Modern Physics Letters B

Topological quantum numbers are often used to characterize the topological order of phase having protected gapless edge modes when the system is kept in a space with the boundary. The famous examples in this category are the quantized electrical Hall conductance and thermal Hall conductance, which encodes the topological order of integer and fractional quantum Hall states. Here, we review the recent thermal transport study of integer and fractional quantum Hall states realized in graphene-based van der Waals heterostructures.

Significance: Heat transport in the blood within a wedge-shaped artery is significant in biomedical engineering field like develop therapeutic strategies, drug delivery to specific regions of the artery, vicinity of narrowed or blocked arteries and catheter-based treatments such as angioplasty or thermal ablation.

Motive: This study investigates the heat transport analysis of trihybrid nanofluid (blood) over wedge-shaped artery with mathematical model of Cross fluid. This study incorporates three nanoparticles, graphene oxide (GO), titanium dioxide (TiO₂), and aluminum oxide (Al₂O₃) in base fluid blood. The wedge-shaped artery is chosen due to its relevance to biomedical applications and it reflects the nature of blood flow in real vascular structures. Heat transport is scrutinized through thermal radiations and flow rate is inspected through inclined magnetic field.

Methodology: The bvp4c and Levenberg–Marquardt Neural Network (LM-NN) supervised neural scheme is used to predict the numerical outcome of this study.

Findings: Incorporation of nanoparticles made rapid heat transport of blood in wedge-shaped artery. Velocity of blood is decreased with high Weissenberg number and magnetic force. The temperature of a blood in a wedge-shaped artery increases with positive non-uniform heat source/sink parameters and decreases with negative non-uniform heat source/sink parameters.

The primary aim of this paper is to investigate the dynamic behavior of generalized nonlinear fractional Tzitzéica-type equations and to derive optical soliton solutions. To achieve this goal, we employ the modified Khater method, focusing on obtaining solitary wave solutions for generalized fractional Tzitzéica-type (TT) equations. Through this approach, we unveil novel solutions for both Tzitzéica and Tzitzéica–Dodd–Bullough (TDB) equations expressed in terms of fractional derivatives. The significance of employing the modified Khater method lies in its ability to yield a diverse array of soliton solutions. These solutions encompass dark, bright, singular, periodic, kink, singular kink, and combined dark–bright solitons. The derived solutions are visually represented through two-dimensional (2D) and three-dimensional (3D) graphs. Our findings underscore that the proposed method serves as a comprehensive and efficient approach to explore exact solitary wave solutions for generalized fractional TT evolution equations. By employing the modified Khater method, we not only enhance our understanding of the dynamic behavior of these equations, but also provide a versatile tool for obtaining precise soliton solutions in the realm of nonlinear fractional evolution equations.

The present boundary layer flow of Maxwell fluid over a stretching sheet has good number of practical applications in metallurgy, drawing of plastics, polymer sheet extrusion including hot rolling extrusion, glass blowing, spinning of fibers, rubber and plastic sheets, crystal growing and many more. Due to these extensive applications of Maxwell fluid in engineering, medicine and manufacturing industries including the above-mentioned applications, authors have motived, inspired and investigated the present problem. However, in this research paper, the influences of Soret and Dufour effects on the steady-state Maxwell fluid flow past a stretching sheet with nonuniform heat source/sink are considered numerically. The thermal and concentration stratifications impacts are also incorporated. The viscous dissipation and magnetic field effects are also included in the respective governing equations. The main novelty and uniqueness of this numerical research is to generalize the earlier studies and describe the salient features of magneto-thermo visco-elastic dissipative Maxwell fluid motion about a stretching sheet with cross-diffusion effects under the influence of double stratification phenomena. To differentiate the non-Newtonian fluids from those of Newtonian fluids, a well-known Maxwell fluid flow model is used in the present study. The investigated physical problem results the highly nonlinear coupled partial differential equations (PDEs) and which are not amenable to any of the direct methods. Suitable similarity transformations are deployed to reduce the highly complex PDEs into the system of ordinary differential equations (ODEs). A robust BVP4C Matlab function is employed to solve the rendered dimensionless system of ODEs. The numerically generated computed data is plotted in terms of velocity, temperature and concentration profiles including engineering quantities of interest such as skin-friction, Nusselt and Sherwood numbers in the flow region. It is evident from the current analysis that, the amplified magnetic field decreases the velocity field and increases the thermal and concentration distribution fields. Accelerating Maxwell’s number diminished the flow velocity and increased the temperature field. Increasing Soret and Dufour numbers enhances the concentration and temperature fields, respectively. Amplifying Maxwell’s number raises the skin-friction coefficient and enlarging the thermal stratification parameter magnifies the thermal transport rate. The mass transport rate amplified with a raise in concentration stratification number in the flow region. Finally, it is provided that, the current results are excellently matching with earlier published results in the literature and it confirms the accuracy of the used numerical method and the produced similarity solutions.

Application: This study focuses on the analysis of nanofluids, which are suspensions of nanoparticles in standard fluid transfer systems. The investigation specifically examines the behavior of nanoparticles over a deformable surface. Purpose and Methodology: Thermal radiation and magnetohydrodynamic forms are incorporated into the energy and momentum equations, respectively. Basic fluid mechanics principles are employed to derive the governing flow equations. The use of similarity transforms facilitates the transformation of ordinary differential equations into partial differential equations. Nonlinear ordinary differential equations are then reduced to a set of initial value problems using the shooting technique. Core Findings: Numerical results are obtained for the thermal profile. The study indicates thermal optimization through the combined inclusion of water with alumina and polymers with copper oxide and titanium dioxide nanoparticles. Graphical analysis explores the absorption of parameters in velocity and temperature profiles. Future Work: Future research could delve deeper into the optimization of thermal properties and investigate additional nanoparticle combinations. Further exploration of the effects of different surface deformations and variations in fluid properties could also be pursued.

This study employs the Extended Kudryashov method to address the fractional-order generalized Burgers–Huxley equation, the fractional-order generalized Huxley equation, the fractional-order generalized Burgers equation, and the fractional-order generalized Fisher equation. Through this approach, exact solutions for these equations are derived. Furthermore, we visualize the obtained results in 3D using Maple $2019.2$. The outcomes underscore the effectiveness and reliability of the Extended Kudryashov method as a clear and efficient tool for solving the specified equations.

Due to its vast industrial applications and thermal engineering, the investigation of the inconsistent heat and mass transfer that drives the flow of squeezing viscous nanofluids between two plates is an interesting topic. In this case study, we have investigated the heat transfer analysis of unsteady viscous nanofluid between two parallel plates by using Response Surface Methodology (RSM). The partial differential equations illustrating the flow model are converted to nonlinear ordinary differential equations by suggesting similarity transformations. The resulting dimensionless and nonlinear ODEs of temperature functions and velocity are solved using the well-known numerical technique bvp4c by transforming the problem into initial value problem from boundary value problem. The results found are consistent with this numerical solution. These numerical values are then used to optimize the different input parameters and to design an experimental model. RSM is used to develop an experimental model for skin friction coefficient. ANOVA tables are generated for input parameters and then sensitivity analysis is performed for output response. Further, the impacts of different parameters on temperature profiles and velocity are graphically explored. The results are compared with the results solved by HPM. The results concurred with this numerical solution. These findings considered much be useful in the application of polymer processing, power transmission, compression, temporary loading of mechanical parts, food processing, cooling water, gravity machinery, modeling of plastic transport in vivo, chemical processing instruments, and demolition due to freezing.

Thermal analysis is carried out on the flow of Sisko fluid over Riga curved stretching sheet in the presence of Lorentz force and heat energy application. Heat transmission is supported by considering Prescribed Heat Flux (PHF) and Surface temperature (PST). This study explores the role of fluids in solving various bioengineering problems and opportunities for clinical measures to treat blood-related diseases. It has been concluded that medical science requires the Sisko model to be explored in understanding blood transfusion problems. Mathematical modeling yields complex partial differential equations, which are transformed into ordinary differential equations via appropriate transformations. The outcome of these parameters is observed and explored for the best match that suits our defined boundary conditions. Numerical solutions are obtained using the Matlab function bvp4c, setting default tolerance for better approximate solutions. Impacts of associated parameters on various profiles are elaborated with tables and graphs. Temperature (PST) reduces by enrichment in Pr. A higher Prandtl number indicates that temperature disturbances spread more slowly through the fluid. This means that the temperature near the surface takes longer to reach equilibrium with the bulk fluid temperature, leading to a decrease in the surface temperature. The temperature (PHF) become declines by enlarging values of Pr. The Prandtl number determines the ratio of momentum diffusivity to thermal diffusivity. A higher value of Prandtl number indicates lower thermal diffusivity, which can result in a thicker thermal boundary layer.

The $(3+1)$-dimensional hyperbolic nonlinear Gardner–Kadomtsov–Petviashvili (GKP) equation is a mathematical model that describes the propagation of nonlinear waves in a four-dimensional space-time. The GKP equation is used as a mathematical tool for studying the dynamics of nonlinear waves in a variety of physical systems including fluid dynamics, nonlinear optics, plasma physics. The GKP equation is a nonlinear partial differential equation (PDE) with mixed spatial and temporal derivatives. It exhibits various interesting phenomena, such as soliton solutions, wave interactions and wave turbulence depending on the values of the conditions. The improved F-expansion technique and generalized Kudryashov technique are successfully employed to evaluate the soliton solutions of governing model. The GKP equation supports various types of soliton solutions, such as bright solitons and dark solitons, depending on the specific parameters. The study of solitons in the GKP equation provides insights into the stability, propagation, and interaction of nonlinear waves in higher-dimensional spaces. The nonlinear terms in the GKP equation are responsible for wave–wave interactions. When multiple waves co-exist in a medium, they can interact with each other, leading to complex phenomena. The nature of wave interactions in the GKP equation depends on the specific values of the coefficients. The GKP equation has many applications in various areas of physics and mathematics. It has been used to model nonlinear waves in several fields and Bose–Einstein condensates.

The primary intent of this paper is to examine the influence of radiation, Soret, and Dufour on the laminar flow of a rotating fluid through a permeable plate undergoing a chemical reaction. The Soret effect, for example, has been employed to differentiate isotopes and to combine gases of different molecular weights. Many real-world applications, including geosciences and chemical engineering, comprise the Soret and Dufour effects. Using similarity variables, the governing equations and allied boundary conditions (BCs) are simplified to a dimensionless form and then solved using the finite element method (FEM). In order to get the numerical approximations of velocity, temperature, and concentration, dimensionless parameters of the flow were utilized, and the consequences were envisioned visually. The most significant results of this research are that raising the Soret and Dufour parameters causes an upsurge in the velocity profile and enhancing the radiation factor causes an upsurge in the temperature distribution. Enhancing the values of permeability causes a reduction in skin friction. Enhancing the accuracy of heat absorption factor estimations leads to an increase in the values of the Nusselt number. A comparison case study has been made among the outcomes of well-existing repository literature with the current solutions and detected a great correlation.

To obtain high performance optoelectronic devices, ferroelectric materials have received a lot of attention due to the various emerging effects on channel materials induced by the ferroelectric polarization. In this work, a special photodetector with the channel material of a triple-layer MoS₂ on a polarized LiNbO₃ substrate was fabricated. The device has a high responsivity of 113.1A/W and a high specific detectivity of up to $7.286\times 10^{12}$ Jones under red illumination, while maintaining the rise and fall time of 32 and 22ms, respectively. Meanwhile, the dark current of this device can be as low as $2.66\times 10^{-11}$A with a bias of 5.0V because the channel material MoS₂ is almost depleted under the internal electrical field induced by the polarized LiNbO₃. This work promises a feasible way for the future development of integrated high-sensitivity photodetectors.

This research explores the intriguing realm of eighth-order embedded solitons in highly dispersive media with cubic–quartic nonlinear susceptibilities ${\chi }^{(2)}$ and ${\chi }^{(3)}$, all within the dynamic context of multiplicative white noise and the framework of Itô calculus. Two different approaches are used in this study. The new auxiliary equation approach produces the bright soliton and singular soliton solutions, while the addendum Kudryashov’s approach produces the bright soliton, singular soliton and combo bright–singular soliton solutions. The system under investigation and the results documented within this work stand as pioneering and original contributions to the field of nonlinear optics. Furthermore, a collection of 2D, 3D and contour plots is produced to visually represent the spatial distribution and progression of different solutions. This not only contributes to the advancement of nonlinear equations in theory but also offers valuable insights for practical applications.