Modern Physics Letters B

In this work, sol–gel auto-combustion technology is used to synthesize nanocrystalline Ni${}_{0.2}$Cu${}_{0.2}$Co${}_{0.6}$Fe₂O₄ with high purity metal nitrate and citric acid as precursor solution. The prepared samples are sintered at different temperatures (400${}^{\circ }$C, 500${}^{\circ }$C, 600${}^{\circ }$C, 700${}^{\circ }$C, 800${}^{\circ }$C, 900${}^{\circ }$C, 1000${}^{\circ }$C and 1100${}^{\circ }$C) for 3.5 h. The structure and magnetic properties of the samples are characterized using X-ray diffraction (XRD), Fourier transform infrared (FT-IR) and vibrating sample magnetometer (VSM). The analysis of the XRD patterns confirms that all the samples have a single-phase cubic spinel structure. The particle size of the prepared samples (between 23 nm and 36 nm) is determined by the Scherrer equation. The effect of particle size is through observation of samples sintered at different temperatures. FT-IR spectroscopy shows the characteristic peak is near 588 cm${}^{-1}$. And the measurement also confirms the formation of spinel structure. The magnetic parameters of the samples are measured by VSM at room temperature with a maximum magnetic field of 1 T. Coercivity, remanent magnetization and saturation magnetization change with the changing sintering temperature. It can be clearly observed that the magnetic properties increase significantly with the temperature increasing from 600${}^{\circ }$C to 700${}^{\circ }$C. The dM/dH versus H curves are obtained by differentiating the hysteresis loop. The increasing peak height of dM/dH at $H_m$, indicates a magnetically stable state for the samples with good crystalline cubic spinel structure.

Motivated by a bound derived in a recent work [C. Arenz, B. Russell, D. Burgarth and H. Rabitz, New J. Phys. 19 (2017) 103015], we apply optimal control theory to the dynamics of qubit systems, with the goal of investigating the lower bound of minimum gate times. In practice, we not only need to reach the desired unitary gates but we need to do so in a reasonable time (below the typical decoherence time). Therefore, we employ the recently introduced lower bound to estimate the minimum gate time and resort to numerical gate optimization in order to study the tightness of the obtained bound and our findings verify the relationship between the internal Hamiltonian and the minimum evolution time remarkably well. Finally, we discuss both challenges and ways forward for obtaining the same efficacy under realistic conditions.

We investigate numerical interactions between two Airy beams with different relative phases in photorefractive (PR) nonlinear media in one transverse dimension. It is shown that solitons and soliton pairs are generated that are not accelerating, although the incident beams exhibit acceleration property. When the relative phase is very small, the attraction between the two Airy beams is strengthened and their propagation behavior is similar to that in in-phase case, where the two Airy beams attract each other and the main lobes can fuse into one single breathing soliton, secondary lobes can generate soliton pairs with symmetric intensity distribution. While the relative phase is close to $\pi$, these beams present out-phase propagation with strong repulsive effect. Their interaction properties are sensitive to both the interval and relative phase between the two Airy beams.

The effects of coverage and torsional angle on the stability, electronic structure and optical properties of S-absorbed graphene system are studied by using density functional theory based on the first-principles. The adsorption energy, band structure, light absorption coefficient and reflectivity are calculated through it. In the current research area, it is found that the coverage has little effect on the adsorption of the system, but the C atoms are pulled up, the graphene plane is distorted, and the band gap of the graphene is opened, which changes graphene from quasi-metal to semiconductors. S-adsorbed graphene system has a blueshift relative to the intrinsic graphene, and the degree of blueshift increases with the increase of coverage. The reflectivity of the system is higher than that of the unabsorbed S atom system. Torsional deformation has a large effect on its band gap. It makes the adsorption system reduce the adsorption energy and the stability. The band structure shows that the band gap decreases as the twist angle increases. The twisted S-adsorbed graphene system shows a slight redshift, and the degree of redshift increases with the angle. The maximum reflectance of the S-adsorbed graphene system with torsional deformation is stronger than that of the untwisted system.

The mixed spin-1/2 and spin-3/2 Blume–Capel (BC) model is considered on the Bethe lattice (BL) with randomly changing coordination numbers (CN) and examined in terms of exact recursion relations. A couple of two different CNs are changed randomly on the shells of the BL in terms of a standard–random approach to obtain the phase diagrams on possible planes of the system parameters. It is found from the thermal analysis of the order-parameters that the model only gives the second-order phase transitions as in the regular mixed case. As the probability of having larger CN increases, the temperatures of the critical lines also increase as expected.

In this paper, we investigate the squared eigenfunction symmetries under the Miura and reverse-Miura transformations, between the discrete KP and modified discrete KP hierarchies, in unconstrained and constrained cases. What is more, the squared eigenfunction symmetries for the constrained discrete KP and constrained modified discrete KP hierarchies are constructed by imposing the additional conditions on the generating eigenfunctions of the corresponding symmetries.

In this paper, the stable state transformation and the effect of the stochastic resonance (SR) for a metapopulation system are investigated, which is disturbed by time delay, the multiplicative non-Gaussian noise, the additive colored Gaussian noise and a multiplicative periodic signal. By use of the fast descent method, the approximation of the unified colored noise and the SR theory, the dynamical behaviors for the steady-state probability function and the SNR are analyzed. It is found that non-Gaussian noise, the colored Gaussian noise and time delay can all reduce the stability of the biological system, and even lead to the population extinction. Inversely, the self-correlation times of two noises can both increase the stability of the population system and be in favor of the population reproduction. As regards the SNR for the metapopulation system induced by the noise terms and time delay, it is discovered that time delay and the correlation time of the multiplicative noise can effectively enhance the SR effect, while the multiplicative noise and the correlation time of the additive noise would all the time suppress the SR phenomena. In addition, the additive noise can effectively motivate the SR effect, but not alter the peak value of the SNR. It is worth noting that the departure parameter from the Gaussian noise plays the diametrical roles in stimulating the SR effect in different cases.

The Sc:Fe:Cu:LiNbO₃ crystals were grown with Fe${}^{3+}$(0.3 wt.%), Cu${}^{2+}$(0.1 wt.%) and Sc${}^{3+}$(1 mol.%) by the Czochralski method with various [Li]/[Nb] ratios (0.946, 1.05, 1.20 and 1.38). The influence of the [Li]/[Nb] ratios on the defect structure of Sc:Fe:Cu:LiNbO₃ crystals was analyzed by the UV-Visible spectra and IR transmission spectra. The spectra show that the absorption edge shift to the red with [Li]/[Nb] ratios enhancing. The Sc:Fe:Cu:LiNbO₃ crystals with [Li]/[Nb] ratio of 1.05 is nearly stoichiometric. A new narrow OH${}^{-}$ associated vibrational peak at 3505 cm${}^{-1}$ was revealed in Sc:Fe:Cu:LiNbO₃ crystals with the ratio of [Li]/[Nb] = 1.38. It is attributed to the (Sc${}_{\mathrm{\text{Nb}}}^{2-}$)-(OH)${}^{-}$. The results show that the defect structure changes with the [Li]/[Nb] ratios variation.

The excitations in graphene and some other materials are described by two-dimensional massless Dirac equation with applied external potential of some kind. Solutions of this zero energy equation are built analytically for a wide class of scalar potentials. In contrast to most publications on analytical solutions of massless two-dimensional Dirac equation, our potentials really depend on both spatial coordinates in some bounded domain. Several examples of such construction are given explicitly.

Identifying community structures in bipartite networks is a popular topic. People usually focus on one of two modes in bipartite networks when uncovering their community structures. According to this understanding, we design a community detection algorithm based on preferred mode in bipartite networks. This algorithm can select corresponding preferred mode according to specific application scenario and effectively extract community information in bipartite networks. The trials in artificial and real-world networks show that the algorithm based on preferred mode has better performances in both small size of bipartite networks and large size of bipartite networks.

Silicene sheet is prepared by atomistic multiscale modeling using molecular dynamics (MD) simulations to evaluate thermal properties of silicene at different temperatures and variable sample sizes. In this paper, by MD simulation study, we have estimated coefficient of linear and surface expansion between a temperature range from 318 K to 398 K, specific heat at constant volume and pressure, melting point, heat of fusion and thermal conductivity of silicene at different sample sizes by both equilibrium molecular dynamics (EMD) and non-equilibrium molecular dynamics (NEMD) approaches. The presented multiscale modeling approaches could guide experimental studies to design silicene sheet with required thermal properties for operation under specific conditions.

In this paper, by introduction of pseudopotentials, the nonlocal symmetry is obtained for the Ablowitz–Kaup–Newell–Segur system, which is used to describe many physical phenomena in different applications. Together with some auxiliary variables, this kind of nonlocal symmetry can be localized to Lie point symmetry and the corresponding once finite symmetry transformation is calculated for both the original system and the prolonged system. Furthermore, the nth finite symmetry transformation represented in terms of determinant and exact solutions are derived.

Employing the non-equilibrium Green’s function technique, we have obtained the formula for dc current of two one-dimensional multi-quantum dot arrays, which couple to each other via tunneling coupling between two quantum dots connected to four leads, respectively. The retarded Green’s function is a staircase type, terminating at the four leads. Furthermore, the four quantum dots case is demonstrated. The influence of inter-dot coupling strength and quantum dot energy level on the transmission probability for TL, TM and TN branches is investigated. A non-resonant band is observed. By adjusting energy levels of quantum dots, a resonance emerges in the region of the non-resonance band. The system can be used as a quantum switch.

In this paper, via the limit technique of long wave, the N-order rational solution of the (2+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is derived from the N-soliton solution. In particular, the bright–dark M-lump solution can be obtained from resulting N-order rational solution. This kind of lump wave in BKP equation exhibits the one-peak-one-valley structure which is different from that in KPI equation. In addition, graphical illustration presents the collision dynamics of multi-bright–dark lump waves.