{\mathrm{\text{N}}}_4(\sim 0.4{\mathrm{\text{G}}}_0)$. Negative differential resistance (NDR) phenomenon of different level is observed in their I–V curves in bias ranges of from $-1.1$ to $-0.8$ V and from 0.7 to 1.1 V.

Deposition of zinc sulfide (ZnS) thin films on Si (1 0 0) and glass substrates has been performed using RF magnetron sputtering method. Film structure has been analyzed by X-ray Diffraction (XRD), while the scanning electron microscope (SEM) images have been used to explore the film morphology. FTIR and Raman spectroscopies have been used to confirm the film composition. The stoichiometry has been verified by Energy dispersive X-ray spectroscopy (EDX) technique. The XRD patterns have indicated that the films possess a polycrystalline nanocrystallite cubic structure. The optical properties of the grown films were characterized by optical transmittance measurements (UV–Vis). The deduced energy bandgaps of the films show an increase from 3.75 eV to 3.88 eV with the power source changes from 90 W to 125 W. Furthermore, Z-scan technique (CW diode laser $\lambda =635$ nm) was employed to estimate the nonlinear optical absorption of the prepared ZnS films.

We investigate the excited state effect of ${\mathrm{\text{He}}}^{+}$ ion on intense harmonic spectrum and attosecond pulse (AP) generation. First step, by using the superposition state model, we find that as the excited state ratio increases, the intensity of harmonic spectrum can be enhanced, and a near-stable intense harmonic yield can be obtained when the ground state (GS) and the excited state remains within a certain ratio range. However, as the excited state ratio further increases, the intensity of harmonic spectrum is decreased. Further, with the introduction of a down-chirp modulation, the harmonic cutoff can be extended, showing a broader spectral continuum with a higher efficiency. Second step, by using the single GS model and with the help of the pump-probe-UV-resonance-ionization mechanism, the high-intensity and broader spectral continuum obtained in the first step can be realized in the experiment. Moreover, this method is not very sensitive to the delay time between the fundamental field and the UV pulse, which is beneficial to experimental implementation. As a result, 3 APs as short as 40 as can be obtained.

In this paper, the new traveling wave solutions containing the trigonometric functions, hyperbolic functions and rational functions of $(3+1)$-dimensional Zakharov–Kuznetsov equation are obtained. The graphs of the solution functions are presented by giving specific values to the constants. Numerical solutions are obtained by using finite difference method with new initial condition. Von Neumann’s Stability, Consistency and Linear Stability analysis of the equation are performed and $L_2$, $L_{\infty }$ norm errors are also examined with the truncation error. The exact solution obtained is presented via numerical solutions and absolute error graphs, and the analysis of exact solution and the numerical solutions are performed. Complex operations and graphical drawings were made using the computer package program.

This research paper applies the modified Khater method and the generalized Kudryashov method to the general Degasperis–Procesi (DP) equation, which is used to describe the dynamical behavior of the shallow water outflows. Some shock peakon wave solutions are obtained by using these methods. Moreover, some figures are sketched for these solutions to explain more physical properties of the general DP equation and to figure out the coincidence between different types of obtained solutions. The stability property by using the features of the Hamiltonian system is tested to some obtained solutions to show their ability for applying in the model’s applications. The obtained solutions were verified with Maple 16 & Mathematica 12 by placing them back into the original equations. The performance of these methods shows their power and effectiveness for applying to many different forms of the nonlinear evolution equations with an integer and fractional order.

Many networks have community structure — groups of nodes within which connections are dense but between which they are sparser. While there exists a range of algorithms for community detection in networks, most of them try to discover this important mesoscale structure from a topological point of view solely. Here we develop a hybrid clustering approach for uncovering the community structure in a network using a combination of information on local topology of the network and on the dynamics of the cascading failures. The originality of the proposed approach is that we introduce a novel fusion of the dynamic behaviors of the cascading failures and topological metric functions in the $k$th-nearest neighbor density scheme, which integrates both the global and local structural information of a given network for community detection. The experimental results on both artificial random and real-world benchmark networks indicate the effectiveness and reliability of our approach.

We consider the problem of finding approximate analytical solutions for nonlinear equations typical of physics applications. The emphasis is on the modification of the method of Padé approximants that are known to provide the best approximation for the class of rational functions, but do not provide sufficient accuracy or cannot be applied at all for those nonlinear problems, whose solutions exhibit behavior characterized by irrational functions. In order to improve the accuracy, we suggest a method of self-similarly corrected Padé approximants taking into account the irrational functional behavior. The idea of the method is in representing the sought solution as a product of two factors, one of which is given by a self-similar root approximant, responsible for irrational functional behavior, and the other being a Padé approximant corresponding to a rational function. The efficiency of the method is illustrated by constructing very accurate solutions for nonlinear differential equations. A thorough investigation is given proving that the suggested method is more accurate than the method of standard Padé approximants.

Using the Hindmarsh–Rose (HR) model, a two-layer neuronal network is constructed to study the spiral wave dynamics. The first layer generates spiral wave induced by random values of boundary under appropriate coupling intensity and external force, and the second layer is in the different states. Coupling channels between the two layers are set in multiple areas and spiral wave of first layer affect second layer via the coupling channels. The spatiotemporal pattern of neuronal network is investigated in the second layer. It is shown that spiral wave can be found under appropriate conditions, multi-area channels are more likely to generate spiral waves and target waves than only one local coupling area. A statistical variable on the second layer is calculated by increasing intensity of channels between layers. The larger the coupling areas between layers, the more obvious the synchronism phenomenon is.

With the hierarchical Green’s function approach, we study a doped Mott insulator described with the Hubbard model by analytically solving the equations of motion of an one-particle Green’s function and related multiple-point correlation functions, and find that the separation of the spin and charge degrees of freedom of the electrons is an intrinsic character of the doped Mott insulator. For enough of large on-site repulsive Coulomb interaction, we show that the spectral weight of the one-particle Green’s function is proportional to the hole doping concentration that is mainly produced by the charge fluctuation of electrons, while the excitation spectrum of the electrons is composed of two parts: One is contributed by the spin fluctuation of the electrons, which is proportional to the hole doping concentration, and another one is coming from the coupling between the charge and spin fluctuations of the electrons that takes the maximum at undoping. All of these low energy/temperature physical properties originate from the strong on-site Coulomb interaction. The present results are consistent with the spectroscopy observations of the cuprate superconductors and the numerical calculations in normal state above the pseudogap regime.