International Journal of Modern Physics B

On the basis of the application in the Bose–Einstein condensation, we investigate a (3 + 1)-dimensional Gross–Pitaevskii equation with distributed time-dependent coefficients. With the aid of the Kadomtsev–Petviashvili hierarchy reduction method, we construct the $N$th-order rogue-wave solutions in terms of the Gram determinant by introducing appropriate constraints. Using different coefficients for the diffraction $\beta (t)$ and gain/loss $\gamma (t)$, we demonstrate the behaviors of the first- and second-order rogue waves by analytical and graphical means. We find that only if $\gamma (t)=3\beta (t)$, the rogue waves appear on the constant backgrounds; otherwise, the heights of the backgrounds change as time goes on. With the different choices of $\beta (t)$ and $\gamma (t)$, the long-live, rapid-reducing and periodic rogue waves are discussed. The separated and aggregated second-order rogue waves are also shown on the constant and periodical backgrounds.

According to new research, methane emissions contribute 25 percent more to global warming than previously assumed. Methane is a crucial precursor gas of tropospheric ozone, a dangerous air pollutant. Methane emissions are responsible for almost half of the reported growth in tropospheric ozone levels on a global scale. But it plays a vital role as an energy source, therefore, the study of methane cut reservoirs is essential. The injection of air can extract additional energy in high methane-cut reservoirs. The analysis is made to compute the theoretical potential of low air flooding in high methane-cut reservoirs. Computational Fluid Dynamics (CFD) is used to study the impact of injecting air on methane. The presence of carbon dioxide and oxygen when injected into the methane cut reservoir produces high-pressure air injection that may cause significant safety damage such as the potential for corrosion or explosion. Past field studies and reported solutions indicate that there are no insurmountable problems in the execution of high-pressure air injection. The results are harmful and need to take useful safety precautions for the engineers who are interested in experiments. The users of CFD use mathematical laws and models that exactly represent the phenomenon they are dealing with. The pressure induced by the air injection is simulated with the help of the Finite Volume Method (FVM). The velocity field near the outlet arises as higher pressure of air from the inlet is observed, whereas, the pressure near the outlet declines. The findings of this study can help for better understanding of outflow of methane from methane reservoirs.

Local available quantum correlations (LAQC), as defined by Mundarain et al., are analyzed for nonsymmetric 2-qubit X states, that is, X states that are not invariant under the exchange of subsystems and therefore have local Bloch vectors whose norms are different. A simple analytic expression for their LAQC quantifier is obtained. As an example, we analyze the local application of the amplitude damping channel for Werner states and general X states. Although this local quantumchannel can create quantum discord in some cases, no such outcome is possible for LAQC, which hints toward their monotonicity under LOCC operations. This work, along with our previous result for the so-called symmetric and anti-symmetric X states, completes the pursuit of exact analytical expressions for the LAQC quantifier for 2-qubit X states.

Nowadays, the heat transfer potential of the base fluids can also be improved by adding nanoparticles to them. These nanotechnology-based fluids, called nanofluid, have superior properties such as high thermal conductivity, large critical heat flux (CHF) and improved heat transfer coefficient. The purpose of this paper is to study the thermal effectiveness of nanoparticles in transient flow of Maxwell fluid together the properties of mixed convection and magnetic field. Thermal field is controlled with the novel aspects of variable conductivity and nonuniform heat sink/source. Additionally, the impact of Brownian and thermophoretic diffusions is considered caused by nanoparticles dispersion in the fluid. The appropriate conversions yield the governing nonlinear ordinary differential system. Homotopic approach has been utilized to attain the solution of differential system and results are envisioned graphically. This study explores that the buoyancy ratio and mixed convection parameters enhance the velocity field. Further, the heat transfer rate rises significantly as the thermophoretic and Brownian diffusion parameters increase. Moreover, the effect of nonuniform heat source/sink on temperature field is noticed to be an increasing trend of temperature profile.

Some physical properties (structural and electronic) of Zn-based wurtzite structures have been theoretically studied by the density functional theory (DFT). Ab-initio calculations were done using the plane-wave pseudo-potential method within the Atomistix ToolKit (ATK) software package. Detailed investigations on the structural and electronic properties of the binary bulk compounds, ZnO and ZnSe, have been conducted and compared with the obtained studies. Using the modified Becke–Johnson potential has successfully improved the calculated bandgap. From the first-principles calculations for investigated compounds, it is obtained that the valence band maximum and the conduction band minimum, mainly originate from O (Se) $p$- and Zn $s$-states. The calculated values of electronic bandgaps of both the compounds are closer to the experimental results, and studied compounds are direct bandgap semiconductors with the transition along with $\mathrm{\Gamma }$–$\mathrm{\Gamma }$ symmetry.

The progress in new inventions in the modern technological world demands outstanding heat transport. Unfortunately, common solvents are unable to produce such desired amount of heat which compelled the scientists and researchers towards the development of new heat transfer fluids (Nanofluids). Therefore, the study of C₈H${}_{18}$ with hybridization of [(MnZnFe₂O₄–NiZnFe₂O${}_4)$]${}_{\mathrm{\text{hnps}}}$ under novel effects of thermal radiations and convective heat conditions over a slippery permeable surface is organized. The modified thermophysical correlations for hybrid nanofluids were used and successfully achieved the modified heat transfer model. After numerical investigation, the results were plotted under varying parameters and provided for comprehensive discussion. The results revealed faster fluid motion and $G^{\prime }(\eta )$ is dominant. The velocities drop significantly due to the permeability of the surface. Further, thermal radiations potentially boost heat transfer by providing extra energy to fluid particles. The temperature coefficient ${\beta }_w$ due to nonlinear thermal radiations also indicated faster heat transport.

In this work, the transmittance spectrum for a defective one-dimensional photonic crystal was calculated. The crystal was composed of alternating GaAs and SiO₂ layers, and its cavity was infiltrated by escherichia coli bacteria, which was surrounded by thin graphene layers. In this study, we assumed that the GaAs dielectric constant depends on the pressure applied. Within the photonic bandgap, a defect mode that tunes to decreasing wavelengths, as pressure increases can be observed. This shift in the transmittance spectrum is coupled with a decrease in the energy stored within the cavity. In addition, when the graphene-layer thickness was increased while maintaining the pressure constant at 0 GPa, the defect mode is tuned to a long wavelength, which favors two confined modes for thicknesses more than 33 nm.

This paper examines nonlinear partial differential equation (PDE) solutions. Scientists and engineers have struggled to solve nonlinear differential equations. Nonlinear equations arrive in nearly all problems in nature. There are no well-established techniques for solving all nonlinear equations, and efforts have been made to enhance approaches for a specific class of problems. Keeping this in mind, we shall investigate the perturbation method’s efficiency in solving nonlinear PDEs. Several techniques work well for diverse issues. We recognize that there may be several solutions to a given nonlinear issue. Methods include homotropy analysis, tangent hyperbolic function, factorization and trial function. However, some of these strategies do not cover all nonlinear issue solutions. In this paper, we use the perturbation technique to solve the zeroth-order Airy equation and also find the Bessel function in the first-order nonhomogeneous differential equation by using self-similar solutions that appears in modified Korteweg–de Vries (KdV) equation. This approach will be used for nonlinear equations in physics and applied mathematics.

In this paper, the thermal analysis is performed on the three-dimensional flow of viscous nanofluid over a rotating disk. The disk rotation is assumed as of the form $(v\sim r^m)$ where $(m\ge 1)$, thus, there are different azimuthal velocities of the disk at different radii, and it increases with the increase in $m$. Also, the effect of nanoparticles on the thermal conductivity of fluid is investigated by thermophoresis and Brownian motion features. For the governing problem, suitable similarity transformations are employed that convert the produced partial differential equations to ordinary differential equations. The flow field and energy transport are presented graphically and discussed in detail for the torsional exponent $m$, $N_t$ and $N_b$, respectively. It is noted that the temperature and concentration profile rise for the thermophoresis parameter while the opposite trend showed for Brownian motion. Moreover, the power-law index parameter $m$ declines the flow field temperature and concentration profiles.

In this paper, a convective fluid flow mixed with different nanoparticles (NPs) flowing on a vertical plate is studied. The impacts of slip boundary wall, Newtonian heating, and magnetic field are also pondered. Using Fourier’s rule of heat conductivity and Caputo-time (CT) fractional derivative (FD), the nondimensional governing equations for this mathematical model are obtained. The Laplace transformation (LT) technique is used to get a generalized solution to the equations of momentum and energy. The physical interpretation of velocity distribution in some particular cases is well recognized in the past research works and is also highlighted to scrutinize some further physical perception into the subject and to fortify the novelty of this research communication. Furthermore, graphical depictions are created using the mathematica program to assess the physical importance of the considered topic. As a result, we concluded that the blood-based aluminium oxide ($\mathrm{\text{A}}{\mathrm{\text{l}}}_2{\mathrm{\text{O}}}_3)$ NPs show more decaying behavior as compared to titanium dioxide ($\mathrm{\text{Ti}}{\mathrm{\text{O}}}_2)$ NPs for temperature and velocity profile. Moreover, changing the fractional parameter’s value for a long period of time improves thermal and velocity profiles.