International Journal of Modern Physics B

This work proposes a semi-analytical new hybrid approach, so-called differential $𝕁$-transform method (D$𝕁$TM), to evaluate the behavior of n-space dimensional fractional-nonlinear hyperbolic-like wave equations, where time-fractional derivative is considered in Caputo format. The D$𝕁$TM is the hybrid method in which projected differential transform is implemented after imposing the recently introduced integral transform, i.e., so-called $𝕁$ transform [W. Zhao and S. Maitama, J. Appl. Anal. Comput. 10, 1223 (2020)]. The efficiency and applicability of the proposed D$𝕁$TM had been tested by considering three different test examples of the Caputo time-fractional nonlinear hyperbolic-like wave equations in terms of absolute error norms, and the different order D$𝕁$TM solutions are compared with exact solution behaviors and the existing results, for the large time level $\tau \in [0,10]$. In addition, the convergence analysis of D$𝕁$TM is studied theoretically and verified it numerically as well as graphically, which confirms that the numerical experiments via D$𝕁$TM for distinct fractional orders support the theoretical findings excellently, and the presented D$𝕁$TM results converge to their exact solution behavior, very fast. The evaluated series approximations are expressed in the compact form of Mittag-Leffler functions.

Particle dissolution is an important process that occurs during heat treatment in the transportation process. We present a one-dimensional model of spherical wax particle dissolution in a fluid. The model includes a nonlinear equation at the free boundary, which was established to describe the dissolution rate of a wax particle assuming a diffusion process. At the moving boundary, we compute the concentration distributions of partial solutions. To estimate wax dissolution in solution and related expressions for the dissolved radius, an analytical solution of a mathematical model for spherical particle dissolution in flow is used.

The hydromagnetic flow of magnetite–water nanofluid due to a rotating stretchable disk has been numerically assessed. The nanofluid flow has been modeled utilizing the adapted Buongiorno model that considers the volume fraction-dependent effective nanofluid properties and the major slip mechanisms. In addition, experimentally gleaned functions of effective dynamic viscosity and effective thermal conductivity are deployed. The modeled equations are transformed into a first-order ODEs scheme employing Von Kármán’s similarity conversions and then resolved via the Runge–Kutta algorithm through the shooting technique. The impact of pertinent terms over the physical quantities, nanoliquid temperature and nanoliquid concentration is explained with the support of graphs. Results show that rising volume fraction of magnetite nanoparticles (NPs) and magnetic field term enhance the drag force. Mass transport rate is demoted with augmenting values of magnetic field parameter whereas is promoted with increase in Schmidt number. Further, it is detected that the changes in stretching strength parameter are directly proportional to Nusselt number and inversely proportional to the thermal field. The findings of this numerical analysis have applications in spin coating, rotating disk reactors, storage devices for computers, food processing, and rotating heat exchangers.

Analyzed in this paper is an investigation of the impacts of the varying source of heat or thermal sink and viscous dissipation on Casson fluid flow from a moving wedge by considering thermal and momentum slips in a mathematical model. Regarding the regulation of concentration fields, we incorporated the Soret and Dufour phenomena. The outcomes are analyzed numerically by using the shooting technique. The governing parametric effects of the flow characteristics are revealed graphically. We also presented the local Sherwood and Nusselt number values for non-Newtonian fluid (Casson fluid) and Newtonian. It is discovered that the thermal and concentration boundary layer is more extensive in Casson fluid while equated with the Newtonian fluid. The thermal and mass transmission in Newtonian fluid is significantly larger than in non-Newtonian fluid. The heat source/sink, Eckert number and Dufour number boost the rate of thermal transport and depreciate the rate of mass transport for both the Newtonian and non-Newtonian fluid cases.

We derive a quantum Langevin equation for a quantum spin in the presence of a magnetic field and coupled to a bath. We have considered two models for the bath: an Ohmic bath model and a non-Markovian Drude bath model with finite memory. The effect of finite memory on the dynamics of the quantum spin is studied in detail. In particular, we have studied the effect of memory on the expectation values of the magnetic moment and the spin correlation functions. The time evolution study of the spin correlation functions shows that the correlation functions exhibit a damped oscillatory behavior with the randomization time being determined by the damping rate. We have analytically shown that the damping gets affected by the finite memory time when the bath retains memory of the interaction with the system. We also analyze the spin response function of the system for the Ohmic bath. Our results qualitatively agree with the findings in spin noise spectroscopy experiments and our predictions can be tested in future ultracold atom experiments.

In this paper, the investigated mixture of liquid crystals shows a spacious range of twist grain boundary phases (TGBPs). Thermo dynamical, optical and dielectric measurements confirmed the presence of TGBPs in the mixtures of nematic and cholesteric liquid crystals. In the heating cycle, differential scanning calorimetry (DSC) thermogram shows the mixed different TGBPs at the high scanning rate. Cylindrical and cone-like textures with brushes of TGBA* is observed under the optical investigation. The grain boundaries and blocks of smectic phases are twisting two times around an axis. Wide-ranging dielectric investigation of nematic and cholesteric liquid crystal mixture have been performed in the 50 Hz–10 MHz range of frequency for the homogeneous conditions. In the absence of direct bias, TGBA* phase exhibits two dielectric relaxation processes, soft mode (SM) and process in the grain boundaries (PGBs). In the presence of electric field, grain boundaries steadily demolished the phases. Whereas the weak dielectric relaxation processes have been distinguished in the presence of the electric field in the TGBPs.

In this paper, we have performed a study on the optical properties of single crystals ZnGa₂S₄ by method of density functional theory (DFT) and ellipsometry measurements. The calculated results for the real ${\epsilon }_r$ and imaginary ${\epsilon }_i$ parts of the dielectric function are compared with the measured experimental spectroscopic ellipsometry (SE) spectra in the 0.7–6.5 eV spectral region. Absorption coefficient-photon energy dependency revealed the existence of direct bandgap transitions with energy 3.5 eV. This result is very close to bandgap obtained from our theoretical calculation.

In this paper, we study bioconvection radiative flow of power-law nanofluid. Nanofluid characteristics are incorporated by utilizing the Buongiorno model. The influence of motile gyrotactic microorganism is retained. Magnetohydrodynamics and time-dependent aspects are under consideration. Related governing expressions are transformed into dimensionless partial differential system. The resulting nonlinear system is tackled through finite difference technique. Outcomes of emerging variables like Prandtl number, Hartmann number, Buoyancy ratio parameter, Grashof number, Peclet number, bioconvection Rayleigh number, Peclet number, radiation and Schmidt number are graphically discussed. Velocity is controlled by higher Hartman number while it boosts against higher Grashof and bioconvection Rayleigh numbers, buoyancy ratio and stretching parameters. Higher radiation, Brownian and thermophoresis parameters lead to intensification in temperature profile while it reduces for higher Prandtl number. Bioconvection profile reduces against higher Peclet and Lewis numbers.

This paper discusses the generalized $(2+1)$-dimensional Hietarinta-type fourth-order nonlinear equation (GHTE) and Resonant nonlinear Schrödinger equation (RNLSE). We will study the soliton solutions of the GHTE as well as RNLSE by the renowned, efficient and successful method called sub-ODE technique. The solutions are categorized as dark soliton, periodic, rational, positive, hyperbolic and Weierstrass elliptic solutions (WES). Stability analysis of the solutions is performed for both the models. Later on, these results will be displayed graphically by 3D, 2D, contour, density and streamline plots which describe the behavior of the waves.

This paper tackles the recently introduced (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation (4D-BLMPE) utilized to model wave phenomena in incompressible fluid and fluid mechanics. Modified extended tanh expansion method (METEM) and the new Kudryashov scheme are implemented to produce analytical soliton solutions for the presented equation. The traveling wave transformation is constructed, and the homogeneous balance principle is utilized to apply the two proposed techniques. Furthermore, the flat-kink, smooth-kink, singular, and periodic singular solutions are successfully extracted. Some produced solutions are illustrated graphically to understand the physical meaning of the presented model. Moreover, for the first time in this study, the effect of model parameters on kink soliton dynamics is examined, and graphical representations are depicted and interpreted.

The examined through analysis of the movement of water-based single wall carbon nanotube (SWCNT) and multiwall carbon nanotube (MWCNT) nanofluids in a coordinate annulated zone under influence of non-uniform heat source/sink. By imposing the appropriate nondimensional variables, the governing partial differential equations are converted into a system of coupled nondimensional partial differential equations. By means of the usage of quadratic polynomials and the Galerkin finite element detail approach, the nonlinear equations have been executed. The expressions representing fluid velocity, temperature and concentration are discussed graphically. While skin friction, heat transfer and mass transfer are revealed in tabular structure. The proposed scheme is shown to have faster convergence than the existing scheme with excellent accuracy. Various parametric values have been analyzed and observed that higher temperatures and concentrations are produced with lower velocities with and bigger velocities with higher radiative heat flux or nanoparticle volume fraction.

Hyper-chaotic systems have useful applications in engineering applications due to their complex dynamics and high sensitivity. This research is supposed to introduce and analyze a new noninteger hyper-chaotic system. To design its fractional model, we consider the Caputo fractional operator. To obtain the approximate solutions of the extracted system under the considered fractional-order derivative, we employ an accurate nonstandard finite difference (NSFD) algorithm. Moreover, the existence and uniqueness of the solutions are provided using the theory of fixed-point. Also, to see the performance of the utilized numerical scheme, we choose different values of fractional orders along with various amounts of the initial conditions (ICs). Graphs of solutions for each case are provided.

The electrohydrodynamics (EHD) instability of two separate overlapping viscous particle fluids moving in a porous medium is the subject of this paper. The incompressible packaging contains microscopic, uniformly sized fine dust particles. The system is influenced by a tangential electric field that remains constant. The abbreviated formulation of Hsieh is employed to account for the impact of mass and heat transfer (MHT). The problem solution follows the viscous potential theory (VPT) because of the problem complexity in mathematics. The significance of fluid-particle mixing in several applications of practical physics and engineering operates as the guiding force behind this investigation. The standard normal modes methodology is used to examine the standard fundamental equations of motion. The essential mechanisms of the nonlinear technique are the formulations of the linear controlling fundamental formulae and the application of the appropriate nonlinear boundary criteria. A number of nondimensional characteristic parameters are produced by the technique. The nonlinear stability results in a nonlinear Landau–Ginzburg equation. By giving the physical parameter numerical values, the stability designs have been graphically represented. Therefore, both linear and nonlinear approaches are depicted to illustrate the impacts of different physical quantities. Using the homotopy perturbation approach and the idea of extended frequency, a uniform approximate solution for a nonlinear interface displacement is provided. He’s frequency approach yields another nonperturbative solution of the surface displacement solution, which is validated using the Runge–Kutta method.

Researchers always like to find way for improving the performance of system integrated with PCM. In this paper, the container was combined with fins and PCM was mixed with nanoparticles to obtain quicker discharging process. Two significant variables related to second technique are fraction of additives ($\varphi )$ and their shapes ($m)$. To involve these factors in equations, single phase formulation was applied. Low magnitude of velocity of liquid material in freezing leads to simplification of equations of this transient procedure. Galerkin method which was applied for this modeling has good accommodation with previous publication. As $\varphi$ soars, the solidification time declines from 4802.97s to 4244.61s and 3738.37s when blade shape particles were applied. This means that adding additive can enhance the rate of process about 22.16%. Moreover, augmenting the shape factor to higher level causes time to drop about 5.7%.

Due to its remarkable thermodynamic development in various engineering sciences, the dispersion of nanostructures in classical base liquids is receiving greater attention from researchers and scientists. In light of the aforementioned inspirations, the suggested research is associated with using a water-based ternary-hybrid nanofluid that contains three unique nanostructures, silicon dioxide, titanium dioxide and aluminum oxide to optimize the heating process in science and engineering. In this situation, the influence of a chemically reactive magneto-hydrodynamics (MHD) Darcy–Forchheimer ternary hybrid composites transport involving nonlinear radiation across an exponentially permeable stretched surface is highlighted with the model’s physical initial and boundary constraints. The simulation of the heat expression also includes the impacts of nonlinear thermal radiations, energy supply, energy dissipation and magnetic force. Furthermore, the interpretation of Buongiorno’s theory involves spontaneous and thermophoresis diffusions. Entropy analysis is explained using the second law of thermodynamics. We converted the model framework for fluid movement, energy and mass transfer (together with ternary hybrid nanofluid characteristics) into self-similar nondimensional differential equations, that were then further analytically evaluated by using the homotopy asymptotic method (HAM) technique via Mathematica software. The acquired results are illustrated numerically and graphically to study the behavior of fluid flow, heat, concentration distribution, drag force, rate of heat and mass transfer for various emergent components to gain scientific comprehension. With the growing values of magnetic, porosity and Forchheimer number, the nature of the velocity profile goes down.