Nonlinear Differential Systems Research Articles

Thermal analysis of hybrid nanoliquid contains iron-oxide (Fe3O4) and copper (Cu) nanoparticles in an enclosure

The major aim of this work is to analyze the thermophysical properties of hybrid nanoliquid inside a square lid driven enclosure under the effect of applied magnetic field and mixed convection. The Hybrid nanofluid is considered a suspension of Iron-oxide (Fe3O4) and Copper (Cu) nanoparticles into water. The cavity walls have varying properties such as top adiabatic wall is moving continuously while the lower wall is maintained at a high constant temperature, in addition, the vertical walls are kept at a low fixed temperature. The magnetic field is applied to the right vertical wall in a horizontal direction. Additionally, the effects of buoyancy forces caused by temperature gradients and shear forces caused by continuous lid motion are considered. The mathematical modelling of problem with all assumptions yields the nonlinear partial differential system. First this system is transferred into non-dimensional form and then transformed system is solved by using Galerkin finite element method (GFEM) along with Gaussian elimination method. Results for isotherms, streamlines and average Nusselt number are obtained versus Richardson number (0.1 ≤ Ri ≤ 15), Grashof number (10 ≤ Gr ≤ 10000), Hartmann number (0 ≤ Ha ≤ 100), volume fractions of solid nanoparticles (0.005 ≤ ϕ1 ≤ 0.02) and (0.005 ≤ ϕ2 ≤ 0.02). It is observed that the Richardson number and Grashof number have significant impacts on both flow velocity and temperature. In addition, concentration of hybrid nanoparticles improves the heat transfer performance. The obtained results may be crucial for thermal management in the cooling of electronics, heat exchangers, solar thermal collectors, industrial operations, medical equipment, HVAC systems, food processing, and renewable energy systems.

Analysis of fluid flow and heat transfer in CNT-infused spiraling disk

This study investigates the fluid flow and heat transfer characteristics influenced by the thermophysical properties of carbon nanotube suspension in engine oil over a stretching-spiraling disk. The surface comprises Homan stagnation point flow impinging normal to a rotating, radially stretching disk, which gives velocity a form of logarithmic spiral. Similarity ansatz transformed coupled nonlinear differential equation system is derived and solved numerically using MATLAB’s bvp4c collocation method. Numerical and asymptotic solutions are also obtained against the controlled parameters via graphical representations and tabular data. Findings indicate that the magnetic field enhances temperature distribution while reducing the velocity field. At the same time, stretching increases radial velocity but decreases azimuthal velocity and temperature profiles, regardless of carbon nanotube type. The asymptotic values of skin friction decline with an increase in the spiralisng angle and in the absence of a magnetic field for both SWCNTs and MWCNTs cases.

Novel intelligent supervised neuro-structures for nonlinear financial crime differential systems

Artificial intelligence (AI)-based applications contribute to monitoring financial transactions and detect fraudulent activity in real-time by analyzing transaction patterns, consumer behavior, and other statistics, making them essential for quickly addressing potential threats in the fight against financial crime dynamics. Leveraging financial crime systems with intelligent supervised neuro-structures exploiting nonlinear autoregressive exogenous networks integrating damped least square (NARX-DLS) optimization methods to achieve an appropriate degree of accuracy and adaptability for the estimation of complex nonlinear financial crime differential systems (NFCDSs). The representative NFCDS for financial crime indicators is expressed as susceptible individuals, financial criminals, individuals under prosecution, imprisoned individuals, and honest individuals. The Adams numerical solver accomplishes the acquisition of synthetic data for the layer structure NARX-DLS algorithm execution to solve NFCDSs for various financial crime parameters, such as recruitment rate, influence rate, conversion rate to honest people, financial criminal prosecution rate per capita, discharge and acquittal rate from prosecutions, percentage of discharge rate from prosecution, transition rate to prison, and freedom rate. A sturdy overlap between the solutions of NARX-DLSs and the reference numerical results of NFCDSs implies that the error value is close to a desirable value of zero. The effectiveness of the NARX-DLSs is evidenced by including a variety of assessment metrics that carefully examine the model’s correctness and efficacy, including mean square error-based convergence arches, adaptive regulating parameters, error distribution, and input-error/cross-correlation analyses.

Numerical study of binary mixture and thermophoretic analysis near a solar radiative heat transfer

The main focus of the current article is to investigate the two-dimensional boundary layer flow of non-Newtonian fluid induced by a linear stretching surface in the streamwise direction. The flow features of non-Newtonian fluid (i.e. shear-thinning and thickening nature of the fluids) are explored with Carreau fluid model. In addition, thermophoresis, Brownian motion, thermal radiation (with Rosseland approximation), binary mixture and activation enthalpy are also incorporated in fluid model for better analysis of thermal and solutal properties. The mathematical modelling of under consider physical problem yields nonlinear partial differential system. The governing mathematical system is first simplified with scaling transformations for the high Reynolds number and then transformed into non-dimensional ordinary differential system by using the similarity variables. Since the governing mathematical system comprised on nonlinear boundary value problem, thus shooting method is utilized for the numerical solution of the fluid flow governing equations. The obtained results followed the qualitative manners of the previously reported data. The computed results for important physical quantities (i.e. velocity, temperature, and concentration) are presented through graphs and then interpreted physically. It is observed that the boundary layer thickness increased for shear thickening fluids (n>1) while it is reduced for shear thinning fluids (n<1). Also, the temperature of shear thinning fluid is higher than shear thickening fluid. In addition, heat generation and thermal radiations enhance the thermal boundary layer. Thermophoretic viscosity effect reduces the concentration profile significantly in the flow domain.

Radiative bioconvective flow with non-uniform heat source and Soret and Dufour impacts

Background and objectiveThe stretched flow with heat transfer has pivotal role in geothermal energy system, oil extraction, continuous casting, metal spinning and electronic cooling. Owing to this fact, the current analysis focuses on non-linear thermal radiation effect in bio-convective stagnation point flow by a stretchable wedge. Darcy relation is used to discuss the porous space. Convective conditions are deliberated. Non-uniform heat source is addressed. Soret and Dufour outcomes are analyzed. Dissipation and magnetohydrodynamics are discussed. Presence of gyrotactic microorganisms along with chemical reaction is considered. MethodologyRelated non-linear partial differential equations (PDEs) are reduced into dimensionless ordinary differential equations (ODEs) through adequate transformations. Optimal homotopy analysis method (OHAM) is adopted for the computations of related nonlinear differential systems. ResultsFlow, microorganism field, concentration and temperature distribution are graphically explored. Numerical analysis for coefficient of skin friction, microorganism density number and Sherwood and Nusselt numbers against emerging parameters are discussed. It is noted that velocity and skin friction coefficient have similar scenario for modified Hartman number. Thermal transport rate and temperature have reverse trends for non-uniform heat source variable. An augmentation in thermal distribution is seen through thermal Biot number. Larger Dufour number has increasing trend for temperature. An increasing trend for solutal Biot number for concentration is noticed. Larger Soret number leads to concentration enhancement. Microorganism field and motile density number against Peclet number have opposite response. There is reduction for bio-convective Lewis number in motile density number.

Fractional view analysis of coupled Whitham- Broer-Kaup and Jaulent-Miodek equations

In this study, I systematically investigate the fractional Whitham-Broer-Kaup (WBK) system and the fractional Coupled Jaulent-Miodek (CJM) equation under the Caputo fractional calculus. The nonlinear fractional differential equation systems are investigated via the Aboodh transform iteration method and the Aboodh residual power series method, thus offering a thorough analytical investigation. The dynamics of the fractional WBK system are accomplished using the Aboodh transform iteration method, and the Aboodh residual power series method is employed to study the behavior of the fractional CJM equation. Using established solutions, we completely analyze their dynamics employing both symbolic computations and numerical simulations. Consequently, novel solutions are identified, and the behavior of these fractional systems in the Caputo operator sense are clarified. The results obtained show good agreement of convergence of the numerical and analytical solutions, highlighting the effectiveness of the schemes adopted for unraveling the complex dynamics of fractional nonlinear systems.

Connecting Poincaré Inequality with Sobolev Inequalities on Riemannian Manifolds

We connect the Poincaré inequality with the Sobolev inequality on Riemannian manifold in a family of integral inequalities $(1.5)$. For these continuum of inequalities, we obtain topological structure theorems of manifolds generalizing previous unification theorems in both intrinsic and extrinsic settings ([33]). Manifolds which admit any of these integral inequalities are nonparabolic, affect topology, geometry, analysis, and admit nonconstant bounded harmonic functions of finite energy. As a consequence, we have proven a Conjecture of Schoen-Yau ([27, p.74]) to be true in dimension two with hypotheses weaker than that used in [1] and [33]$($ which were weaker than the hypotheses set in the conjecture, $($ cf. Remark 1.5$)$. In the same philosophy and spirit as in ([31]), we prove that if $M$ is a complete $n$-manifold, satisfying $\operatorname{(i)}$ the volume growth condition $(1.1)$, $\operatorname{(ii)}$ Liouville Theorem for harmonic functions, and either $\operatorname{(v)}$ a generalized Poincaré- Sobolev inequality $(1.5)$, or $\operatorname{(vi)}$ a general integral inequality $(1.6)$, and Liouville Theorem for harmonic map $u : M \to K$ with $\operatorname{Sec}^K \le 0$, then $(1)$ $M$ has only one end and $(2)$ there is no nontrivial homomorphism from fundamental group $\pi_1(\partial D)$ into $\pi_1 (K)$ as stated in Theorem $1.5$. Some applications in geometry $(\S 3)$, geometric analysis $(\S 4)$, nonlinear partial differential systems $(\S 5)$, integral inequalities on complete noncompact manifolds $(\S 6)$ are made $($cf. e.g., Theorems $3.1$, $4.1$, $5.1$, and $6.1)$. Whereas we made the first study in ([29, 32]) on how the existence of an essential positive supersolution of a second order partial differential systems $Q(u)=0$ on a Riemannian manifold $M$, (by which we mean a $C^2$ function $v \ge 0$ on $M$ that is positive almost everywhere on $M$, and that satisfies $Q(v)=\operatorname{div}(A(x,v,\nabla v)\nabla v)+b(x,v,\nabla v)v\leq 0\quad (5.1)\, $) affects topology, geometry, analysis and variational problems on the manifold $M$. Whereas we generate the work in [35], under $p$-parabolic stable condition without assuming the $p$-th volume growth condition $\lim _{r \to \infty} r^{-p}\operatorname{Vol}(B_r) =0$. The techniques, concepts, and results employed in this paper can be combined with those of essential positive supersolutions of degenerate nonlinear partial differential systems $($cf. for example, Theorems 5.1 - 5.5, 6.1, etc.$)\, $ generalizing previous work in [32, 4.11], which in term recaptures the work of Schoen-Simon-Yau ([25, Theorem 2]). The combined techniques, concepts and method of [32] and [35] can also be used in other new manifolds we found by an extrinsic average variational method ([34]).

Nonlinear thermal radiation analysis for bioconvection peristaltic transport of fourth-grade nanofluid

Nanoparticles mixed with base liquids result in the formation of nanofluids, known for their exceptional thermal conductivity and their ability to enhance the performance of electrical and mechanical devices. Therefore, this study investigates the peristaltic activity of fourth-grade nanomaterial by taking the consideration of magnetic aspects. Analysis is carried out in the presence of motile gyrotactic microorganisms, Ohmic heating, and viscous dissipation. Thermal transport incorporated effects of nonlinear thermal radiation along with Brownian motion and thermophoresis. Thermal and mass convective conditions are imposed on elastic symmetric channels. The assumptions of low Reynolds number and long wavelength approximations have led to the simplification of the nonlinear partial differential equations system into ordinary differential equations. The governing system is solved numerically by NDSolve technique via Mathematica. Graphs are plotted and examined for velocity, thermal field, density of motile gyrotactic microorganisms, and heat transfer rate.

Mass and heat transfer in the boundary layer region of modified second-grade fluid flow over a linearly stretched sheet embedded in porous media

Here, we have improved a model to describe the flow variables, velocity, mass and heat transfer in the boundary layer region of modified second-grade fluid flow over a linearly stretched sheet in a porous media. The modified model is used to study the qualitative impact of buoyancy parameter, second-grade fluid parameter, magnetic parameters, porous parameter, power-law index, and chemical reaction parameter on the flow profiles, radial and axial velocities, temperature, and concentration. Starting with the steady-state governing equations of mass, momentum, heat, and concentration of the fluid flow, we obtained the boundary layer approximations of the flow near the linearly stretched sheet with the no-slip boundary condition. Similarity transformation has been used to convert the partial differential equations system into a nonlinear ordinary differential equations system. The radial velocities, temperature, and concentration profiles have been solved numerically, and the qualitative influence of the flow parameters on the flow variables has been simulated and graphically presented for comparison. We have observed that radial and axial velocities were increasing for the shear-thinning and shearthickening fluids with solutal Grashof number, thermal Grashof number and second-grade fluid parameters. In contrast, the porous and chemical reaction parameters slow down both fluids’ radial and axial velocities. The temperature and concentration increase with the porous and magnetic parameters. However, thermal and solutal Grashof and second-grade fluid parameters suppress temperature and concentration. In shear-thickening fluids, chemical reaction parameters enhance concentration but suppress in shear-thinning fluids.

Boundedness and stability of nonlinear hybrid neutral stochastic delay differential equation with Lévy jumps under different structures

This paper investigates the boundedness and stability of a class of nonlinear hybrid neutral stochastic differential delay systems with Lévy jumps and different structures. The coefficients in this system satisfy the local Lipschitz condition and a suitable Khasminskii-type condition, and the state space of the system is separated into two subsets, the existence uniqueness, asymptotic boundedness, and exponential stability of the system are obtained by designing a new Lyapunov function and applying the M-matrix technique as well as dealing with the non-differentiable delay function. Different with the existing work, we not only consider the neutral term, but also the case of the delay function being bounded and non-differentiable. At last, numerical examples are performed to manifest the obtained results.

Design of Neuro-Stochastic Bayesian Networks for Nonlinear Chaotic Differential Systems in Financial Mathematics

Design of Neuro-Stochastic Bayesian Networks for Nonlinear Chaotic Differential Systems in Financial Mathematics

Conjugate Mixed Convection of a Micropolar Fluid Over a Vertical Hollow Circular Cylinder

This work conducts a numerical examination into the influence of a magnetic field and viscosity dissipation on the movement of a micropolar fluid over the surface of a vertical, hollow circular cylinder via conjugate mixed convection. In this investigation, we obtained a numerical solution for a non-linear differential equations-based modeling system by employing MATLAB and the bvp4c solver, which operates on a two-equation model. We show graphically how micropolar materials, conjugate heat transfer, viscous energy dissipation, buoyancy factors and magnetic field affect the temperature at the interface, local skin friction and heat transfer. By contrasting the acquired results with those found in the published research, which exhibit a high degree of concordance, the validity of the methodology is proven.

Nonisothermal analysis of two uniform boundary layer shear flows

AbstractThe heat transfer phenomenon on the multiphase flows plays an imperative role in several biological and industrial processes, like the oil production industries, catalytic reactors, energy losses in several thermal systems, energy storage, paper manufacture, and heat exchanger systems. Therefore, this study scrutinized the heat transfer characteristic between two uniform boundary layer shear flows with different strengths flowing in the same direction. This problem involves the simulation of the convergence of boundary layers with varying shear strengths. The nonlinear differential system is scrutinized and converted into dimensionless ordinary differential equations by employing appropriate dimensionless variables. The resulting set of highly nonlinear ordinary differential equations is resolved numerically utilizing the Matlab solver “bvp4c.” The resulting numerical solutions are used to construct graphs that illustrate and elucidate the impact of numerous physical parameters on flow patterns. For both fluids, results for the Nusselt number and shear stress are also presented graphically for various parameters. The acquired results demonstrate that the velocity profile upsurges for both upper and lower fluids by enhancing the shear parameter. Furthermore, the number of streamlines is enhanced by augmenting the values of the viscosities ratio parameter. The present problem applies to the trailing edge flow over a thin airfoil with camber.

Iterative learning based convergence analysis for nonlinear impulsive differential inclusion systems with randomly varying trial lengths

SummaryThis paper studies the finite‐time tracking problem for nonlinear impulsive differential inclusion systems with randomly varying trial lengths. First, we convert the set‐valued mapping in the differential inclusion systems to single‐valued mapping by a Steiner‐type selector. For the tracking problem of random discontinuous output trajectories, this paper defines a piecewise continuous variable by zero‐order holder to correct the tracking error of segmented continuity. Then, we introduce the average operator with forgetting factor to design three novel learning schemes, and establish convergence results by using the mathematical analysis tools such as impulsive Gronwall inequality and ‐norm. Finally, a numerical example verifies the validity of the theoretical results, and we compare the tracking performance of the output trajectories for different forgetting factors.

ANALYSIS AND SIMULATION OF THE SIR MODEL ON THE SPREAD OF COVID-19 BY CONSIDERING THE VACCINATION FACTOR

Covid-19 is a serious respiratory disease that can be fatal for those affected. Governments have tried various strategies to conquer the Covid-19 pandemic. One of them is to vaccinate people with 6 years old and over. The vaccination program aims to form herd immunity so that the number of confirmed positive cases can be reduced. The purpose of this research is to form a mathematical model of the SIR (Susceptible-Infected-Recovery) spread of Covid-19 by considering vaccination factors. The SIR model is combined with a vaccination factor to forestall the unfold of Covid-19. The research method includes deriving models of nonlinear differential equation systems, solving qualitative models, deriving the basic reproduction ratio ( ), analysis of equilibrium points, and building simulation models. This model has an asymptotically stable disease-free equilibrium point. At the same time, the endemic equilibrium point is unstable. Model simulation is obtained by using different parameter values. This is proven through the outcomes of the model analysis vaccination coverage is a key parameter that can be controlled to reduce so that the pandemic ends soon.

On a singular mathematical model for brain lactate kinetics

In this paper, we consider a singular nonlinear differential system that characterizes the intricate dynamics of brain lactate kinetics between cells and capillaries, as described by System (1.1) below. We begin by establishing the existence and uniqueness of nonnegative solutions for our system through the application of Schauder's fixed‐point theorem. Subsequently, we explore the behavior of these solutions as the viscosity term approaches zero, shedding light on the system's dynamic evolution in such scenarios. To provide empirical validation for our theoretical findings, we offer a series of numerical simulations. These simulations not only confirm the results we have obtained but also reinforce prior research, underscoring the model's efficiency in capturing the complexities of the brain's lactate kinetics. Our work contributes not only to the theoretical underpinning of this field but also to its practical implications, making it a valuable resource for both researchers and practitioners seeking to comprehend and manipulate these vital biological processes.

SPREADING PATTERN OF INFECTIOUS DISEASES: SUSCEPTIBLE INFECTED RECOVERED MODEL WITH VACCINATION AND DRUG-RESISTANT CASES (APPLICATION ON TB DATA IN INDONESIA)

Mycobacterium tuberculosis is the causative agent of the infectious illness tuberculosis (TB). Indonesia is the world's third-highest TB burden country. TB transmission is prevented by the BCG vaccination. A directly observed treatment, short-course (DOTS) treatment approach can cure TB illness. Recurrent TB may occur due to either relapse or reinfection with drug-resistant bacteria. The goals of this article are formulating the SVITR model with relapse and drug-resistant cases, applying the model to the TB data in Indonesia, determining the model accuracy, determining the spreading pattern and interpreting the result, and simulating the parameters. Literature study and application methods are used in this research. The SVITR model with relapse and drug-resistant cases is a first-order nonlinear differential equation system. The model is applied to TB in Indonesia based on annual data from Indonesian Health Profile, World Bank, and WHO. The model is solved by the fourth-order Runge-Kutta method. The model is accurate enough to explain the spread of TB in Indonesia with a MAPE value of 15,5%. The spreading pattern of tuberculosis infection is upward from 2010 to 2050. In 2050, there are still 8.115.976 TB cases in Indonesia. Hence in 2050, Indonesia's free of TB target has yet to be achieved. Simulation is conducted by increasing BCG vaccination to 95%, reducing contact with TB patients to 5%, increasing treatment to 95%, and lowering relapses and drug-resistant cases to 0.00005%, so the Indonesia free of TB target in 2050 can be achieved from 2042.

Rheological properties of water-based Fe3O4 and Ag nanofluids between boundary layers due to shear flow over a still fluid

This study focused on the heat transfer characteristic between two uniform boundary layer shear flows of viscous fluid above and another nanofluid with different strengths flowing in the same direction. The nanofluid is comprised of Iron (II, III) OxideFe3O4and Silver Ag nanoparticles mixed with water as a base fluid.The problem models the merging of unequal boundary layers. A real-world example can be found in the trailing edge flow of an airfoil with a camber, where the shear layers originating from the upper and lower surfaces possess unequal strengths. The nonlinear differential system is examined, and it is transformed into dimensionless ordinary differential equations (ODEs) through the utilization of suitable dimensionless variables. The resultant set of significantly nonlinear ODEs is then numerically solved using the 'bvp4c' solver in MATLAB. The resulting numerical solutions are used to construct graphs that illustrate and elucidate the effects of various physical parameters on flow patterns. For both fluids, results for the Nusselt number as well as shear are also presented graphically for dissimilar parameters. The obtained results show that the velocity profile increases for both upper and lower fluids by enhancing the shear parameter. Moreover, nanoparticles manifest exceptional heat transfer capabilities due to their remarkably high thermal conductivity. Furthermore, the number of streamlines is enhanced by augmenting values of the viscosities ratio.

Melting and dissipative effects about entropy induced Darcy-Forchheimer flow involving ternary-hybrid nanofluids

Here we examine melting heat in flow of ternary-hybrid nanoliquid bounded by stretching surface. Alumina (Al2O3), Silica (SiO2) and Copper Oxide (CuO) are three utilized nanoparticles. Conventional liquid employed here is water. Heat generation, dissipation and radiation comprise energy equation. Analysis of entropy generation rate is carried out. Implementation of adequate variables converts nonlinear partial differential system to ODEs. ND-solve approach is implemented to achieve solution. Quantities of interest are deliberated. It is noticed that an opposite trend of temperature for radiation and heat generation is found. Augmentation against melting heat and radiation for thermal transport rate is observed. Velocity decays for higher Forchheimer number. Reduction for velocity against melting and porosity is noticed. Temperature enhancement through Forchheimer number is witnessed. Rise in entropy production for Brinkman and Eckert numbers is noticed. Skin friction for Forchheimer number and melting variable has opposite trends.

Applications of Soret and Dufour effects for Maxwell nanomaterial by convectively heated surface

The intension of recent analysis is to discuss the radiated magnetized flow of Maxwell nanoliquid. Flow is induced due to stretching the surface. Convective and zero mass flux conditions are taken into account. Influence of Soret and Dufour are under consideration. Internal heat source, magnetic field and thermal radiation are discussed in energy expression. Random diffusion and thermophoresis characteristics in presence of chemical reaction are deliberated. Thermal conductivity and viscosity depend upon temperature. Similarity transformation is utilized to transform nonlinear partial differential systems into ordinary systems. ND-solve technique is used to get the numerical solutions for nonlinear nondimensional system. Graphical analysis for flow, concentration and thermal distribution versus emerging variables are examined. Computational outcomes for solutal transport rate and Nusselt number via sundry variables are explored. Velocity profile declines against magnetic field, whereas reverse trend found for temperature profile. Thermal field has increasing trend for thermal Biot and Dufour numbers. Larger Maxwell variable has opposite effect on flow field.