Noval soliton solution, sensitivity and stability analysis to the fractional gKdV-ZK equation.

This work examines the fractional generalized Korteweg-de-Vries-Zakharov-Kuznetsov equation (gKdV-ZKe) by utilizing three well-known analytical methods, the modified [Formula: see text]-expansion method, [Formula: see text]-expansion method and the Kudryashov method. The gKdV-ZK equation is a nonlinear model describing the influence of magnetic field on weak ion-acoustic waves in plasma made up of cool and hot electrons. The kink, singular, anti-kink, periodic, and bright soliton solutions are observed. The effect of the fractional parameter on wave shapes have been analyzed by displaying various graphs for fractional-order values of [Formula: see text]. In addition, we utilize the Hamiltonian property to observe the stability of the attained solution and Galilean transformation for sensitivity analysis. The suggested methods can also be utilized to evaluate the nonlinear models that are being developed in a variety of scientific and technological fields, such as plasma physics. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complex models.

Construction of diverse water wave structures for coupled nonlinear fractional Drinfel'd-Sokolov-Wilson model with Beta derivative and its modulus instability.

This paper aims to analyze the coupled nonlinear fractional Drinfel'd-Sokolov-Wilson (FDSW) model with beta derivative. The nonlinear FDSW equation plays an important role in describing dispersive water wave structures in mathematical physics and engineering, which is used to describe nonlinear surface gravity waves propagating over horizontal sea bed. We have applied the travelling wave transformation that converts the FDSW model to nonlinear ordinary differential equations. After that, we applied the generalized rational exponential function method (GERFM). Diverse types of soliton solution structures in the form of singular bright, periodic, dark, bell-shaped and trigonometric functions are attained via the proposed method. By selecting a suitable parametric value, the 3D, 2D and contour plots for some solutions are also displayed to visualize their nature in a better way. The modulation instability for the model is also discussed. The results show that the presented method is simple and powerful to get a novel soliton solution for nonlinear PDEs.

Energy computation and multiplier-less implementation of the two-dimensional FitzHugh-Nagumo (FHN) neural circuit.

In this work, with the aim of reducing the cost of the implementation of the traditional 2D FHN neuron circuit, a pair of diodes connected in an anti-parallel direction is used to replace the usual cubic nonlinearity (implemented with two multipliers). Based on the stability of the model, the generation of self-excited firing patterns is justified. Making use of the famous Helmholtz theorem, a Hamilton function is provided for the estimation of the energy released during each electrical activity of the model. From the investigation of the 1D evolution of the maxima of the membrane potential of the model, it was recorded that the considered model is able to experience a period of doubling bifurcation followed by a crisis that enables the increasing of the volume of the attractor. This contribution ends with the realization of a neural circuit without analog multipliers for the validation of the obtained results.

Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms.

Nonlinear chains of atoms (NCA) are complex systems with rich dynamics, that influence various scientific disciplines. The lie symmetry approach is considered to analyze the NCA. The Lie symmetry method is a powerful mathematical tool for analyzing and solving differential equations with symmetries, facilitating the reduction of complexity and obtaining solutions. After getting the entire vector field by using the Lie scheme, we find the optimal system of symmetries. We have converted assumed PDE into nonlinear ODE by using the optimal system. The new auxiliary scheme is used to find the Travelling wave solutions, while graphical behaviour visually represents relationships and patterns in data or mathematical models. The multiplier method enables the identification of conservation laws, and fundamental principles in physics that assert certain quantities remain constant over time.

Investigation of an improved FitzHugh-Rinzel neuron and its multiplier-less circuit implementation.

Circuit implementation of the mathematical model of neurons represents an alternative approach for the validation of their dynamical behaviors for their potential applications in neuromorphic engineering. In this work, an improved FitzHugh-Rinzel neuron, in which the traditional cubic nonlinearity is swapped with a sine hyperbolic function, is introduced. This model has the advantage that it is multiplier-less since the nonlinear component is just implemented with two diodes in anti-parallel. The stability of the proposed model revealed that it has both stable and unstable nodes around its fixed points. Based on the Helmholtz theorem, a Hamilton function that enables the estimation of the energy released during the various modes of electrical activity is derived. Furthermore, numerical computation of the dynamic behavior of the model revealed that it was able to experience coherent and incoherent states involving both bursting and spiking. In addition, the simultaneous appearance of two different types of electric activity for the same neuron parameters is also recorded by just varying the initial states of the proposed model. Finally, the obtained results are validated using the designed electronic neural circuit, which has been analyzed in the Pspice simulation environment.

The Lower Limb Movements of the Fetus in Uterus: A Narrative Review.

The fetus movements play an important role in fetal well-being. With the continuous advancement of real-time scanning machines, it is feasible to observe the fetus movement in detail. The characteristics of fetal lower limb movements in prenatal examination have not been systematically investigated. This review proposes the patterns of fetal lower limb movements, the maternal influence on fetal lower limb movements, and the application of fetal lower limb movements for the diagnosis of prenatal diseases. A systematic search of literature on the lower limb movements of the fetus in uterus was performed in the databases, namely, Web of Science and Scopus. Thirty-four publications were selected. This review demonstrates that isolated fetal lower limb movements are rare and always accompanied with the movements of other body segments. Detection of the presence of fetal leg movements seems to be of no diagnostic value for fetuses with prenatal diseases. The isolated lower limb movement was statistically significant different between fetuses of low- and high-risk pregnant women. The coordinated movements of the fetal lower limbs and other parts should be considered when analyzing fetal movements in the future study.

Thermal Transmission Comparison of Nanofluids over Stretching Surface under the Influence of Magnetic Field.

Heat transfer at industrial levels has been revolutionized with the advancement of nanofluid and hybrid nanofluid. Keeping this development in view, this article aims to present the rate of heat transfer for conventional and hybrid nanofluids, incorporating the Hall Effect over a stretchable surface. The flow governing equations are obtained with the help of suitable assumptions, and the problem is attempted with the boundary value problem technique in MATLAB. The highly non-linear partial differential equations are transformed into non-dimensional forms using suitable similarity transforms. The criterion of convergence for solution or tolerance of a problem is adjusted to 10-7. Water is considered as a base fluid; copper (Cu) and silver (Ag) nanoparticles are mixed to obtain nanofluid. This novel work is incorporated for conventional and hybrid nanofluid with the effect of Hall current above the stretching/shrinking surface. Increasing the Stefan blowing parameter reduces the flow rate; it increases the heat transfer rate and nano-particle concentration of conventional and hybrid nanofluid. Both velocity components decreases by increasing the magnetic field. The Hall Effect also decreases the velocity of nanofluid. The outcomes are compared to previously published work, demonstrating that the existing study is legitimate. The heat transfer rate of the hybrid nanofluid is higher than the convential nanofluid. This study suggests more frequent use of hybrid nanofluid because of high heat transfer rates and reduced skin friction.

Biochar-Mediated Zirconium Ferrite Nanocomposites for Tartrazine Dye Removal from Textile Wastewater.

To meet the current challenges concerning the removal of dyes from wastewater, an environmentally friendly and efficient treatment technology is urgently needed. The recalcitrant, noxious, carcinogenic and mutagenic compound dyes are a threat to ecology and its removal from textile wastewater is challenge in the current world. Herein, biochar-mediated zirconium ferrite nanocomposites (BC-ZrFe2O5 NCs) were fabricated with wheat straw-derived biochar and applied for the adsorptive elimination of Tartrazine dye from textile wastewater. The optical and structural properties of synthesized BC-ZrFe2O5 NCs were characterized via UV/Vis spectroscopy, Fourier transform Infra-red (FTIR), X-Ray diffraction (XRD), Energy dispersive R-Ray (EDX) and Scanning electron microscopy (SEM). The batch modes experiments were executed to explore sorption capacity of BC-ZrFe2O5 NCs at varying operative conditions, i.e., pH, temperature, contact time, initial dye concentrations and adsorbent dose. BC-ZrFe2O5 NCs exhibited the highest sorption efficiency among all adsorbents (wheat straw biomass (WSBM), wheat straw biochar (WSBC) and BC-ZrFe2O5 NCs), having an adsorption capacity of (mg g-1) 53.64 ± 0.23, 79.49 ± 0.21 and 89.22 ± 0.31, respectively, for Tartrazine dye at optimum conditions of environmental variables: pH 2, dose rate 0.05 g, temperature 303 K, time of contact 360 min and concentration 100 mg L-1. For the optimization of process variables, response surface methodology (RSM) was employed. In order to study the kinetics and the mechanism of the adsorption process, kinetic and equilibrium mathematical models were used, and results revealed 2nd order kinetics and a multilayer chemisorption mechanism due to complexation of hydroxyl, Fe and Zr with dyes functional groups. The nanocomposites were also recovered in five cycles without significant loss (89 to 63%) in adsorption efficacy. This research work provides insight into the fabrication of nanoadsorbents for the efficient adsorption of Tartrazine dye, which can also be employed for practical engineering applications on an industrial scale as efficient and cost effective materials.

Multiple slip effects on time dependent axisymmetric flow of magnetized Carreau nanofluid and motile microorganisms.

This presented work investigate the bio-convections effects of the magnetized time dependent axisymmetric flow of Carreau-nanomaterial performances with multiple slip effects over a stretching sheet. The momentum, heat, concentration and density of motile micro-organism are renovated into the system of equation via using well known similarity revolution. Well known Mathematical computational techniques and software (i.e. bvp4c and MATLAB) are used to draw graphical and tabular results. Velocity profile equation [Formula: see text], energy equation [Formula: see text], volumetric nanoparticles [Formula: see text], density motile microorganism [Formula: see text].The Carreau viscosity model is use to reduce the viscosity of fluid when [Formula: see text] and [Formula: see text]. Besides we moderate this into power law index with [Formula: see text] and [Formula: see text] partial slip condition of velocity is also instigated at the surface. Gravity dependent gyrotactic nanoparticles are utilized for well observing axisymmetric flow with convective boundary layer condition and comparatively better heat transfer rate result and applicable to maximum realistic approach.

Effectiveness of splitter plate to control fluid forces on a circular obstacle in a transient flow: FEM computations.

The reliability of the usage of a splitter plate (passive control device) downstream of the obstacle, in suppressing the fluid forces on a circular obstacle of diameter [Formula: see text] is studied in this paper. The first parameter of the current study is the attachment of a splitter plate of various lengths [Formula: see text] with the obstacle, whereas the gap separation [Formula: see text] between the splitter plate and the obstacle, is used as a second parameter. The control elements of the first and second parameters are varied from [Formula: see text] to [Formula: see text]. For the attached splitter plates of lengths [Formula: see text] and [Formula: see text], the oscillatory behavior of transient flow at [Formula: see text] is successfully controlled. For the gap separation, [Formula: see text] and [Formula: see text] similar results are obtained. However, it is observed that a splitter plate of too short length and a plate located at the inappropriate gap from the obstacle, are worthless. A computational strategy based on the finite element method is utilized due to the complicated representative equations. For a clear physical depiction of the problem, velocity and pressure plots have been provided. Drag and lift coefficients the hydrodynamic benchmark values are also evaluated in a graphical representation surrounding the obstacle's peripheral surface as well as the splitter plate. In a conclusion, a splitter plate can function to control fluid forces whether it is attached or detached, based on plate length and gap separation between obstacle and plate, respectively.

Significance of concentration-dependent viscosity on the dynamics of tangent hyperbolic nanofluid subject to motile microorganisms over a non-linear stretching surface.

The communication describes a theoretical framework for tangent hyperbolic fluid of nano-biofilm due to an extending or shrinking sheet that comprises a stagnation point flow, chemical reaction with activation energy, and bioconvection of gyrotactic microorganisms. The varying transport features due to dynamic viscosity, thermal conductivity, nano-particle mass permeability and microbe organisms diffusivity are taken into account for the novelty of this work. The inspiration is developed to enhance heat transfer. A set of leading partial differential equations is formed along with appropriate boundary constraints. Using similarity transformations, the basic formulation is transitioned into non-linear differential equations. To produce observational data, the shooting technique and Runge-Kutta fourth order method are employed. The coding of numerical scheme is developed in Matlab script. The visual representation of the effects of diverse fluid transport properties and distinctive parameters on speed, temperature, concentration and motile density are evaluated. The velocity become faster when the parameters [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are enhanced. Brownian motion, thermal conductivity, heat generation as well as thermophoresis factors all strengthen the temperature distribution, however the nano-particle concentration profile is enhanced as the nano-particle mass conductivity variable, activation energy as well as the thermophoresis variable are boosted. The microorganism density improves significantly when the microorganism diffusivity factor increases. The skin friction, Sherwood number, Nusselt number and motile density number decline against the incremented transport parameters.

Soret and Dufour effects on unsteady MHD second-grade nanofluid flow across an exponentially stretching surface.

The unsteady energy and mass transport of magnetohydrodynamics (MHD) second grade nanofluid via an exponentially extending surface with Dufour and Soret effects are investigated in this study. Variable thermal conductivity and mixed convection effects are used to investigate the heat transfer mechanism. There are also new characteristics such as slip flow, viscous dissipation, Brownian motion, nonlinear thermal radiation, and thermophoresis. In the problem formulation, the boundary-layer approximation is used. Using the suitable transformations, the energy, momentum, and concentration equations are generated into non-linear ordinary differential equations (ODEs). The solution to the resultant problems was calculated via the Homotopy analysis method (HAM). The effects of environmental parameters on velocity, temperature, and concentration profiles are graphically depicted. When comparing the current results to the previous literature, there was also a satisfactory level of agreement. In comparison to a flow based on constant characteristics, the flow with variable thermal conductivity is shown to be significantly different and realistic. The temperature of the fluid grew in direct proportion to the thermophoresis motion, buoyancy ratio, and Brownian motion parameters. According to the findings, the slippery porous surface may be employed efficiently in chemical and mechanical sectors that deal with a variety of very viscous flows.

Coexistence of infinitely many patterns and their control in heterogeneous coupled neurons through a multistable memristive synapse.

The phenomenon of hidden heterogeneous extreme multistability is rarely reported in coupled neurons. This phenomenon is investigated in this contribution using a model of a 2D FitzHugh-Nagumo neuron coupled with a 3D Hindmarsh-Rose neuron through a multistable memristive synapse. The investigation of the equilibria revealed that the coupled neuron model is equilibrium free and, thus, displays a hidden dynamics. Some traditional nonlinear analysis tools are used to demonstrate that the heterogeneous neuron system is able to exhibit the coexistence of an infinite number of electrical activities involving both periodic and chaotic patterns. Of particular interest, a noninvasive control method is applied to suppress all the periodic coexisting activities, while preserving only the desired chaotic one. Finally, an electronic circuit of the coupled neurons is designed in the PSpice environment and used to further support some results of the theoretical investigations.

Insight into the Dynamics of Fractional Maxwell Nano-Fluids Subject to Entropy Generation, Lorentz Force and Heat Source via Finite Difference Scheme.

In recent times, the loss of useful energy and solutions to those energy challenges have a wide scope in different areas of engineering. This work focuses on entropy analysis for unsteady viscoelastic fluids. The momentum boundary layer and thermal boundary layer are described under the effects of a magnetic field in the absence of an induced magnetic field. The study of a fractional model of Maxwell nanofluid by partial differential equation using Caputo time differential operator can well address the memory effect. Using transformations, the fractional ordered partial differential equations (PDEs) are transfigured into dimensionless PDEs. Numerical results for fractional Maxwell nanofluids flow and heat transfer are driven graphically. The Bejan number is obtained following the suggested transformation of dimensionless quantities like entropy generation. A mathematical model of entropy generation, Bejan number, Nusselt number and skin friction are developed for nanofluids. Effects of different physical parameters like Brickman number, Prandtl number, Grashof number and Hartmann number are illustrated graphically by MAPLE. Results depict that the addition of nanoparticles in base-fluid controls the entropy generation that enhances the thermal conductivity and application of magnetic field has strong effects on the heat transfer of fractional Maxwell fluids. An increasing behavior in entropy generation is noticed in the presence of source term and thermal radiation parameter.

Natural Convection Water/Glycerin-CNT Fractionalized Nanofluid Flow in a Channel with Isothermal and Ramped Conditions.

This article investigates heat and mass transport enrichment in natural convection fractionalized nanofluid flow inside a channel with isothermal and ramped wall conditions under the effects of chemical reactions, radiation, heat absorption, and the Soret effect. To obtain the fractional model, the Caputo time-fractional derivative definition is used, and analytical results are obtained by the Laplace transform. In two base fluids, water and glycerin, the impacts of two nanoparticles, single-wall carbon nanotubes (SWCNTs) and multiple-wall carbon nanotubes (MWCNTs), are investigated. The comparison of six distinct fluids, including water, water-SWCNT, water-MWCNT, glycerin, glycerin-SWCNT and glycerin-WMCNT, is explored graphically. Physical parameters' effects on isothermal and ramped conditions are graphically depicted and explained in depth. For isothermal wall conditions, the variation in concentration, temperature and velocity is exponential, while for ramped wall conditions, the variation is steady. Finally, the results of skin frictions, Nusselt numbers and Sherwood numbers and for both ramped wall and isothermal wall conditions are evaluated in tabular form for various values of volume fraction. Moreover, it is observed that the temperature, velocity, Nusselt numbers and skin frictions increase by increasing the volume fraction of CNTs.

Numerical analysis of a second-grade fuzzy hybrid nanofluid flow and heat transfer over a permeable stretching/shrinking sheet.

In this work, the heat transfer features and stagnation point flow of Magnetohydrodynamics (MHD) hybrid second-grade nanofluid through a convectively heated permeable shrinking/stretching sheet is reported. The purpose of the present investigation is to consider hybrid nanofluids comprising of Alumina [Formula: see text] and Copper [Formula: see text] nanoparticles within the Sodium Alginate (SA) as a host fluid for boosting the heat transfer rate. Also, the effects of free convection, viscous dissipation, heat source/sink, and nonlinear thermal radiation are considered. The converted nonlinear coupled fuzzy differential equations (FDEs) with the help of triangular fuzzy numbers (TFNs) are solved using the numerical scheme bvp4c. The numerical results are acquired for various engineering parameters to study the Nusselt number, skin friction coefficient, velocity, and temperature distribution through figures and tables. For the validation, the current numerical results were found to be good as compared to existing results in limiting cases. It is also inspected by this work that with the enhancement of the volume fraction of nanoparticles, the heat transfer rate also increases. So, it may be taken as a fuzzy parameter for a better understanding of fuzzy variables. For the comparison, the volume fraction of nanofluids and hybrid nanofluid are said to be TFN [0, 0.1, 0.2]. In the end, we can see that fuzzy triangular membership functions (MFs) have not only helped to overcome the computational cost but also given better accuracy than the existent results. Finding from fuzzy MFs, the performance of hybrid nanofluids is better than nanofluids.

Computational Analysis of Fluid Forces on an Obstacle in a Channel Driven Cavity: Viscoplastic Material Based Characteristics.

In the current work, an investigation has been carried out for the Bingham fluid flow in a channel-driven cavity with a square obstacle installed near the inlet. A square cavity is placed in a channel to accomplish the desired results. The flow has been induced using a fully developed parabolic velocity at the inlet and Neumann condition at the outlet, with zero no-slip conditions given to the other boundaries. Three computational grids, C1, C2, and C3, are created by altering the position of an obstacle of square shape in the channel. Fundamental conservation and rheological law for viscoplastic Bingham fluids are enforced in mathematical modeling. Due to the complexity of the representative equations, an effective computing strategy based on the finite element approach is used. At an extra-fine level, a hybrid computational grid is created; a very refined level is used to obtain results with higher accuracy. The solution has been approximated using P2 - P1 elements based on the shape functions of the second and first-order polynomial polynomials. The parametric variables are ornamented against graphical trends. In addition, velocity, pressure plots, and line graphs have been provided for a better physical understanding of the situation Furthermore, the hydrodynamic benchmark quantities such as pressure drop, drag, and lift coefficients are assessed in a tabular manner around the external surface of the obstacle. The research predicts the effects of Bingham number (Bn) on the drag and lift coefficients on all three grids C1, C2, and C3, showing that the drag has lower values on the obstacle in the C2 grid compared with C1 and C3 for all values of Bn. Plug zone dominates in the channel downstream of the obstacle with augmentation in Bn, limiting the shear zone in the vicinity of the obstacle.

Dynamical analysis of coronavirus disease with crowding effect, and vaccination: a study of third strain.

Countries affected by the coronavirus epidemic have reported many infected cases and deaths based on world health statistics. The crowding factor, which we named "crowding effects," plays a significant role in spreading the diseases. However, the introduction of vaccines marks a turning point in the rate of spread of coronavirus infections. Modeling both effects is vastly essential as it directly impacts the overall population of the studied region. To determine the peak of the infection curve by considering the third strain, we develop a mathematical model (susceptible-infected-vaccinated-recovered) with reported cases from August 01, 2021, till August 29, 2021. The nonlinear incidence rate with the inclusion of both effects is the best approach to analyze the dynamics. The model's positivity, boundedness, existence, uniqueness, and stability (local and global) are addressed with the help of a reproduction number. In addition, the strength number and second derivative Lyapunov analysis are examined, and the model was found to be asymptotically stable. The suggested parameters efficiently control the active cases of the third strain in Pakistan. It was shown that a systematic vaccination program regulates the infection rate. However, the crowding effect reduces the impact of vaccination. The present results show that the model can be applied to other countries' data to predict the infection rate.

Breakdown of a Nonlinear Stochastic Nipah Virus Epidemic Models through Efficient Numerical Methods.

Background: Nipah virus (NiV) is a zoonotic virus (transmitted from animals to humans), which can also be transmitted through contaminated food or directly between people. According to a World Health Organization (WHO) report, the transmission of Nipah virus infection varies from animals to humans or humans to humans. The case fatality rate is estimated at 40% to 75%. The most infected regions include Cambodia, Ghana, Indonesia, Madagascar, the Philippines, and Thailand. The Nipah virus model is categorized into four parts: susceptible (S), exposed (E), infected (I), and recovered (R). Methods: The structural properties such as dynamical consistency, positivity, and boundedness are the considerable requirements of models in these fields. However, existing numerical methods like Euler-Maruyama and Stochastic Runge-Kutta fail to explain the main features of the biological problems. Results: The proposed stochastic non-standard finite difference (NSFD) employs standard and non-standard approaches in the numerical solution of the model, with positivity and boundedness as the characteristic determinants for efficiency and low-cost approximations. While the results from the existing standard stochastic methods converge conditionally or diverge in the long run, the solution by the stochastic NSFD method is stable and convergent over all time steps. Conclusions: The stochastic NSFD is an efficient, cost-effective method that accommodates all the desired feasible properties.

Higher-Dimensional Fractional Order Modelling for Plasma Particles with Partial Slip Boundaries: A Numerical Study.

We integrate fractional calculus and plasma modelling concepts with specific geometry in this article, and further formulate a higher dimensional time-fractional Vlasov Maxwell system. Additionally, we develop a quick, efficient, robust, and accurate numerical approach for temporal variables and filtered Gegenbauer polynomials based on finite difference and spectral approximations, respectively. To analyze the numerical findings, two types of boundary conditions are used: Dirichlet and partial slip. Particular methodology is used to demonstrate the proposed scheme's numerical convergence. A detailed analysis of the proposed model with plotted figures is also included in the paper.