Nonlinear Coupled Equations Research Articles

Enhanced convective heat transfer in lid-driven porous cavity with aspiration

A scope of enhancing heat transfer during thermal convection in enclosure is explored in this work considering the free aspiration of surrounding fluid. The illustration is made using a two-sided lid-driven porous cavity under differential heating, which is expanded into possible four (assisting, opposing, upward and downward) flow-configurations. The aspiration ports are provided diagonally opposite corners for partial inflow of cold surrounding fluid and partial venting of hot cavity fluid. It leads to primary (or bottom) aspiration and depending upon the direction of sidewall motion, secondary (or top) aspiration. The resulting complex mixed-flow (shear flow, buoyant flow and aspirated flow) through porous medium is modeled by applying Brinkman-Forchheimer-Darcy model (BFDM) and Boussinesq approximation. The evolved nonlinear-coupled equations are solved by an in-house code for the wide ranges of parameters (Reynolds number Re=10–500, Richardson number Ri=0.1–100), Darcy number Da=10−3–10−7 and porosity ε=0.1–1) rigorously. The results reveal heightened heat transfer from the aspirated cavity compared to the identical non-aspirated cavity. Depending upon the combination of the parameters, the enhancement could be as high as ∼180%. The upward-flow configuration yields the maximum heat transfer when no external baffle is used for flow partitioning during the case of top aspiration. With the baffle, the opposing flow shows the maximum heat transfer of ∼339%. The study reveals that the aspiration can magnificently enhance heat transfer without any additional expenses for pumping power of it.

Electric Charge transmission through Four Bosons

A non-Maxwellian model based on four bosons is considered. Based on an enlarged U(1)SO(2) abeliansymmetry and preserving the postulates of light invariance and electric charge conservation its aim is to transfer electriccharge Q = 0 and | Q|= 1 . For this, it enlarges Maxwell by associating a fields set { , , }    A U V . Anelectromagnetic system with four intermediary bosons is proposed. It introduces a new electric charge physics, a newelectromagnetic transmission and a new photon physics.Thus, this work says that, while Maxwell electromagnetism focus on charge distribution and forces, there is stillroom for an electromagnetism based on charge transmission and gauge bosons. A new interpretation on the meaning ofelectric charge flux through gauge bosons is taken. Instead of just mediating different nature forces, the gauge bosonsphysics should be first understood as a mechanism for transferring energy-momentum and quantum numbers as electriccharge. At this way, for electric charge transportation four connected gauge bosons are necessary. They are the photon,massive photon and two charged fields.For this, a whole quantum field theory supported on the set principle is generated. It is based on the fields familymeaning associated to a same Lorentz representation (i, j) and tied up by a common gauge symmetry. Our physical caseare four bosons from )21,21( representation sharing an abelian symmetry. This four set provides the physicity necessaryfor transmitting any electric charge value.A new perception for the electromagnetic phenomena is envisaged. It is generalized for a four fields abelianLagrangian made of with antisymmetric and symmetric fields strengths, producing three and four abelian vertices, andgenerating whole relativistic equations with seven new features. It holds a dynamics carrying spin-1 and spin-0, based ongranular and collective fields strengths, set determinism with directive and chance, quanta network, nonlinearity, neutralcharges, photonics.A new scale for electromagnetic interaction is proposed. New intensities and range are derived through couplednonlinear equations, massive particles and the presence of coupling constants beyond the electric charge. A lightuniversality is obtained. Light becomes an absolute (light invariance), ubiquous (couplings constants diverse from electriccharge), directive (fields set vector), contingencies producer (relativism and chance), inner light (selfinteracting photons).

Chebyshev Wavelet Quasilinearization Scheme for Coupled Nonlinear Sine-Gordon Equations

Radial basis function (RBF) has been found useful for solving coupled sine-Gordon equation with initial and boundary conditions. Though this approach produces moderate accuracy in a larger domain, it requires more grid points. In the present study, we develop an alternative numerical scheme for solving one-dimensional coupled sine-Gordon equation to improve accuracy and to reduce grid points. To achieve these objectives, we make use of a wavelet scheme and solve coupled sine-Gordon equation. Based on the numerical results from the wavelet-based scheme, we conclude that our proposed method is more efficient than the radial basic function method in terms of accuracy.

Fluid-Structure-Interaction in Rocket Thrust Chambers Simulation and Validation

This paper describes the simulation approach for the analysis of fluid structure interactions(FSI) of rocket thrust chambers. It is based on a partitioned approach and includes several buildingblocks: codes for computational fluid dynamics (CFD) and computational structural mechanics(CSM) as well as techniques to handle non conforming surface grid and to solve the nonlinear coupledequations in time. One target application is the life time prediction and to simulate the structuralfatigue behaviour. Thus, cyclic loading conditions are important and are the motivation for a surrogatemodel, which is the focus of this contribution. It uses nonlinear mapping algorithms between surfacetemperature and heat flux in combination with a reduction of dimensionality via proper orthognal decomposition(POD). It can be used as a replacement of the time consuming CFD code and acceleratesthe FSI analysis several orders in time. Some applications regarding the validation of the FSI softwareenvironment finalize the description of the simulation approach showing that the simulation ofcomplex and multidisciplinary problems is laborious and needs a widespread understanding.

Coupled nonlinear stochastic differential equations generating arbitrary distributed observable with 1/f noise

Nonlinear stochastic differential equations provide one of the mathematical models yielding 1/f noise. However, the drawback of a single equation as a source of 1/f noise is the necessity of power-law steady-state probability density of the signal. In this paper we generalize this model and propose a system of two coupled nonlinear stochastic differential equations. The equations are derived from the scaling properties necessary for the achievement of noise. The first equation describes the changes of the signal, whereas the second equation represents a fluctuating rate of change. The proposed coupled stochastic differential equations allow us to obtain a spectrum in a wide range of frequencies together with the almost arbitrary steady-state density of the signal.

Approximate Solution for Nonlinear Gas Dynamic and Coupled KdV Equations Involving Local Fractional Operator

In this paper, the nonlinear gas dynamic and coupled KdV equations within localfractional operator are discussed. The approximate solutions are obtained by using thelocal fractional variational iteration method (LFVIM). This method is able to solve largeclass of linear and nonlinear equations effectively, more easily and accurately; and thusthe method has been widely applicable to solve any class of equations in sciences andengineering.

Application of Tanh Method to Complex Coupled Nonlinear Evolution Equations

M.A. Abdelkawy, A.H. Bhrawy, E. Zerrad and A. Biswas Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University, Riyadh-11566, Saudi Arabia Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt Department of Physics and Engineering, Delaware State University, Dover, DE 19901-2277, USA Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah-21589, Saudi Arabia

A Compact Finite Difference Schemes for Solving the Coupled Nonlinear Schrodinger-Boussinesq Equations

In this paper we are going to derive two numerical methods for solving the coupled nonlinear Schrodinger-Boussinesq equation. The first method is a nonlinear implicit scheme of second order accuracy in both directions time and space; the scheme is unconditionally stable. The second scheme is a nonlinear implicit scheme of second order accuracy in time and fourth order accuracy in space direction. A generalized method is also derived where the previous schemes can be obtained by some special values of l. The proposed methods will produced a coupled nonlinear tridiagonal system which can be solved by fixed point method. The exact solutions and the conserved quantities for two different tests are used to display the robustness of the proposed schemes.

Stability Analysis of Traveling Wave Solutions for Generalized Coupled Nonlinear KdV Equations

Stability Analysis of Traveling Wave Solutions for Generalized Coupled Nonlinear KdV Equations

Numerical Wave Solutions for Nonlinear Coupled Equations using Sinc-Collocation Method

In this paper, numerical solutions for nonlinear coupled Korteweg-de Vries(abbreviated as KdV) equations are calculated by the Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. The first step is to discretize time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Dynamic analysis of a rotating double-tapered cantilever Timoshenko beam

Based on the nonlinear von Karman strain and the associated linear stress, the coupling nonlinear dynamic equations of a rotating, double-tapered, cantilever Timoshenko beam are derived using the Hamilton principle. The equation of motion is discretized via the Galerkin method in which the eigenfunctions of a clamped-free Euler–Bernoulli beam are utilized. The natural frequencies and the nonlinear responses of the rotating Timoshenko beam are investigated. Some interesting phenomena of frequency veering and mode shift are observed in the rotating tapered beam due to the coupling effect. The effects of the dimensionless parameters on the natural frequencies of a rotating double-tapered Timoshenko beam are studied through numerical examples.

Global existence and blowup of solutions for nonlinear coupled wave equations with viscoelastic terms

In this paper, we study a system of nonlinear coupled wave equations with damping, source, and nonlinear strain terms. We obtain several results concerning local existence, global existence, and finite time blow‐up property with positive initial energy by using Galerkin method and energy method, respectively. Copyright © 2015 John Wiley & Sons, Ltd.

English

This paper investigates an eco-system with two prey species and a predator. The model equations constitute a set of three first order non-linear coupled difference equations. All possible positive equilibrium points of the model are computed and criteria for the stability of all equilibrium states are established. Simulations are performed in order to illustrate the theoretical results and gain further insight into the behaviour of the system

Numerical Solutions of Coupled Nonlinear Evolution Equations via El-gendi Nodal Galerkin Method

In this research the solution of coupl ed modified Korteweg -de Vries equation (mKdV) and the generalized Hirota–Satsuma coupled KdV equation by using El-gendi nodal Galerkin (EGG) approaches are presented. El-gendi nodal Galerkin (EGG) (EGG) approaches consist of two approaches, the first is El-gendi Chebyshev nodal Galerkin (ECG) and the second approach is called El-gendi Legendre nodal Galerkin (ELG). In these new approaches spaces of the solution and the weak form to the system are presented. The resulted systems of ODES are solved by the fourth order Runge-Kutta solver. The convergence and the stability of these new methods are analyzed numerically. Numerical results are presented and compared with the results obtained by pseudo-spectral method. Original Research Article

Algorithms and Some New Traveling Wave Solutions via New Extension of (G'/G) -expansion Method of Coupled Nonlinear Equations

Algorithms and Some New Traveling Wave Solutions via New Extension of (G'/G) -expansion Method of Coupled Nonlinear Equations

Power and Load Coupling in Cellular Networks for Energy Optimization

We consider the problem of minimization of sum transmission energy in cellular networks where coupling occurs between cells due to mutual interference. The coupling relation is characterized by the signal-to-interference-and-noise-ratio (SINR) coupling model. Both cell load and transmission power, where cell load measures the average level of resource usage in the cell, interact via the coupling model. The coupling is implicitly characterized with load and power as the variables of interest using two equivalent equations, namely, non-linear load coupling equation (NLCE) and non-linear power coupling equation (NPCE), respectively. By analyzing the NLCE and NPCE, we prove that operating at full load is optimal in minimizing sum energy, and provide an iterative power adjustment algorithm to obtain the corresponding optimal power solution with guaranteed convergence, where in each iteration a standard bisection search is employed. To obtain the algorithmic result, we use the properties of the so-called standard interference function; the proof is non-standard because the NPCE cannot even be expressed as a closed-form expression with power as the implicit variable of interest. We present numerical results illustrating the theoretical findings for a real-life and large-scale cellular network, showing the advantage of our solution compared to the conventional solution of deploying uniform power for base stations.

Decoupled Range and Orientation Sensing in Long-Range Magnetoquasistatic Positioning

A technique using magnetoquasistatic fields has been shown to enable accurate ranging in non-line-of-sight environments. Due to the nonlinear field coupling equations, the technique suffers when extended to 2-D and 3-D due to the coupling of range and orientation errors combined with the nonlinear convergence of the solution. Using a 2-axis transmit–receive concept, a theory is presented to decouple range and orientation. The results are linear orientation-invariant ranging and linear range-invariant orientation sensing. Measurements inverted using the decoupled equations demonstrate peak orientation-invariant range errors of 0.2–0.4 m for a range of up to over 40 m, and peak range-invariant orientation errors of $1^{\circ}{\hbox{–}}7^{\circ} $ .

Limit cycles and acoustic radiation analysis of a van der Pol oscillator-plate-medium system

The approximate analytical solution of the limit cycle and the acoustic radiation characteristics of a nonlinear vibro-acoustic coupling system consisting of a non-autonomous van der Pol oscillator, a plate, and the surrounding acoustic medium are investigated. The nonlinear coupling equations of the vibro-acoustic coupling system under external excitation are derived using variational theory. The modal expression method and the incoherent superposition assumption are employed to discretize the displacements and the surface acoustic pressure of the plate, and then the incremental harmonic balance (IHB) method is used to drive the approximate analytical expressions for the limit cycles of the coupling system. The acoustic radiation power level and the surface average velocity under multi-frequency excitation are defined to describe the response of the plate. The results are that there are limit cycle motions in the vibration of the vibro-acoustic coupling system due to the van der Pol oscillator’s excitation, and there are more harmonic components in the system when the parameters are increased. The vibro-acoustic characteristics of the plate present nonlinear variation because of the oscillator’s nonlinear damping force. The method combining the IHB method and the modal expression method can be used to investigate the nonlinear vibro-acoustic coupling characteristics of a structure under external and self-excited excitation.

Modeling and simulation of non-linear dynamic process of the induction motor system with fluctuating potential loads

The induction motor system with fluctuating potential loads is a non-linear complex electro-mechanical system. With beam pumping motors as an example, this paper proposes a multiple factor non-linear mathematical model to study the operating performance of the induction motor system. This model consists of non-linear time varying electromagnetic field equations, mechanical wave equations of sucker rods and non-linear coupling equation of reducer and four-bar linkage. The equations are numerically solved by combining time-step finite element method (TS-FEM), finite difference method (FDM), a linear dimension reduction method and the Newton-Raphson method. Simulation results, which are validated by experiments, reveal the influence of the fluctuating potential load on magnetic field distributions, stator and rotor currents, the input power and the power factor. The model and simulation results provide theoretical and technical supports for subsequent researches on model simplification and energy saving technologies.

Coupled fractional nonlinear differential equations and exact Jacobian elliptic solutions for exciton–phonon dynamics

Abstract An improved quantum model for exciton–phonon dynamics in an α-helix is investigated taking into account the interspine coupling and the influence of power-law long-range exciton–exciton interactions. Having constructed the model Hamiltonian, we derive the lattice equations and employ the Fourier transforms to go in continuum space showing that the long-range interactions (LRI) lead to a nonlocal integral term in the equations of motion. Indeed, the non-locality originating from the LRI results in the dynamic equations with space derivatives of fractional order. New theoretical frameworks are derived, such that: fractional generalization of coupled Zakharov equations, coupled nonlinear fractional Schrodinger equations, coupled fractional Ginzburg–Landau equations, coupled Hilbert–Zakharov equations, coupled nonlinear Hilbert–Ginzburg–Landau equations, coupled nonlinear Schrodinger equations and coupled nonlinear Hilbert–Schrodinger equations. Through the F-expansion method, we derive a set of exact Jacobian solutions of coupled nonlinear Schrodinger equations. These solutions include Jacobian periodic solutions as well as bright and dark soliton which are important in the process of energy transport in the molecule. We also discuss of the impact of LRI on the energy transport in the molecule.