Modern Physics Letters B

In this paper, we investigate a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili (mKP) equation in fluid dynamics. With the binary Bell-polynomial and an auxiliary function, bilinear forms for the equation are constructed. Based on the bilinear forms, multi-soliton solutions and Bell-polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton interactions are presented. Based on the graphic analysis, Parametric conditions for the existence of the shock waves, elevation solitons and depression solitons are given, and it is shown that under the condition of keeping the wave vectors invariable, the change of $\alpha (t)$ and $\beta (t)$ can lead to the change of the solitonic velocities, but the shape of each soliton remains unchanged, where $\alpha (t)$ and $\beta (t)$ are the variable coefficients in the equation. Oblique elastic interactions can exist between the (i) two shock waves, (ii) two elevation solitons, and (iii) elevation and depression solitons. However, oblique interactions between (i) shock waves and elevation solitons, (ii) shock waves and depression solitons are inelastic.

A photonic hypercrystal is a subwavelength periodic structure consisting of alternate layers of hyperbolic metamaterial and dielectric material. The structure can be treated as an effective medium as well as a periodic medium. Since two length scales are involved, the better treatment is to treat the hyperbolic metamaterial as an effective medium and the overall structure as a periodic medium. The dispersion relations are derived and plotted to show the appearance of propagating bands and gaps in the frequency and wave vector domains. Then using the transfer matrix approach, the transmissivity versus the frequency plot for propagating waves and grayscale plot of the transmission coefficient in the frequency versus wave vector plane for the evanescent waves are plotted and analyzed.

The local structures and spin Hamiltonian parameters are theoretically studied for Cu${}^{2+}$ in alkaline earth alumino borate (XAB, X = Mg, Ca and Sr) glasses by using the perturbation calculations for tetragonally elongated octahedral 3d⁹ groups. The ${[{\mathrm{\text{CuO}}}_6]}^{10-}$ groups are subject to the large relative tetragonal elongation ratios of 15.4%, 13.4% and 13.0% for MgAB, CaAB and SrAB glasses, respectively, arising from the Jahn–Teller effect. The decreasing cubic field parameter Dq, orbital reduction factor k and relative elongation ratio with the increase of the radius of alkaline earth ion X from Mg to Ca or Sr are analyzed for the studied systems in a uniform way.

In this paper, we study experimentally the stress relaxation behavior of soft solids such as gelatin hydrogels on a smooth glass surface in direct shear sliding. It is observed experimentally that irrespective of pulling velocity, the sliding block relaxes to the same level of nonzero residual stress. However, residual stress increases with increasing gelatin concentration in the hydrogels. We have also validated a friction model for strong bond formation during steady relaxation in light of the experimental observations. Our theoretical analysis establishes that population of dangling chains at the sliding interface significantly affects the relaxation process. As a result, residual stress increases with increasing gelatin concentration or decreasing mesh size of the three-dimensional structures in the hydrogels. It is also found that the transition time, at which a weak bond converts to strong bond, increases with increasing mesh size of the hydrogels. Moreover, relaxation time constant of a strong bond decreases with increasing mesh size. However, activation length of a strong bond increases with mesh size. Finally, this study signifies the role of residual strength in frictional shear sliding and it is believed that these results should be useful to understand the role of residual stress in stick-slip instability.

The electronic structures and magnetic properties of Fe₃Si films epitaxial on Si(001) were systematically investigated by using the first-principle calculations on plane-wave pseudo-potential theory. The calculated results show that Fe₃Si films epitaxial on Si(001) have the most stable equilibrium state at the lattice constant c = 5.63 Å. The negative heat of formation and cohesive energy of Fe₃Si(001)//Si(001) imply that Fe₃Si films epitaxial on Si(001) formed in this manner have high structural stability. The calculated spin polarized energy band structures and density of states indicate that Fe₃Si films epitaxial on Si(001) have characteristic of metal, whose bonding modes are covalent bond and metallic bond. The band through Fermi level is mainly due to the Fe 3d states and the Si 3p states. Ferromagnetic properties of Fe₃Si(001)//Si(001) are attributed to 3d states of the Fe atoms. The atomic magnetic moments of Fe[A,C] and Fe[B] are different from each other, likewise implying Fe₃Si films epitaxial on Si(001) is ferromagnetic.

This paper investigates the dynamic evolution characteristics of the hydropower station by introducing the fractional order damping forces. A careful analysis of the dynamic characteristics of the generator shaft system is carried out under different values of fractional order. It turns out the vibration state of the axis coordinates has a certain evolution law with the increase of the fractional order. Significantly, the obtained law exists in the horizontal evolution and vertical evolution of the dynamical behaviors. Meanwhile, some interesting dynamical phenomena were found in this process. The outcomes of this study enrich the nonlinear dynamic theory from the engineering practice of hydropower stations.

We present a systematic theoretical investigation on the work functions of five closed surfaces of metal hexaborides including LaB₆, BaB₆, CaB₆, CeB₆, SrB₆ and SmB₆. The results are in a close agreement with available experimental measurements and previous theoretical findings. The variations of the work function display a good trend. For BaB₆, CaB₆ and SrB₆, the increasing order is $\varphi$(100) $<\varphi$(110) $<\varphi$(211) $<\varphi$(112) $<\varphi$(111). For CeB₆, LaB₆, and SmB₆, the sequence is somewhat different: $\varphi$(100) $<\varphi$(211) $<\varphi$(112) $<\varphi$(110) $<\varphi$(111). The work function changes with the metal hexaborides series have also been discussed. The increasing order of the (100) surface is LaB₆(100) $<$ CeB₆(100) $<$ SmB₆(100) $<$ SrB₆(100) $<$ BaB₆(100) $<$ CaB₆(100). The orders for the (110) and (111) surface are similar: BaB₆(110, 111) $<$ SrB₆(110, 111) $<$ LaB₆(110, 111) $<$ CeB₆(110, 111) $<$ CaB₆(110, 111) $<$ SmB₆(110, 111). For the (112) and (211) surface, the sequence is BaB₆(112, 211) $<$ LaB₆(112, 211) $<$ CeB₆(112, 211) $<$ SrB₆(112, 211) $<$ SmB₆(112, 211) $<$ CaB₆(112, 211).

Nano-scale Multifunctional Logic Gates based on Si hybrid plasmonic waveguides (HPWGs) are designed by utilizing the multimode interference (MMI) effect. The proposed device is composed of three input waveguides, three output waveguides and an MMI waveguide. The functional size of the device is only 1000 nm × 3200 nm, which is much smaller than traditional Si-based all-optical logic gates. By setting different input signals and selecting suitable threshold value, OR, AND, XOR and NOT gates are achieved simultaneously or individually in a single device. This may provide a way for ultrahigh speed signal processing and future nanophotonic integrated circuits.

An inductorless noise-canceling CMOS low-noise amplifier (LNA) with wideband linearization technique is proposed. The complementary configuration by stacked NMOS/PMOS is employed to compensate second-order nonlinearity of the circuit. The third-order distortion of the auxiliary stage is also mitigated by that of the weak inversion transistors in the main path. The bias and scaling size combined by digital control words are further tuned to obtain enhanced linearity over the desired band. Implemented in a 0.18 $\mu$m CMOS process, simulated results show that the proposed LNA provides a voltage gain of 16.1 dB and a NF of 2.8–3.4 dB from 0.1 GHz to 1.4 GHz. The IIP3 and IIP2 of 13–18.9 and 24–40 dBm are obtained, respectively. The circuit core consumes 19 mW from a 1.8 V supply.

This paper gives an analytical study of dynamic behavior of the exact solutions of nonlinear Korteweg–de Vries equation with space–time local fractional derivatives. By using the improved $(\frac{G^{\prime }}{G})$-expansion method, the explicit traveling wave solutions including periodic solutions, dark soliton solutions, soliton solutions and soliton-like solutions, are obtained for the first time. They can better help us further understand the physical phenomena and provide a strong basis. Meanwhile, some solutions are presented through 3D-graphs.

In this paper, a class of difference equations with variable-time impulses is considered. By applying comparison principle, we shall show that difference equations with variable-time impulse can be reduced to the corresponding difference equations with fixed-time impulses under well-selected conditions. Meanwhile, the fixed-time impulsive systems can be regarded as the comparison system of the difference equations with variable-time impulses. Furthermore, we use a series of sufficient criteria to illustrate the same stability properties between variable-time impulsive difference equations and the fixed-time ones. We then establish several sufficient conditions guaranteeing the global exponential stability of variable-time impulsive difference equations by comparison principle. As an application, global exponential stability of discrete-time neural networks with variable-time impulses is discussed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results.

In this paper, we consider a coupled nonlinear Maccari’s system (CNMS) which describes the motion of isolated waves localized in a small part of space. There are some integration tools that are adopted to retrieve the solitary wave solutions. They are the modified F-Expansion and the generalized projective Riccati equation methods. Topological, non-topological, complexiton, singular and trigonometric function solutions are derived. A comparison between the results in this paper and the well-known results in the literature is also given. The derived structures of the obtained solutions offer a rich platform to study the nonlinear CNMS. Numerical simulation of the obtained solutions are presented with interesting figures showing the physical meaning of the solutions.

We use theoretical and numerical calculations in the framework of the effective-field theory to examine the rigorous effects of the crystal field interactions of the mixed spin-2 and spin-$\frac{3}{2}$ Blume–Capel model on the honeycomb lattice in the presence of an external magnetic field. The ground state phase diagram has been constructed. Thermal changes of the order parameters and other thermodynamic quantities of interest and their influence on the phase diagrams of the model have been thoroughly investigated. The system shows very interesting critical properties including continuous and discontinuous phase transitions, tricritical points and compensation temperatures which are revealed in specific ranges of the parameters space. Our numerical findings are compared to those obtained by other methods and reliable agreements are recovered.

In this paper, a 3 × 3 matrix spectral problem with six potentials is considered. With the help of the compatibility condition, a hierarchy of new nonlinear evolution equations which can be reduced to the coupled derivative nonlinear Schrödinger (CDNLS) equations is obtained. By use of the trace identity, it is proved that all the members in this new hierarchy have generalized bi-Hamiltonian structures. Moreover, infinitely many conservation laws of this hierarchy are constructed.