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The human immunodeficiency viruses are two species of Lentivirus that infect humans. Over time, they cause acquired immunodeficiency syndrome, a condition in which progressive immune system failure allows life-threatening opportunistic infections and cancers to thrive. Human immunodeficiency virus infection came from a type of chimpanzee in Central Africa. Studies show that immunodeficiency viruses may have jumped from chimpanzees to humans as far back as the late 1800s. Over decades, human immunodeficiency viruses slowly spread across Africa and later into other parts of the world. The Susceptible-Infected-Recovered (SIR) models are significant in studying disease dynamics. In this paper, we have studied the effect of irresponsible immigrants on HIV/AIDS dynamics by formulating and considering different methods. Euler, Runge Kutta, and a Non-standard finite difference (NSFD) method are developed for the same problem. Numerical experiments are performed at disease-free and endemic equilibria points at different time step sizes 'h'. The results reveal that, unlike Euler and Runge Kutta, which fail for large time step sizes, the proposed Non-standard finite difference (NSFD) method gives a convergence solution for any time step size. Our proposed numerical method is bounded, dynamically consistent, and preserves the positivity of the continuous solution, which are essential requirements when modeling a prevalent disease. [ABSTRACT FROM AUTHOR]

In this study, nonlinear vibration and stability of a pipe conveying fluid, with axially moving supports, immersed in an external fluid is studied. The equation of motion is derived with the aid of the Newtonian method via employing the Euler–Bernoulli beam theory and plug flow assumption. Considering the stretching effect, the nonlinear equation of motion is obtained, and it is discretized via the Galerkin method. Afterward, the stability of the system is investigated using two different approaches, and their results are compared. Numerical simulations show the system has complex dynamic behavior. To unveil the dynamics of the system, various analysis techniques such as bifurcation diagram of Poincaré map, phase portrait, power spectrum, and time trajectories are used. Limit cycle, period-n, quasi-periodic, and chaotic regime are observed. It is found that pipe can flutter around the trivial solution or post-buckling equilibrium points. Moreover, the influences of some system parameters on the chaotic behavior of the pipe are discussed. [ABSTRACT FROM AUTHOR]

Amoebiasis is a parasitic intestinal infection caused by the highly pathogenic amoeba Entamoeba histolytica. It is spread through person-to-person contact or by eating or drinking food or water contaminated with feces. Its transmission rate depends on the number of cysts present in the environment. The traditional models assumed a homogeneous and contradictory transmission with reality. The heterogeneity of its transmission rate is a significant factor when modeling disease dynamics. The heterogeneity of disease transmission can be described mathematically by introducing fuzzy theory. In this context, a fuzzy SEIR Amoebiasis disease model is considered in this study. The equilibrium analysis and reproductive number are studied with fuzziness. Two numerical schemes forward Euler method and a nonstandard finite difference (NSFD) approach, are developed for the learned model, and the results of numerical simulations are presented. The numerical and simulation results reveal that the proposed NSFD method provides an adequate representation of the dynamics of the disease despite the uncertainty and heterogeneity. Moreover, the obtained method generates plausible predictions that regulators can use to support decision-making to design and develop control strategies. [ABSTRACT FROM AUTHOR]

On the basis of the analysis of thermoelastic motion, the current research develops a novel model of modified thermoelasticity. The rotating long hollow cylinders with fixed surfaces are considered in a generalized Moore–Gibson–Thompson thermoelastic model (MGTTE) framework, including the modified Ohm's law. The cylinders are made of a thermoelastic material that rotates at a uniform rotational speed and is elastic in the transverse direction. The set of equations for the MGT heat conduction in the new model is built under the influence of the electromagnetic field by including a delay time in the context of Green–Naghdi of the third kind (GN-III). The inner boundary of the hollow cylinder is not only restricted but also sensitive to heat loading. The outer surface, on the other hand, is also restricted but insulates the heat. The Laplace transform method is utilized to deal with the differential equations produced in the new domain and transfer the problem to the space domain. The Dubner and Abate method is used to compute dynamically and graphically depict the theoretical findings for an isotropic transverse material. After comparing the results of several thermoelastic theories, the implications for the electromagnetic field are discussed. [ABSTRACT FROM AUTHOR]

The application of fuzzy theory is vital in all scientific disciplines. The construction of mathematical models with fuzziness is little studied in the literature. With this in mind and for a better understanding of the disease, an SEIR model of malaria transmission with fuzziness is examined in this study by extending a classicalmodel of malaria transmission. The parameters ß and d, being function of the malaria virus load, are considered fuzzy numbers. Three steady states and the reproduction number of the model are analyzed in fuzzy senses. A numerical technique is developed in a fuzzy environment to solve the studied model, which retains essential properties such as positivity and dynamic consistency. Moreover, numerical simulations are carried out to illustrate the analytical results of the developed technique. Unlike most of the classical methods in the literature, the proposed approach converges unconditionally and can be considered a reliable tool for studying malaria disease dynamics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This investigation presents the fuzzy nanoparticle volume fraction on heat transfer of second-grade hybrid 2 3 Al O +Cu/EO nanofluid over a stretching/shrinking Riga wedge under the contribution of heat source, stagnation point, and nonlinear thermal radiation. Also, this inquiry includes flow simulations using modified Hartmann number, boundary wall slip and heat convective boundary condition. Engine oil is used as the host fluid and two distinct nanomaterials (Cu and 2 3 Al O) are used as nanoparticles. The associated nonlinear governing PDEs are intended to be reduced into ODEs using suitable transformations. After that 'bvp4c,' a MATLAB technique is used to compute the solution of said problem. For validation, the current findings are consistent with those previously published. The temperature of the hybrid nanofluid rises significantly more quickly than the temperature of the second-grade fluid, for larger values of the wedge angle parameter, the volume percentage of nanomaterials. For improvements to the wedge angle and Hartmann parameter, the skin friction factor improves. Also, for the comparison of nanofluids and hybrid nanofluids through membership function (MF), the nanoparticle volume fraction is taken as a triangular fuzzy number (TFN) in this work. Membership function and σ-cut are controlled TFN which ranges from 0 to 1. According to the fuzzy analysis, the hybrid nanofluid gives a more heat transfer rate as compared to nanofluids. Heat transfer and boundary layer flow at wedges have recently received a lot of attention due to several metallurgical and engineering physical applications such as continuous casting, metal extrusion, wire drawing, plastic, hot rolling, crystal growing, fibreglass and paper manufacturing. [ABSTRACT FROM AUTHOR]

The main aim of the article is to define a criterion of dynamic stability based on the Flash--Hogan principle and the ZMP method. The gait researches were focused on analysis and observation of the human biomechanism with the optical system Optitrack. The smooth reference trajectory is defined forming a stability pattern. The optimal, due to the minimum jerk criterion, ZMP trajectory is illustrated in the results Section in order to demonstrate the dynamic stability pattern for the needs of rehabilitation in cases of neuromuscular damage or injuries affecting gait stability. [ABSTRACT FROM AUTHOR]

We established some new α -conformable dynamic inequalities of Hardy–Knopp type. Some new generalizations of dynamic inequalities of α -conformable Hardy type in two variables on time scales are established. Furthermore, we investigated Hardy's inequality for several functions of α -conformable calculus. Our results are proved by using two-dimensional dynamic Jensen's inequality and Fubini's theorem on time scales. When α = 1 , then we obtain some well-known time-scale inequalities due to Hardy. As special cases, we derived Hardy's inequality for T = R , T = Z and T = h Z . Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

Paper is devoted to the effective stationary heat conductivity for the fibre composite materials. We are aimed on getting on analytical expression for effective thermal conductivity coefficient. Asymptotic homogenization approach, based on the multiple scale perturbation method, is used. This allows to reduce the original boundary value problem in multiply connected domain to the sequence of boundary value problems in simply connected domains. These problems include: the local problem for the periodically repeated cell and homogenized problem with effective coefficient. It is shown that for densely packed and high contrast fibre composites, the cell problem can be solved analytically. For this aim, lubrication approach (asymptotics of thin layer) has been employed. We also generalise obtained solution to the case of medium‐sized inclusions in the framework of the Padé approximants. [ABSTRACT FROM AUTHOR]

10.3390/app12052333 23 Hong J., Jiang L., Wang Y., Su Z., Ma Y. Nonlinear Dynamics of an Elastic Stop System and Its Application in a Rotor System. Nonlinear phenomena occur in engineering structures, biological systems, social processes, and in economics. Particle weight adjustment can ensure the stability, tracking efficiency, and continuity of the particle filter control process. Xu et al. [[8]] develop a particle filter design scheme for a robust nonlinear control system of an uncertain heat exchange process against noise and communication delay. [Extracted from the article]

The main purpose of this research is to propose a new methodology to observe a class of time-fractional generalized fifth-order Korteweg–de Vries equations. Laplace transform along with a homotopy perturbation algorithm is utilized for the solution and analysis purpose in the current study. This extended technique provides improved and convergent series solutions through symbolic computation. The proposed methodology is applied to time-fractional Sawada–Kotera, Ito, Lax's, and Kaup–Kupershmidt models, which are induced from a generalized fifth-order KdV equation. For validity purposes, obtained and existing results at integral orders are compared. Convergence analysis was also performed by computing solutions and errors at different values in a fractional domain. Dynamic behavior of the fractional parameter is also studied graphically. Simulations affirm the dominance of the proposed algorithm in terms of accuracy and fewer computations as compared to other available schemes for fractional KdVs. Hence, the projected algorithm can be utilized for more advanced fractional models in physics and engineering. [ABSTRACT FROM AUTHOR]

In the present article, we prove some new generalizations of dynamic inequalities of Hardy-type by utilizing diamond- α dynamic integrals on time scales. Furthermore, new generalizations of dynamic inequalities of Hardy-type in two variables on time scales are proved. Moreover, we present Hardy inequalities for several functions by using the diamond- α dynamic integrals on time scales. The results are proved by using the dynamic Jensen inequality and the Fubini theorem on time scales. Our main results extend existing results of the integral and discrete Hardy-type inequalities. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

In this article, we introduce bipolar neutrosophic (BN) aggregation operators (AOs) as a revolutionary notion in aggregation operators (AOs) by applying Einstein operations to bipolar neutrosophic aggregation operators (AOs), with its application related to a real-life problem. The neutrosophic set is able to drawout the incomplete, inconsistent and indeterminate information pretty efficiently. Initially, we present essential definitions along with operations correlated to the neutrosophic set (NS) and its generalization, the bipolar neutrosophic set (BNS). The Einstein aggregation operators are our primary targets, such asthe BN Einstein weighted average (BNEWA), BN Einstein ordered weighted average (BNEOWA), BN Einstein hybrid average (BNEHA), BN Einstein weighted geometric (BNEWG), BN Einstein ordered weighted geometric (BNEOWG) and BN Einstein hybrid geometric (BNEHG), as well as their required properties. The most important benefit of using the suggested approaches is that they provide decision-makers with complete sight of the issue. These techniques, when compared to other methods, provide complete, progressive and precise findings. Lastly, by means of diverse types of newly introduced aggregation operators and a numerical illustration by an example, we suggest an innovative method to be used for multi-criteria community decision-making (DM). This illustrates the utility and applicability of this new strategy when facing real-world problems. [ABSTRACT FROM AUTHOR]

In this paper, a unique overview of intelligent machines and mathematical methods designed and developed to measure and to control the water level in industrial or laboratory setups of coupled and cascaded configurations of tanks is made. A systematized and concise overview is made of the mechatronic systems used in the measurement, identification, and control of the water level enumerates, the software used in the associated scientific research, modern techniques and sensors, and mathematical models, as well as analysis and control strategies. The broad overview of applications of the last decade is finalized by a proposition of a control system that is based on a parameter estimation of a new experimental setup, an integral dynamic model of the system, a modern mechatronic machine such as the Watson-Marlow peristaltic pump, the Anderson Negele sensor of level, the NI cRIO-9074 controller, and LabVIEW virtual instrumentation. The results of real experimental tests, exploiting a hybrid proportional control, being improved by a numerically predicted water level, are obtained using a few tools, i.e., the static characteristics, the classical step response, and a new pyramid-shaped step function of a discontinuous path-following reference input, being introduced to evaluate the effectiveness and robustness of the regulation of the level height. [ABSTRACT FROM AUTHOR]

Whooping cough is a highly transmitted disease around the world. According to the World Health Organization (WHO), 0.15 million cases had reported globally in 2018. Most of the Asian and African states are infected regions. Through the study, we investigated the whole population into the four classes susceptible (S), exposed (E), infected (I), and vaccinated or recovered (R). The transmission dynamics of whooping cough disease are studied analytically and numerically. Analytical analyses are positivity, boundedness, reproduction number, equilibria, and local and global stabilities. In numerical analysis, we developed an implicit numerical integration scheme consistent with the biological problem's properties. The analysis of the implicit method for the said model is dynamically consistent, positive, and bounded. Furthermore, an implicit numerical integration scheme is suitable for studying a particular epidemic model such as the whooping cough disease. [ABSTRACT FROM AUTHOR]

We use two parameters for functions whose second (q, ω)-derivatives are bounded in order to prove several recent extensions of the Ostrowski inequality and its companion inequalities on (q, ω)-Hahn difference operator. Furthermore, we procure some q-integral and continuous inequalities as special cases of the main results as well these generalizations. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

In this research, a numerical analysis is accomplished aiming to investigate the effects of adding a new design fins arrangement to a vertical triplex tube latent heat storage system during the melting mechanism and evaluate the natural convection effect using Ansys Fluent software. In the triplex tube, phase change material (PCM) is included in the middle tube, while the heat transfer fluid (HTF) flows through the interior and exterior pipes. The proposed fins are triangular fins attached to the pipe inside the PCM domain in two different ways: (1) the base of the triangular fins is connected to the pipe, (2) the tip of the triangular fins is attached to the pipe and the base part is directed to the PCM domain. The height of the fins is calculated to have a volume equal to that of the uniform rectangular fins. Three different cases are considered as the final evaluation toward the best case as follows: (1) the uniform fin case (case 3), (2) the reverse triangular fin case with a constant base (case 12), (3) the reverse triangular fin case with a constant height (case 13). The numerical results show that the total melting times for cases 3 and 12 increase by 4.0 and 10.1%, respectively, compared with that for case 13. Since the PCM at the bottom of the heat storage unit melts slower due to the natural convection effect, a flat fin is added to the bottom of the heat storage unit for the best case compared with the uniform fin cases. Furthermore, the heat storage rates for cases 3 and 12 are reduced by 4.5 and 8.5%, respectively, compared with that for case 13, which is selected as the best case due to having the lowest melting time (1978s) and the highest heat storage rate (81.5 W). The general outcome of this research reveals that utilizing the tringle fins enhances the thermal performance and the phase change rate. [ABSTRACT FROM AUTHOR]

This article is an attempt to explore the heat transfer features of the steady three-dimensional rotating flow of magneto-hydrodynamic hybrid nanofluids under the effect of nonlinear radiation over the bi-directional stretching surface. For this purpose, two different nano-particles, namely silver (Ag) and molybdenum di-sulfide (MoS2), were selected. Three different conventional base fluids were utilized to form desired hybrid nanofluids such as water (H2O), engine oil (EO), and ethylene glycol (EG). We obtained steady three-dimensional highly nonlinear partial differential equations. These highly nonlinear partial differential equations cannot be solved analytically, so these equations were handled in MATLAB with the BVP-4C technique with convergence tolerance at 10−6. The graph depicts the effect of the magnetization effect, thermal radiation, and stretching ratio on rotating hybrid nanofluids. Additionally, the impact of thermal radiation on the heat coefficient of three different hybrid nanofluids is being investigated. The augmentation in magnetization decreases the primary velocity, whereas the increment in radiation enhances the primary velocity. The stretching ratio and the presence of higher magnetic forces increase the temperature profile. The concentration profile was enhanced with an increment in the magnetic field, stretching, and rotation ratio. The maximum Nusselt number was achieved for the Ag-MoS2/EO hybrid nanofluid. It was concluded that augmentation in nonlinear radiation enhances the heat transfer coefficient for the examined cases (I) and (II) of the hybrid nanofluids. The Nusselt number doubled for both the examined cases under nonlinear radiation. Moreover, it was discovered that Ag-MoS2/water produced the best heat transfer results under nonlinear radiation. Therefore, the study recommends more frequent exploration of hybrid nanofluids (Ag-MoS2/water) when employing nonlinear radiation to analyze the heat transfer coefficient. [ABSTRACT FROM AUTHOR]

Model construction for different physical situations, and developing their solutions, are the major characteristics of the scientific work in physics and engineering. Korteweg–de Vries (KdV) models are very important due to their ability to capture different physical situations such as thin film flows and waves on shallow water surfaces. In this work, a new approach for predicting and analyzing nonlinear time-fractional coupled KdV systems is proposed based on Laplace transform and homotopy perturbation along with Caputo fractional derivatives. This algorithm provides a convergent series solution by applying simple steps through symbolic computations. The efficiency of the proposed algorithm is tested against different nonlinear time-fractional KdV systems, including dispersive long wave and generalized Hirota–Satsuma KdV systems. For validity purposes, the obtained results are compared with the existing solutions from the literature. The convergence of the proposed algorithm over the entire fractional domain is confirmed by finding solutions and errors at various values of fractional parameters. Numerical simulations clearly reassert the supremacy and capability of the proposed technique in terms of accuracy and fewer computations as compared to other available schemes. Analysis reveals that the projected scheme is reliable and hence can be utilized with other kernels in more advanced systems in physics and engineering. [ABSTRACT FROM AUTHOR]

In the present paper, some new generalizations of dynamic inequalities of Gronwall–Bellman–Pachpatte-type on time scales are established. Some integral and discrete Gronwall–Bellman–Pachpatte-type inequalities that are given as special cases of main results are original. The main results are proved by using the dynamic Leibniz integral rule on time scales. To highlight our research advantages, several implementations of these findings are presented. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

We prove some new dynamic inequalities of the Gronwall–Bellman–Pachpatte type on time scales. Our results can be used in analyses as useful tools for some types of partial dynamic equations on time scales and in their applications in environmental phenomena and physical and engineering sciences that are described by partial differential equations. [ABSTRACT FROM AUTHOR]

We prove new Hardy–Copson-type (γ , a) -nabla fractional dynamic inequalities on time scales. Our results are proven by using Keller's chain rule, the integration by parts formula, and the dynamic Hölder inequality on time scales. When γ = 1 , then we obtain some well-known time-scale inequalities due to Hardy. As special cases, we obtain new continuous and discrete inequalities. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

As a new usage of Leibniz integral rule on time scales, we proved some new extensions of dynamic Gronwall–Pachpatte-type inequalities on time scales. Our results extend some existing results in the literature. Some integral and discrete inequalities are obtained as special cases of the main results. The inequalities proved here can be used in the analysis as handy tools to study the stability, boundedness, existence, uniqueness and oscillation behavior for some kinds of partial dynamic equations on time scales. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities. [ABSTRACT FROM AUTHOR]

In this article, with the help of Leibniz integral rule on time scales, we prove some new dynamic inequalities of Gronwall–Bellman–Pachpatte-type on time scales. These inequalities can be used as handy tools to study the qualitative and quantitative properties of solutions of the initial boundary value problem for partial delay dynamic equation. [ABSTRACT FROM AUTHOR]

Nonlinear vibration control of the twelve-poles electro-magnetic suspension system was tackled in this study, using a novel control strategy. The introduced control algorithm was a combination of three controllers: the proportional-derivative (P D) controller, the integral resonant controller (I R C) , and the positive position feedback (P P F) controller. According to the presented control algorithm, the mathematical model of the controlled twelve-poles rotor was established as a nonlinear four-degree-of-freedom dynamical system coupled to two first-order filters. Then, the derived nonlinear dynamical system was analyzed using perturbation analysis to extract the averaging equations of motion. Based on the extracted averaging equations of motion, the efficiency of different control strategies (i.e., P D ,   P D + I R C ,   P D + P P F ,   and   P D + I R C + P P F ) for mitigating the rotor's undesired vibrations and improving its catastrophic bifurcation was investigated. The acquired analytical results demonstrated that both the P D and P D + I R C controllers can force the rotor to respond as a linear system; however, the controlled system may exhibit the maximum oscillation amplitude at the perfect resonance condition. In addition, the obtained results demonstrated that the P D + P P F controller can eliminate the rotor nonlinear oscillation at the perfect resonance, but the system may suffer from high oscillation amplitudes when the resonance condition is lost. Moreover, we report that the combined control algorithm ( P D + I R C + P P F ) has all the advantages of the individual control algorithms (i.e., P D ,   P D + I R C ,   P D + P P F ), while avoiding their drawbacks. Finally, the numerical simulations showed that the P D + I R C + P P F controller can eliminate the twelve-poles system vibrations regardless of both the excitation force magnitude and the resonant conditions at a short transient time. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Evolutionary approaches have a critical role in different disciplines such as real-world problems, computer programming, machine learning, biological sciences, and many more. The design of the stochastic model is based on transition probabilities and non-parametric techniques. Positivity, boundedness, and equilibria are investigated in deterministic and stochastic senses. An essential tool, Euler–Maruyama, is studied for the solution of said model. Standard and nonstandard evolutionary approaches are presented for the stochastic model in terms of efficiency and low-cost approximations. The standard evolutionary procedures like stochastic Euler–Maruyama and stochastic Runge–Kutta fail to restore the essential features of biological problems. On the other hand, the proposed method is efficient, of meager cost, and adopts all the desired feasible properties. At the end of this paper the comparison section is presented to support efficient analysis. [ABSTRACT FROM AUTHOR]

Concerns about the environment, the cost of energy, and safety mean that low-energy cold-mix asphalt materials are very interesting as a potential replacement for present-day hot mix asphalt. The main disadvantage of cold bituminous emulsion mixtures is their poor early life strength, meaning they require a long time to achieve mature strength. This research work aims to study the protentional utilization of waste and by-product materials as a filler in cold emulsion mixtures with mechanical properties comparable to those of traditional hot mix asphalt. Accordingly, cold mix asphalt was prepared to utilize paper sludge ash (PSA) and cement kiln dust (CKD) as a substitution for conventional mineral filler with percentages ranging from 0–6% and 0–4%, respectively. Test results have shown that the incorporation of such waste materials reflected a significant improvement in the mixture's stiffness and strength evolution. The cementitious reactivity of PSA produces bonding inside the mixtures, while CKD is used as an additive to activate the hydration process of PSA. Therefore, based on the results, it will be easier to build cold mixtures by shortening the amount of time needed to reach full curing conditions. [ABSTRACT FROM AUTHOR]

The solitary wave solutions of the (2 + 1) -dimensional nonlinear Chiral Schrödinger ((2 + 1) -D CNLS) equation by making use of the modern extended direct algebraic approach are investigated in this paper. Such a nonlinear model's different categories of solitary waves solutions are found. The division of semi-dark solitons, singular dark-pitch solitons, single solitons of type 1 along with 2, intermixed hyperbolically, trigonometrically and rational solitons are developed and evaluated using software tools for numerical calculations. Detailed graphical interpretation of results with deliberation is also discussed. This paper effectively depicts 3D- and 2D-contour plots to provide further detail about the physical characteristics of the obtained solutions. We compare our solutions to previously reported findings along with study motivation and future directions. The fractional quantum hall effect's edge states are defined by the discussed model. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The purpose of this research is to analyze the general equations of double diffusive magneto-free convection in a rate type fluid presented in non-dimensional form, and apply to a moving heated vertical plate as in the boundary layer flow up, with existence of externally magnetic fields which are either moving or fixed consistent with the plate. Thermal transport phenomenon is discussed in the presence of constant concentration coupled with first-order chemical reaction with exponential heating. An innovative definition in power law (CF) and Mittag-Leffler (ABC) kernels form time fractional operators are implemented to hypothecate the constitutive mass, heat and momentum equations. The results based on special functions are obtained by using the technique of Laplace transformation to tackle the non-dimensional equations for velocity, mass and energy. The contribution of mass, thermal and mechanical components on the dynamics of fluid is presented and discussed independently. An interesting property regarding the behavior of the fluid velocity is found when the movement is observed in the magnetic intensity along with the plate. In that situation, the fluid velocity is not to be zero when it is far and away from the plate. Moreover, the heat transfer aspects, flow dynamics and their credence on the parameters are drawn out by graphical illustrations along with some special cases for the movement of the plate which are also studied. [ABSTRACT FROM AUTHOR]