Modern Physics Letters B

Manganese substituted nickel–copper–cobalt ferrite nanoparticles having the basic composition ${\mathrm{\text{Ni}}}_{0.2}{\mathrm{\text{Cu}}}_{0.2}{\mathrm{\text{Co}}}_{0.6-x}{\mathrm{\text{Mn}}}_x{\mathrm{\text{Fe}}}_2{\mathrm{\text{O}}}_4$ (x = 0.0, 0.1, 0.2, 0.3 and 0.4) were synthesized by sol–gel auto-combustion method. X-ray diffraction (XRD) was used to estimate phase purity and lattice symmetry. All the prepared samples show the single-phase cubic spinel structure. Fourier transform infrared (FTIR) measurements also confirm the cubic spinel structure of the ferrite that is formed. The preparation of samples show these nearly spherical particles by Transmission electron microscopy (TEM). The magnetic properties of Mn${}^{2+}$ ion substituted in nickel–copper–cobalt ferrite were studied by Vibrating sample magnetometer (VSM). The saturation magnetization ($M_s$), remanent magnetization $(M_r)$, coercivity $(H_c)$, magnetic moment $({\mu }_B)$ and anisotropy constant $(K)$ first increase and then decrease with the increase of ${\mathrm{\text{Mn}}}^{2+}$ ions content. They had better magnetism than pure sample and other substituted samples when the substitution amount of ${\mathrm{\text{Mn}}}^{2+}$ ions was $x=0.1$. At $x=0.1$, the maximum values of remanent magnetization $(M_r)$, saturation magnetization $(M_s)$ and coercivity $(H_c)$ are 25.58 emu/g, 61.95 emu/g and 689.76 Oe, respectively. This indicates that the magnetism of ferrite can improve by substituting with the appropriate amount of manganese. However, due to the excess ${\mathrm{\text{Mn}}}^{2+}$ ions instead, ferrite magnetism is weakened. This means that these materials can be used in magnetic data storage and recording media.

In this work, we consider the generalized (3+1)-dimensional Boussinesq equation, which can describe the propagation of gravity wave on the surface of water. Based on the Bell polynomial theory, a powerful technique is employed to explicitly construct its bilinear formalism and two-soliton solutions, based on which the new rational solution is well-constructed. Moreover, the extended homoclinic test approach is presented to succinctly construct the breather wave and rogue wave solutions of the Boussinesq equation. Then the main characteristics of these solutions are graphically discussed. More importantly, they reveal that the extreme behavior of the breather wave can give rise to the rogue wave.

A new coupled Burgers equation and a new coupled KdV equation which are associated with $3\times 3$ matrix spectial problem are investigated for complete integrability and covariant property. For integrability, Lax pair and conservation laws of the two new coupled equations with four potentials are established. For covariant property, Darboux transformation (DT) is used to construct explicit solutions of the two new coupled equations.

We have studied the Berry-phase interference in single-molecule magnets ${\mathrm{\text{Mn}}}_{12}$ and ${\mathrm{\text{Fe}}}_8$ coupled to polarized electrodes in the Coulomb blockade regime under external magnetic field. We show that for the oppositely fully polarized leads, the current is completely blockaded as a consequence of the topologically quenched tunnel splitting, which is called as Berry-phase blockade; whereas for the partially polarized leads, the current oscillates periodically with increasing external transverse magnetic field (Berry-phase oscillations). The reason is that different quantum spin tunneling trajectories can combine and give rise to either constructive or destructive interference effects.

High-pressure technique is an effective route to synthesize thermoelectric materials and tune transport properties simultaneously. In this work, S-doped copper–selenium compounds $({\mathrm{\text{Cu}}}_2{\mathrm{\text{Se}}}_{1-x}{\mathrm{\text{S}}}_x$, $0\le x\le 0.05)$ were successfully synthesized by high-pressure and high-temperature (HPHT) technology in just 30 min. ${\mathrm{\text{Cu}}}_2{\mathrm{\text{Se}}}_{1-x}{\mathrm{\text{S}}}_x$ samples show layered morphology composed of abundant pores and lattice defects. The appropriate S introduction ($x=0.01$ and 0.03) can effectively enhance Seebeck coefficient and reduce the thermal conductivity of ${\mathrm{\text{Cu}}}_2\mathrm{\text{Se}}$. Compared with the pure ${\mathrm{\text{Cu}}}_2\mathrm{\text{Se}}$ sample, ${\mathrm{\text{Cu}}}_2{\mathrm{\text{Se}}}_{0.97}{\mathrm{\text{S}}}_{0.03}$ exhibits a 30% lower thermal conductivity, but the decline of power factor by the distinctly increased electrical resistivity at high temperature results in a smaller zT at temperature $>650$ K. The variations of thermoelectric properties are resulted from the competitive effects between S-doping and actual composition change (Cu:S). It indicates that S-doping is not so effective in improving the zT value of ${\mathrm{\text{Cu}}}_2\mathrm{\text{Se}}$ materials by high-pressure synthesis.

In order to investigate the transverse vibration of eccentric rotor in a 12/8 switched reluctance motor (SRM), a whole nonlinear coupled vibration equation of eccentric rotor is built with finite element method (FEM). Based on single tooth radial force and the key parameters variation with rotor position, an analytical formula of magnetic resultant taking into account of the rotor’s vibration displacement is deduced in detail, which is applied onto the intermediate node of eccentric rotor in form of concentrated force. Once the windings currents obtained either by experiments or numerical simulations is input, the vibration response can be solved numerically by Newmark-$\beta$ method. Six phase windings currents under angle position control (APC) strategy are chosen as an example and the vibration response are discussed to reflect intrinsic vibration characteristics. From radical resultant vector and its amplitude spectrum, it is proved that the magnetic resultant vector presents multi-petals star shape. The frequency components in magnetic resultant are $X$, $5X$, and $24kX\pm X$, $24kX\pm 5X$, related to rotational speed, current waveform and minimum common multiple of stator and rotor teeth. However, from displacement locus and its amplitude spectrum, the frequency component of the rotor vibration displacement is also related to the critical whirl speed of the rotor. Transverse superharmonic resonance of eccentric rotor appears at some particular rotational speed and result in a larger rotor vibration. If the rotor runs at the superharmonic speed of 1/19 of first-order critical whirl speed, the maximum vibration displacement radius of the eccentric rotor reaches almost four times that of the rated speed. The vibration locus at these particular speed show rich diversity.

The temperature range of $T$ = 77–770 K in the system alloys: Holl coefficient $(R)$, thermo-emf $(S)$, electric conductivity $(\sigma )$, measured $d$-density of components and analyzed. It has been established that samarium additive atoms contain donor-type properties and the effectiveness increases with the temperature increase: up to 40% proportional to $T\le 440$ K in $p$-type specimens, whereas in $n$-type samples this increase is higher and covers the contents of pH varying from $p$ to $n$. An electrical conductivity of compounds increased due to the carrier activation with further increase of temperature. The activation energy of carriers at low temperatures ($T\le 400$ K) is $\mathrm{\Delta }{E}_g\approx 0.37$ eV for $x=0.05$ mol.% and $x=0.10$ mol.% compounds at $T$ = 77–320 K and for $x=1.00$ mol.% and $x=3$ mol.% compounds are $\mathrm{\Delta }{E}_g\approx 0.39$ eV. $\sigma (T)\approx$ const at $T=300$–400 K for $x=0.05$ mol.% and $x=0.10$ mol.% compounds, and passing with minimum increases at $T$ = 400–500 K.

The invariant subspace method (ISM) is a powerful tool for investigating analytical solutions to fractional differential–difference equations (FDDEs). Based on previous work by other people, we apply the ISM to the space-time fractional differential and difference equations, including the cases of the scalar space-time FDDEs and the multi-coupled space-time FDDEs. As a result, we obtain some new analytical solutions to the well-known scalar space-time Lotka–Volterra equation, the space-time fractional generalized Hybrid lattice equation and the space-time fractional Burgers equation as well as two couple space-time FDDEs. Furthermore, some properties of the analytical solutions are illustrated by graphs.

Temperature-dependent (5–200 K) electrical resistivity and magnetoresistance (MR) measurements were carried out on ${\mathrm{\text{Zn}}}_{1-x}{\mathrm{\text{V}}}_x\mathrm{\text{O}}$ (x = 0.5–4 at.%) thin films grown by pulsed laser deposition (PLD). The free electron concentration in the films was found to be in the range of $\sim$(1.7–4.7) $\times 10^{20}{\mathrm{\text{cm}}}^{-3}$ which is much higher compared to the Mott critical density required for the onset of insulator-to-metal transition in ZnO. All the films exhibited small negative MR in the entire temperature and magnetic field range indicating weak-localization as the dominant effect. However, some unusual MR behavior was observed at 5 K for the film with highest static-disorder parameter. Such characteristics have been well-explained by considering the interplay of negative MR (arising due weak-localization and spin-disorder scattering) and positive MR (caused by s–d exchange interaction induced spin-splitting of the conduction band).

In this paper, the Oskolkov–Benjamin–Bona–Mahony–Burgers (OBBMB) equation has been investigated by Lie symmetry analysis. Lie group analysis method is implemented to derive the vector fields and symmetry reductions. The OBBMB equation has been reduced into nonlinear ordinary differential equation (ODE) by exploiting symmetry reduction method. Using the similarity reduction equation, the exact solutions are obtained by extended $(G^{\prime }/G)$-method. Finally, the new conservation theorem proposed by Ibragimov has been utilized to construct the conservation laws of the aforesaid equation.

In the anomalous diffusions, the transition phenomena from superdiffusion (or subdiffusion) to normal diffusion have been found in several experiments and studied by stochastic models. In this study, we found the diffusion transition which occurs twice in a stochastic process, first from superdiffusion to subdiffusion, and then from subdiffusion to normal diffusion by using the nonstationary Markovian replication process with the memory of the previous step exponentially decaying with time. In the early stage, when the walker strongly follows the previous step, superdiffusive behaviors occur, while in the intermediate stage in which the memory effect decays exponentially, the motion of the walker shows subdiffusive behaviors. Eventually, as the memory effect almost disappears, the motion reduces to normal diffusion. We also found that the Hurst exponent in the intermediate subdiffusive region becomes smaller when the change of the memory effect is more abrupt.

The geometric structure, energy barrier and electronic properties of H-incorporated ${\mathrm{\text{Ti}}}_3{\mathrm{\text{SiC}}}_2/\mathrm{\text{Zr}}$ heterojunctions were investigated by first-principles calculations. Hydrogen atom settles in ${\mathrm{\text{Ti}}}_3{\mathrm{\text{SiC}}}_2/\mathrm{\text{Zr}}$ as interstitial impurity due to its small radius. Through calculating and analyzing the total energies of H-incorporated ${\mathrm{\text{Ti}}}_3{\mathrm{\text{SiC}}}_2/\mathrm{\text{Zr}}$ heterojunction, a much higher potential barrier (1.75 eV) was found when H atom diffuses from the interface into the ${\mathrm{\text{Ti}}}_3{\mathrm{\text{SiC}}}_2$ material than that (0.25 eV) into the Zr metal. The encountered potential barriers of H atom diffusing from vacuum into the ${\mathrm{\text{Ti}}}_3{\mathrm{\text{SiC}}}_2$ and Zr metal are also calculated, and they are both positive. These findings indicate that ${\mathrm{\text{Ti}}}_3{\mathrm{\text{SiC}}}_2$ is a suitable coating material to prevent the hydrogen embrittlement and corrosion in Zr metal. The electronic properties and valence bond properties of H-incorporated ${\mathrm{\text{Ti}}}_3{\mathrm{\text{SiC}}}_2/\mathrm{\text{Zr}}$ were analyzed based on the band structure, electronic density of states and Mulliken distribution. The calculated results show that all the H-incorporated ${\mathrm{\text{Ti}}}_3{\mathrm{\text{SiC}}}_2/\mathrm{\text{Zr}}$ heterojunctions exhibit metallic, covalent and ionic properties. These investigations may provide new insight into the underlying mechanisms of hydrogen diffusion in the ${\mathrm{\text{Ti}}}_3{\mathrm{\text{SiC}}}_2/\mathrm{\text{Zr}}$ heterojunction.

We consider the hyperbolic type fuzzy fractional differential equation and derive the second-order fuzzy fractional differential equation using scaling transformation. We present a theoretical and a numerical method to find the invariant solutions of such equations. Also, we prove the existence and uniqueness results using Banach fixed point theorem. Numerical solutions are approximated using finite difference method. Finally, numerical examples are given to illustrate the obtained results.

Motivated by the recent novel electronic features extracted from the magic-angle graphene superlattices, we studied the ground state superconducting pairing correlations within the Hubbard model on a twisted bilayer honeycomb lattice. Using Constrained-Path Quantum Monte Carlo method, we found that the $d+id$ pairing correlation dominates over other pairing patterns among various electron fillings and interaction strengths, and the effective pairing interaction was enhanced as the on-site Coulomb interaction increased. We further examined the effect of the nearest neighbor interaction $V$, and the effective pairing interaction with $d+id$ pairing symmetry was also enhanced by either a repulsive or attractive interaction. Our intensive numerical results confirm the interaction driven superconductivity with a dominant $d+id$ pairing symmetry in twisted bilayer graphene.