Coupled Differential Equations Research Articles

Adaptive-frequency event-based approach to finite horizon state estimation for complex networks using multi-channel random access protocol

The issue of H∞ state estimation is addressed for complex networks (CNs) with inner coupling disturbance (ICD) while utilizing adaptive-frequency event-triggered mechanism (AFETM) and multi-channel random access protocol (MRAP). To maintain transmission frequency as much as possible while reducing data transmission, the proposed AFETM dynamically modifies the threshold based on the historical number of transmissions within a defined time interval. Data transmission after AFETM is scheduled by the MRAP, which enables the random selection and transmission of multiple signals, thereby avoiding network conflicts and congestion. The primary objective is to devise a estimator that guarantees the estimation errors meet the prescribed H∞ performance. The attainment of sufficient conditions to achieve this objective involves the utilization of stochastic analysis. On this basis, the expected estimator gain is determined through the solution of the backward coupled difference equations. Ultimately, the performance of the devised estimator is validated by simulation.

Non-similar analysis of micropolar magnetized nanofluid flow over a stretched surface

The study of micropolar nanofluids unveils intriguing applications, propelled by their exceptional heat transfer capabilities in comparison to conventional fluids. This investigation focuses on analyzing the behavior of magnetized micropolar nanofluid flow over a stretched surface, taking into account crucial factors such as viscous dissipation and heat source. The chosen base fluid is blood, with Copper [Formula: see text] nanoparticles serving as the selected material. Incorporating the single-phase (Tiwari-Das) model with boundary layer assumptions for micropolar nanofluid flow, we introduce the volume fraction of nanoparticles to assess heat transport. The governing system undergoes transformation into a set of dimensionless non-linear coupled differential equations through appropriate transformations. This transformation involves the utilization of a combination of the local non-similarity technique and bvp4c (MATLAB tool) to derive the system of nondimensional partial differential equations (PDEs) for micropolar nanofluid. Our systematic exploration delves into the consequences of nondimensional parameters on velocity, microrotation, and temperature profiles within the boundary layer, including the Eckert number, micropolar parameter, magnetic field parameter, heat source, Prandtl number, and microorganism parameter. Graphical representations vividly demonstrate that the velocity and temperature of micropolar nanofluid increase with the rise in material parameter values, while the microrotation profile decreases. Increasing the magnetic field parameter leads to a reduction in the velocity profile. Moreover, the micropolar temperature profile shows an increase with the rising Eckert number. Crucially, the research emphasizes that factors like the heat source and Eckert number play a role in decreasing the local Nusselt number. In contrast, an increase in the local Nusselt number is observed for material parameters. Furthermore, the skin friction coefficient decreases as micropolar parameter values increase, whereas an increase in the skin friction coefficient is noted for the magnetic field. The primary focus of this research lies in the development of suitable non-similar transformations for the investigated problem, aiming to yield authentic and efficient results. These results hold substantial promise to make meaningful contributions to future research on nanofluid flows.

Electronic Motion and Path Study in Presence of Varying Electric Field Using SciLab 6.1.1 for Coupled Differential Equations

The study of electronic motion of the electron and its path has been investigated usingcoupledlinear differential equations in presence of electric field. The program executed using Scilabfor the electronic motion.2-D & 3-D trajectories of the electronic path and the variation and the distances in x &y directionswith constant Electric field studied. Plotting oftrajectories successfully done with Scilab software 6.1.1.Here L.T and with D’operator methods shows same results. 3-D trajectoryof the electronic motion is periodic at particular frequencies; along y direction the electrons gain more energy and having more potential with increasing frequency and theinvestigation of oscillations under given conditions is found to be much higher.

Non-similar analysis of bio-convective micropolar nanofluid flow including gyrotactic microorganisms across a stretched geometry

This study explores the novel interaction of gyrotactic microorganisms within a two-dimensional bioconvective micropolar nanofluid flow along a stretched surface, employing the Tiwari-Das nanofluid model. Uniquely, blood is modeled as a micropolar fluid incorporating titanium dioxide ( Ti O 2 ) and silver ( Ag ) nanoparticles. The analysis incorporates influential factors such as viscous dissipation, magnetic field, and heat source effects. By converting the control system into dimensionless nonlinear coupled differential equations, a complete understanding of the system is attained through the application of the local non-similarity approach and bvp4c (MATLAB tool). Particularly, the study provides valuable insight into the influence of dimensionless control parameters on key profiles such as velocity, microrotation, temperature, concentration, and microbial profiles. The findings show that temperature, microrotation, and velocity profiles are all improved by raising the values of micropolar parameters. Furthermore, the microbe profile shows an inverse connection with the Lewis number and a positive association with the Peclet number, whereas the concentration profile declines with increasing Schmidt number values. Furthermore, the study provides a quantitative analysis through tables, revealing variations in the drag coefficient and Nusselt number. This innovative exploration sheds light on the unique behavior of micropolar bioconvective nanofluids, offering valuable contributions to the field of fluid dynamics and bioengineering.

Triple-diffusive magneto-nanofluid flow over a nonlinearly stretching sheet

Magnetic nanofluid constitutes a special class of nanofluids that exhibit both magnetic and fluid properties. Due to its extensive applications, researchers used the magneto-nanofluid to investigate the thermos-diffusion effects on boundary layer flows. The impact on the thermos-diffusion of magneto-nanofluid over a linear stretching sheet was first introduced by Awad et al., (boundary value problems, 1–13, 2013), then Goyal et al., (microfluidics and nano fluidics, 17(3), 591–604) examined the effects of Brownian motion, thermophoresis, and cross-diffusion on the enhancement of convection features of the power-law stretching sheet. In the present study, we extend Goyal’s finding of the thermophoresis effect by including a magnetic field. Consequently, now five partial differential equations with the magnetic field parameter need to be solved, which are converted to ordinary differential equations with similarity transformations. Then, the resulting nonlinear coupled differential equations are solved analytically using the method of Directly Defining the inverse Mapping with the help of Maple software. This is the first time this novel method is used to solve a system with four non-linear coupled differential equations. The analytical results of the study are compared with the available numerical results for a special case and found good agreement. This leads to the conclusion that this novel method is accurate and can be applied to solve not only higher order but also a system of several non-linear differential equations. Further, the skin friction is analyzed for various values of the magnetic parameter. It is observed that, the velocity profile decreases as the magnetic parameter increases. However, quite the opposite is true on the skin friction.

Microbic flow analysis of nano fluid with chemical reaction in microchannel with flexural walls under the effects of thermophoretic diffusion

The current investigation examines the peristaltic flow, in curved conduit, having complaint boundaries for nanofluid. The effects of curvature are taken into account when developing the governing equations for the nano fluid model for curved channels. Nonlinear & coupled differential equations are then simplified by incorporating the long wavelength assumption along with smaller Reynolds number. The homotopy perturbation approach is used to analytically solve the reduced coupled differential equations. The entropy generation can be estimated through examining the contributions of heat and fluid viscosities. The results of velocity, temperature, concentration, entropy number, and stream functions have been plotted graphically in order to discuss the physical attributes of the essential quantities. Increase in fluid velocity within the curved conduit is noticed for higher values of thermophoresis parameter and Brownian motion parameter further entropy generation number is boosted by increasing values of Grashof number.

Bioconvection in a Porous Medium Saturated with a Casson Nanofluid

The bio-convective heat transfer of an incompressible, viscous, electrically conducting Casson nanofluid past a wedge has been analyzed. Furthermore, using a similarity variable, the governing flow equations are transformed to non-linear coupled differential equations corresponding to a two-point boundary value problem, which is solved numerically. A comparison of the solution technique is carried out with previous work and the results are found to be in good agreement. Numerical results for the coefficient of skin friction, Nusselt number, Sherwood number, micro-organism flux as well as the velocity, temperature, nanoparticles and micro-organisms concentration profiles are presented for different physical parameters. The analysis of the obtained results shows that the field of flow is significantly influenced by these parameters.

Uniqueness of Solutions for Boundary Value Problems of Nonlinear Coupled Fractional Differential Equations with Integral Boundary Conditions

Uniqueness of Solutions for Boundary Value Problems of Nonlinear Coupled Fractional Differential Equations with Integral Boundary Conditions

Existence Result for Coupled Random First-Order Impulsive Differential Equations with Infinite Delay

In this paper, we consider a system of random impulsive differential equations with infinite delay. When utilizing the nonlinear variation of Leray–Schauder’s fixed-point principles together with a technique based on separable vector-valued metrics to establish sufficient conditions for the existence of solutions, under suitable assumptions on Y1, Y2 and ϖ1, ϖ2, which greatly enriched the existence literature on this system, there is, however, no hope to discuss the uniqueness result in a convex case. In the present study, we analyzed the influence of the impulsive and infinite delay on the solutions to our system. In addition, to the best of our acknowledge, there is no result concerning coupled random system in the presence of impulsive and infinite delay.

A novel numerical note on the enhanced thermal features of water-ethylene glycol mixture due to hybrid nanoparticles (MnZnFe2O4 – Ag) over a magnetized stretching surface

In this article, we presented a numerical solution of steady-state magnetohydrodynamic (MHD) flow of an incompressible, electrically conducting Casson hybrid nanofluid through a stretching surface under the incitement of viscous dissipation, heat generation and induced magnetism. A viscous mixture of water and ethylene glycol ( W : E G = 60 % : 40 % ) is considered as a base fluid. Enhanced thermal aspects of the working fluid due to suspended manganese zinc ferrite ( MnZnFe 2 O 4 ) and silver ( Ag ) nanoparticles are analyzed by successive over relaxation iterative method. A self-similar procedure is adopted to obtain dimensionless system of governing equations. Order reduction and finite differences discretization of nonlinear coupled differential equations lead to the approximate solution of proposed problem. Impacts of various dominant parameters on the hybridized Casson fluid are examined through the graphs sketched for the functions of velocity, temperature, and induced magnetism. Skin friction coefficient and thermal transfer characteristics at the stretching surface have been simultaneously observed via tabular data prepared for pure nanofluid ( Ag-WEG ) as well as for hybrid nanofluid ( MnZnFe 2 O 4 -Ag/WEG ). It is perceived that induced magnetic field tends to decline the Nusselt number while exhibits a significant growth in the surface drag. Moreover, a significant enhancement in temperature of working fluid has been observed due to Eckert number and heat generation parameter. This decisive role of enhanced thermal features will help to improve industrial growth, waste-water treatment, and automobiles engine efficiency.

Mixed convection of two layers with radiative electro-magnetohydrodynamics nanofluid flow in vertical enclosure

Mixed convection flow of two layers nanofluid in a vertical enclosure is studied. The channel consists of two regions. Region I is electrically conducting while Region II is electrically non-conducting. Region I is filled with base fluid water with copper oxides nanoparticles and Region II is filled with base fluid kerosene oil with iron oxides. The simultaneous effects of electro-magnetohydrodynamics and Grashof number are also taken into account. The governing flow problem consists of nonlinear coupled differential equations which is tackled using analytical technique. Analytical results have been obtained by the homotopy analysis method (HAM). The results for the leading parameters, such as the Hartmann numbers, Grashof numbers, ratio of viscosities, width ratio, volume fraction of nanoparticles, and the ratio of thermal conductivities for three different electric field scenarios under heat generation/absorption were examined. It is found that the effect of the negative electric load parameter assists the flow while the effect of the positive electric load parameter opposes the flow as compared to the case when the electric load parameter is zero. All outcomes for significant parameters on velocity and temperature are discussed graphically.

A System of Coupled Impulsive Neutral Functional Differential Equations: New Existence Results Driven by Fractional Brownian Motion and the Wiener Process

Conditions for the existence and uniqueness of mild solutions for a system of semilinear impulsive differential equations with infinite fractional Brownian movements and the Wiener process are established. Our approach is based on a novel application of Burton and Kirk’s fixed point theorem in extended Banach spaces. This paper aims to extend current results to a differential-inclusions scenario. The motivation of this paper for impulsive neutral differential equations is to investigate the existence of solutions for impulsive neutral differential equations with fractional Brownian motion and a Wiener process (topics that have not been considered and are the main focus of this paper).

Encryption-Decryption-Based State Estimation With Multirate Measurements Against Eavesdroppers: A Recursive Minimum-Variance Approach

This paper is concerned with the secure state estimation problem for a networked system with multi-rate measurements. The measurement data are transmitted to the estimator over a communication network, where an eavesdropper could intercept the transmitted information and generate the state estimates based on the overheard signals. In order to protect the privacy of the system state from information leakage, a novel encryptor is proposed to encrypt the measurement signals into codewords before being transmitted, and a decryptor is then adopted at the user side to decrypt the received codewords into the desired measurement signals, based on which a recursive state estimator is developed whose parameter is calculated by solving several coupled difference equations. Here, the secret key for decryption is available to the user but is unknown to the eavesdropper. The encryptor and the estimator are co-designed such that 1) at the user side, the estimation error covariance has an upper bound that is subsequently minimized in the sense of the matrix trace, where the uniform boundedness of the error covariance is also examined; and 2) at the eavesdropper side, the corresponding state estimation error is divergent. Two simulation examples are provided to demonstrate the effectiveness of our developed secure state estimation scheme.

Thermal analysis of MHD casson-sutterby fluid flow over exponential stretching curved sheet

The two-dimensional flow of Sutterby-Casson fluid flow over an exponentially curved sheet is considered. Incompressible and steady flow is taken into account. The magnetic and electric fields are ignored due to the small Reynolds number in the flow assumptions. Magnetic and chemical dipoles are considered at stretchable curved sheet. Heat generation and slip phenomena have been considered in the present analysis. The governing models of the above assumptions are reduced by implementing the boundary layer approximations and gained nonlinear coupled differential equations. The couple differential equation system is reduced in a dimensionless system (ordinary differential equations) using appropriate transformations. The dimensionless system is solved through a numerical scheme due to finding the results involving physical factors. The results are highlighted in graphs and as well as tables. Concentration achieved higher values by enlargement in the Brownian factor. The movement of particles becomes faster due to the enlargement of the Brownian factor, ultimately increment in concentration. Energy activation factor values enlarged which gained lesser values of Nusselt factor and mass transfer factor while friction factor remains constant. The reaction of chemical factor impact on mass transfer, friction factor, and heat transfer have been debated.

Markov decision processes approximation with coupled dynamics via Markov deterministic control systems

Abstract This article presents an approximation of discrete Markov decision processes with small noise on Borel spaces with an infinite horizon and an expected total discounted cost by the corresponding deterministic Markov process. In both cases, the dynamics evolve through a system consisting of two coupled difference equations. It is assumed that the difference equations of the system are perturbed by a small noise. Under our assumptions, a bound for the stability index is given, and the optimal cost convergence rate is estimated using a small perturbation parameter. Moreover, the convergence of the optimal policy on compact subsets is verified. Finally, two examples are presented to illustrate the developed theory.

Dirichlet Graph Convolution Coupled Neural Differential Equation for Spatio-temporal Time Series Prediction

Dirichlet Graph Convolution Coupled Neural Differential Equation for Spatio-temporal Time Series Prediction

Adaptive Fuzzy Boundary Observer Design for Uncertain Linear Coupled Hyperbolic Partial Differential Equation Systems

Joint uncertainties and state estimation of a class of linear coupled hyperbolic partial differential equation systems in the presence of unstructured and structured uncertainties are studied in this paper. For unstructured uncertainties which are completely unknown, by employing Takagi-Sugeno fuzzy logic system to approximate the unstructured uncertainties, a novel adaptive fuzzy boundary observer is developed to estimate both unknown system states as well as unknown weights in the fuzzy logic system, and the estimation errors are ultimately bounded. Therein, in the design of the proposed observer, a set of swapping filters and infinite dimensional backstepping technique are combined. On the other hand, for structured uncertainties that can be described in a concrete parameterized form, the proposed method can easily achieve the exact estimation of weights and states to their true values. The rigorous proof is provided to show that the ultimately bounded estimation errors for the case of unstructured uncertainties and the exponential convergent estimation errors for the case of structured uncertainties can be realized. Finally, three illustrative simulations are carried out to show the feasibility and effectiveness of the developed methods in this paper.

Exploring the dynamics of active swimmers microorganisms with electromagnetically conducting stretching through endothermic heat generation/assimilation flow: Observational and computational study

Enhancements brought about by motile gyrotactic microorganisms encompass improved mixing, efficient oxygen and nutrient transfer, environmental sensing, and reactions, as well as potential applications in bioremediation, contributing to the advancement of knowledge in fluid dynamics and biological locomotion. These microorganisms find utility in various fields such as biotechnology, environmental engineering, and fluid dynamics research, among others, playing a pivotal role in numerous ecological processes. The present study places its focus on the investigation of the effects associated with mass and heat transport in a fluid flow scenario featuring the presence of a heat source or sink. Specifically, the study aims to examine the impact of nanoparticles on Powell-Eyring fluid flow in the presence of a magnetic field (MHD) across a stretched sheet, taking into account factors such as activation energy, heat sources, and thermal radiation. Furthermore, the study explores the influence of motile gyrotactic microorganisms on various parameters. Recognizing the dearth of research in the realm of polymer extrusion processes, this study strives to bridge this research gap. Its primary objective is to develop a mathematical formulation employing a boundary layer approach, which encompasses the consideration of the interrelated effects of mass and heat transport in Eyring-Powell fluid flow across a stretched sheet in the presence of thermal radiation and chemical reactions from figure it shows that temperature profile rises as result of radiation parameter's increasing values (0.1<Rd<0.4). The impact of Lb is also showed with the help of graph. Greater diffusive mixing is implied by higher Lb for (0.1<Lb<0.4), which tends to distribute the microbes more equally throughout the fluid. This research study serves as an inspiration for the innovation of endogenous heat generation/consumption within the flow of motile organisms exhibiting gyro-taxis in the presence of magnetic flux density on a stretching sheet. To address the complexity of the problem, the renowned BVP4C package, a computational software tool in MATLAB, is utilized for solving a set of highly intricate and nonlinear coupled differential equations. The nonlinear nature of these equations poses significant challenges, necessitating the application of specialized numerical methods to ensure accurate and efficient solutions.

Dissipative Lorentz force influence on mass flow over a micro‐cantilever sensor sheet under magnetic Ohmic heating

AbstractThe novelty and main aim of the present numerical analysis is to explore the magneto‐thermo‐fluid characteristic features of incompressible, time‐dependent electrically conducting second‐grade fluid flow about a micro‐cantilever sensor sheet suspended in a squeezed regime between two parallel plates under the influence of Lorentz force field and viscous dissipation effects. Pertaining to this physical situation, the primitive forms of produced coupled nonlinear partial differential equations are rendered to non‐dimensional ordinary differential equations through appropriate scaling transformations. The resultant coupled nonlinear boundary value physical problem is solved by deploying a robust BVP4C Matlab function. The key features of the emerged different fluid flow parameters are documented in terms of extensive graphical visualization and tabular discussion. The current numerical investigation showed that, the increasing second‐grade fluid parameter significantly decreases the flow field and enhances the thermal and mass diffusion fields. Magnifying permeable velocity number decreases the velocity and increases the heat and concentration transport process. The thermal distribution over a sensor region is boosted with increasing Eckert number through viscous dissipation and magnetic Ohmic heating. Further, the elevating squeezing number decreases the skin friction and enhancing second‐grade fluid number boosted the skin‐friction coefficient. In addition to this, the increasing Schmidt and squeezing parameters decreases the local Sherwood number. Finally, a reasonable agreement between the present numerical solutions with the former results is presented.

A new model of time-dependent fractional second grade fluid for two-dimensional channel flow with heat transfer

The goal of the current paper is to create a novel model for the two-dimensional flow (TDF) of a second-grade fluid and the transfer of heat due to free convection. The second-grade fluid travels through the porous media and is electrically conducted. The governing equation for fluid velocity and temperature is formulated as a set of partial differential equations jointly. The model is developed in fractional form by applying the Caputo-Fabrizio (CF) fractional derivative approach. The two-dimensional flow problem is modeled in terms of one-sided coupled fractional partial differential equations with corresponding physical conditions imposed on the fluid flow and temperature. The problem is initially converted to a dimensionless form and then solved for the exact solutions by applying joint Fourier and Laplace transforms. Exact solutions are examined for fluid velocity and temperature and then in limiting cases are reduced to some well-known fluid motions. Some special cases are also obtained from the general solutions. For the numerical results, Mathcad-15 software is used and the results are plotted in various graphs. The temperature, and velocity profiles are discussed and highlighted for embedded flow parameters. The model obtained in this work is new and can be extended for other fluid models hence this article provides a base for future research.