Modern Physics Letters B

Nanocrystalline Ni–Zn–Al spinel ferrite was synthesized via citrate-gel auto combustion method. The as-prepared powders have been separated into two batches in which one batch of powders were sintered at 1000${}^{\circ }$C for 4 h and the other batch were pressed into pellets and were sintered at the same temperature. Sintering of the samples was done in air atmosphere followed by natural cooling to room temperature. The heat treated powders have then been characterized using TG–DTA, XRD, SEM and TEM for thermal, structural and microstructural aspects while the DC electrical resistivity measurements were carried out on the sintered pellets. The X-ray diffraction patterns displayed the formation of the spinel phase for all powders and the lattice parameter was obtained using Bragg’s law. The crystallite size for all compositions were found to be in nano dimensions and obtained from the Williamson–Hall method. TG–DTA analysis of the undoped ${\mathrm{\text{Ni}}}_{0.5}{\mathrm{\text{Zn}}}_{0.5}{\mathrm{\text{Fe}}}_2{\mathrm{\text{O}}}_4$ indicated the formation of the spinel phase is around 400${}^{\circ }$C while almost uniform microstructure with a more or less spherical grains has been noticed in the SEM micrograph. An enhancement in the DC electrical resistivity ($\ge 10^8\mathrm{\Omega }$-cm) has been observed in ${\mathrm{\text{Ni}}}_{0.5}{\mathrm{\text{Zn}}}_{0.5}{\mathrm{\text{Fe}}}_2{\mathrm{\text{O}}}_4$ synthesized using this technique in comparison with that processed through conventional ceramic technique and a modification in the resistivity has been observed on substituting ${\mathrm{\text{Al}}}^{3+}$ in place of ${\mathrm{\text{Fe}}}^{3+}$. High electrical resistivity makes these ferrites suitable for high-frequency applications due to possible reduction of the eddy current losses. The observed variation in resistivity has been discussed on amendments in structure, microstructure and unavailability of ${\mathrm{\text{Fe}}}^{3+}$ ions with increasing ${\mathrm{\text{Al}}}^{3+}$ ions in the light of existing understanding. The decrease in resistivity with increasing temperature confirms the semiconducting behavior of all samples. Activation energies for conduction were obtained from the slope of the log $\rho$ versus $1/T$ plots and observed to be in the range of 0.6–0.45 eV. The variation in the activation energy for conduction followed a similar trend as the DC resistivity. The drift mobility decreases with increasing ${\mathrm{\text{Al}}}^{3+}$ ions concentration and increases with increasing temperature.

Under investigation in this paper is an inhomogeneous nonlinear Schrödinger equation, which describes the propagation of a large-wavelength small-amplitude electron plasma wave in a parabolic-distributed and constant-interactional-damping inhomogeneous plasma. Via the Hirota method, Bell-polynomial approach and symbolic computation, bilinear form, Bäcklund transformation and $N$-soliton solutions are obtained. Influence of the linear density coefficient $\alpha$ and damping coefficient $\beta$ on the soliton envelopes is also discussed, i.e. $\alpha$ can affect the soliton position, while $\beta$ is related to the soliton intensity, velocity and phase shift. Periodically attractive and repulsive interactions are shown. Asymptotic analysis shows that the interactions between/among the solitons are elastic.

It is well known that traffic flow presents multi-fractal characteristics at time scales. The aim of this study is to test its multi-fractality at spacial scales. The vehicular cellular automation (CA) model is chosen as a tool to get vehicle positions on a single lane road. First, multi-fractal of vehicle distribution is checked, and multi-fractal spectrums are plotted. Second, analysis results show that the width of a multi-fractal spectrum expresses the ratio of the maximum to minimum densities, and the height difference between the left and right vertexes represents the relative size between the numbers of sections with the maximum and minimum densities. Finally, the effects of the random deceleration probability and the average density on homogeneity of vehicle distribution are analyzed. The results show that random deceleration increases the ratio of the maximum to minimum densities, and deceases the relative size between the numbers of sections with the maximum and minimum densities, when the global density is limited to a specific range. Therefore, the multi-fractal spectrum can be used to quantify the homogeneity of spacial distribution of traffic flow.

The influence of ${\mathrm{\text{R}}}^{3+}$ ion sizes on the electrical resistivity, Seebeck coefficients, thermal conductivity and $ZT$ values of ${\mathrm{\text{RBaCo}}}_4{\mathrm{\text{O}}}_{7+\delta }$ prepared by the solid-state reaction method was investigated from 373 K to 973 K. The electrical resistivity decreases with decreasing ${\mathrm{\text{R}}}^{3+}$ ion sizes. Both the electrical resistivity and the Seebeck coefficients have a transition at about 630 K. Especially, the transition phenomenon disappears gradually with decreasing ${\mathrm{\text{R}}}^{3+}$ ion sizes, and is attributed to the oxygen adsorption of ${\mathrm{\text{RBaCo}}}_4{\mathrm{\text{O}}}_{7+\delta }$. The $ZT$ values increase with rising temperature or decreasing ${\mathrm{\text{R}}}^{3+}$ ion sizes. The ${\mathrm{\text{InBaCo}}}_4{\mathrm{\text{O}}}_{7+\delta }$ with the smallest ${\mathrm{\text{R}}}^{3+}$ size has the maximum $ZT$ value that reaches 0.1 at 973 K.

Molecular dynamics simulations are used to study the mechanical behavior of single-walled carbon nanotube reinforced composites. Polyethylene and polyketone are selected as the polymer matrices. The effects of nanotube atomic structure and diameter on the mechanical properties of polymer matrix nanocomposites are investigated. It is shown that although adding nanotube to the polymer matrix raises the longitudinal elastic modulus significantly, the transverse tensile and shear moduli do not experience important change. As the previous finite element models could not be used for polymer matrices with the atom types other than carbon, molecular dynamics simulations are used to propose a finite element model which can be used for any polymer matrices. It is shown that this model can predict Young’s modulus with an acceptable accuracy.

For the first time in this paper, we have studied sonic propagation and causal evolution for dissipative relativistic superfluid in the framework of second-order dissipative theory. General features of the evolution modes are provided and the sound speeds are identified as the propagation of discontinuity, in agreement with earlier theoretical studies. Moreover, the growth equation is obtained to describe the decay and growth of the discontinuity propagating along its normal trajectory. The solution is in an integral form and various cases are discussed. Some important features of the second-order theory are also presented for the first time, which may be meaningful for future experiments to identify the dissipative theory of relativistic superfluidity.

In this paper, we use car-following model to explore each commuter’s trip cost and the system’s total trip cost in the commuter’s system allowing late arrival. The numerical results show that each commuter’s trip cost and the system’s total trip cost are related to each commuter’s time headway at the origin and the proportion of the commuters’ late arrival, but the system’s total trip cost has the minimum value that is irrelevant to the proportion of the commuters’ late arrival.

${\mathrm{\text{La}}}_{0.1}{\mathrm{\text{Bi}}}_{0.9-x}{\mathrm{\text{Sr}}}_x{\mathrm{\text{FeO}}}_{(3-x/2)}({\mathrm{\text{LBFS}}}_{x}0\le x\le 0.8)$ ceramics were synthesized by solid-state reaction method, and their magnetic properties and conductive characteristics were investigated and discussed. It is found that La-doped ${\mathrm{\text{BiFeO}}}_3$ ceramic without ${\mathrm{\text{Sr}}}^{2+}$ doping is a rhombohedrally distorted perovskite structure, and with the increase of the ${\mathrm{\text{Sr}}}^{2+}$ concentration, the phase transits gradually from rhombohedral to pseudo cubic symmetry. Electrical and magnetic properties show strong dependence on ${\mathrm{\text{Sr}}}^{2+}$ dopant level. The measurement demonstrates that ${\mathrm{\text{LBFS}}}_x$ with 30% ${\mathrm{\text{Sr}}}^{2+}$ dopant exhibits the lowest values of the leakage current, dielectric constant $(\epsilon )$ and dielectric loss $(tan\delta )$. And the highest value of saturation magnetization of about 4.5 emu/g is observed in 60% Sr-doped ${\mathrm{\text{LBFS}}}_x$. An abnormal enhancement of the conductivity was observed in ${\mathrm{\text{LBFS}}}_x$ ceramics with $x$ = 0.60 and 0.70, and their magnitude of conductivity is nearly six orders larger than that of pure ${\mathrm{\text{LBFS}}}_x$.