Polaron effects and charge carrier mobility in high-$T_c$ cuprate superconductors (HTSCs) have been investigated theoretically. The appropriate Boltzmann transport equations under relaxation time approximation were used to calculate the mobility of polaronic charge carriers and bosonic Cooper pairs above and below the pseudogap (PG) temperature $T^\ast$. It is shown that the scattering of polaronic charge carriers and bosonic Cooper pairs at acoustic and optical phonons are responsible for the charge carrier mobility above and below the PG temperature. We show that the energy scales of the binding energies of large polarons and polaronic Cooper pairs can be identified by PG cross-over temperature on the cuprate phase diagram.

A rigorous theoretical investigation has been carried out on the propagation of nonplanar (cylindrical and spherical) dust-acoustic shock waves (DASHWs) in a collisionless four-component unmagnetized dusty plasmasystem containing massive, micron-sized, positively and negatively charged inertial dust grains along with $q$ (nonextensive) distributed electrons and ions. The well-known reductive perturbation technique has been used to derive the modified Burgers equation (which describes the shock wave properties) and its numerical solution. It has been observed that the effects of charged dust grains of opposite polarity, nonextensivity of electrons and ions, and different dusty plasma parameters have significantly modified the fundamental properties (viz., polarity, amplitude, width, etc.) of the shock waves. The properties of DASHWs in nonplanar geometry are found tobe significantly different from those in one-dimensional planar geometry. The findings of our results from this theoretical investigation may be useful in understanding the nonlinear features of localized electrostatic disturbancesin both space and laboratory dusty plasmas.

We introduce local filters as a means to detect the entanglement of bound entangled states which do not yield to detection by witnesses based on positive maps which are not completely positive.We demonstrate how suchnon-detectable bound entangled states can be locally filtered into detectable bound entangled states. Specifically, we show that a bound entangled state in the orthogonal complement of the unextendible product bases (UPB), canbe locally filtered into another bound entangled state that is detectable by the Choi map. We reinterpret these filters as local measurements on locally extended Hilbert spaces. We give explicit constructions of a measurement-basedimplementation of these filters for 2$\otimes$2 and 3$\otimes$3 systems. This provides us with a physical mechanism to implement such local filters.

Vanadium pentoxide layer deposited on the fluorine-doped tin oxide (FTO) anode by vacuum deposition has been investigated in organic light-emitting diode (OLED).With 12nm optimal thickness of $V_{2}O_{5}$, the luminance efficiency is increased by 1.66 times compared to the single FTO-based OLED. The improvement of current efficiency implies that there is a better charge injection and better controlling of hole current. To investigate the performance of OLED by the buffer layer, $V_{2}O_{5}$ films of different thicknesses were deposited on the FTO anode and their $J–V$ and $L–V$ characteristics were studied. Further analysis was carried out by measuring sheet resistance, optical transmittance and surface morphology with the FE-SEM images. This result indicates that the $V_{2}O_{5}$ (12 nm) buffer layer is a good choice for increasing the efficiency of FTO-based OLED devices within the tunnelling region. Here the maximum value of current efficiency is found to be 2.83 cd/A.

Inspired by the works of Ohta and Yang, we construct general high-order rogue wave solutions for the $(2 + 1)$-dimensional Hirota equation using the bilinear transformation method. The formula of the solutions can be represented in terms of determinants. It is shown that the order of rogue waves will depend on the roots of determinants. These rogue waves are line rogue waves, which arise from the constant background with a line profile and then disappear into the constant background again. In addition, some interesting dynamic patterns of rogue waves are exhibited in the $(x, y)$ and $(x, t)$ planes.

We calculate quark number density and susceptibility under one-loop correction in the mean-field potential. The calculation shows continuous increase in the number density and susceptibility up to the temperature $T = 0.4 \rm{GeV}$. Then the values of number density and susceptibility approach the very weakly result with higher values of temperature. The result indicates that the calculated values fit well with increase in temperature to match the lattice QCD simulations of the same quantities.

A direct rational exponential scheme is introduced and applied to construct exact multisoliton solutions of the clannish random walker’s parabolic and the Vakhnenko–Parkes equations. We discuss the nature of solitonsolutions before and after their interactions, and present their fusion (non-elastic) and elastic collisions of the soliton solutions. These soliton solutions of the equations are connected to physical phenomena: weakly non-linearsurface, internal waves in a rotating ocean and interacting population motions. In addition, some three-dimensional and contour plots of the soliton wave solutions are presented to visualize the dynamics of the models.

In order to further understand a self-exciting Faraday disc dynamo (Hide $\it{et al}$, in $\it{Proc. R. Soc}.$ A $\bf{452}$, 1369 1996), showing chaotic attractors with very complicated topological structures, we present codimension one and two (degenerate) Hopf bifurcations and prove the existence of periodic solutions. In addition, numerical simulations are given for confirming the theoretical results.

Nickel–zinc ferrites with the general chemical formula, $Ni_{0.3}Zn_{0.7−x}Mg_{x}Fe_{2}O_{4}$ with $x$ varying from 0.00 to 0.25 in steps of 0.05, have been prepared by conventional solid-state method. Final sintering of the samples was carried out at 1200$^{\circ}$C for 6h in air to investigate their structural and magnetic properties. X-ray diffraction patterns of all the samples confirm the cubic spinel structure. Percent porosity and lattice constants of the samples are similar for all the samples except for the sample with $x = 0.05$ implying that the changes in magnetic properties could be solely attributed to the effects caused by substitutions only. The saturation magnetization has been observed to increase continuously with the substitution of $Mg_{2+}$ ions in the place of $Zn_{2+}$ ions. Curie temperature of the system was also found to increase from 261$^{\circ}$C $(x = 0.00)$ to 364$^{\circ}$C $(x = 0.25)$ with the increase in magnesium content. Smooth coercivity variation suggests better structural homogeneity. The results are discussed in the light of the distribution of the cations among octahedral and tetrahedral sites.

The Saha equations for the photoionization process of hydrogen atoms and the creation of electron–positron pairs at high temperature are investigated in a reference frame undergoing a uniform accelerated motion. It is known as the Rindler space.

Accuracy of the Kramers approximate formula for the thermal decay rate of the metastable state is studied for the two-dimensional potential pocket. This is done by comparing with the quasistationary rate resulting from the dynamical modelling. It is shown that the Kramers rate is in agreement with the quasistationary rate within the statistical errors provided the absorptive border is far enough from the potential ridge restricting the metastable state. As the absorptive border (or its part) gets closer to the ridge, the Kramers formula underestimates the quasistationary rate. The difference reaches approximately the factor of 2 when the absorptive border coincides with the ridge.

In this paper, the methodology to achieve combination synchronization of time-delay chaotic system via robust adaptive sliding mode control is introduced. The methodology is implemented by taking identical time-delayLorenz chaotic system. The selection of switching surface and the design of control law is also discussed, which is an important issue. By utilizing rigorous mathematical theory, sufficient condition is drawn for the stability of error dynamics based on Lyapunov stability theory. Theoretical results are supported with the numerical simulations. The complexity of this methodology is useful to strengthen the security of communication. The hidden message can be partitioned into several parts loaded in two master systems to improve the accuracy of communication.

We present three schemes for the joint remote state preparation (JRSP) of an arbitrary four-qubit W-type entangled state with complex coefficients via four and two three-qubit GHZ states as the quantum channel. In these schemes, two senders (or $N$ senders) share the original state which they wish to help the receiver to remotely prepare. To complete the JRSP schemes, some novel sets of mutually orthogonal basis vectors are introduced. It isshown that, only if two senders (or N senders) collaborate with each other, and perform projective measurements under suitable measuring basis on their own qubits, the receiver can reconstruct the original state by means of some appropriate unitary operations. It is shown that, in all our schemes, the total success probability of the JRSP can reach 1. Specially, compared with the first scheme in our paper, the entanglement resource in the second scheme can be reduced. This means that the scheme is more efficient and economical.

The search for extra dimensions has so far yielded no positive results at the LHC. Along with the discovery of a 125 GeV Higgs boson, this implies a moderate degree of fine-tuning in the parameter space of the Randall–Sundrum model. Within a six-dimensional warped compactification scenario, with its own interesting phenomenological consequences, the parameters associated with the additional spatial direction can be used to eliminate the need for fine-tuning.We examine the constraints on this model due to the 8 TeV LHC data and survey the parameter space that can be probed at the 14 TeV run of the LHC. We also identify the region of parameter space that is consistent with the recently reported excess in the diphoton channel in the 13 TeV data. Finally, as an alternative explanation for the observed excess, we discuss a scenario with brane-localized Einstein–Hilbert terms with Standard Model fields in the bulk.