Perturbation Procedure Research Articles

Implementation of Analytical Techniques for the Solution of Nonlinear Fractional Order Sawada–Kotera–Ito Equation

This article uses the Yang transform decomposition method and the homotopy perturbation transform method to study the seventh-order time-fractional Sawada–Kotera–Ito equation. The fractional derivative is taken into account in the Caputo sense. We used the Yang transform with the Adomian decomposition process and homotopy perturbation procedure on the time-fractional Sawada–Kotera–Ito problem to obtain the solution. We looked at a single case and contrasted it with the actual result to validate the methodologies. These techniques create recurrence relations representing the proposed problem’s solution. We then produced graphical representations that allowed us to visually check all of the outcomes in the proposed case for various fractional order values. The results of applying the current methodologies revealed strong connections to the precise resolution of the problem under investigation. The present study also illustrates error analysis. The numerical results obtained using the suggested techniques show that the methods are both simple and have excellent computational merit.

Analytical investigation of asymmetric forced vibration behavior of functionally graded porous plates with structural damping

This research presents a first attempt to analytically determine the asymmetric dynamic transverse characteristics of thin to moderately thick viscoelastic functionally graded porous (VFGP) annular plates. Firstly, the material properties of the plate are assumed to have various nonlinear distributions in terms of porosity coefficient. Secondly, the motion equations are obtained through the first-order shear deformation theory (FSDT) of elasticity, the energy method, and the variations calculus. Thirdly, the standard linear solid (SLS) model is adopted to consider the viscoelastic behavior of the plate. Finally, the perturbation procedure together with Fourier series are utilized to solve the system of partial differential equations, and the asymmetrically dynamic response is found in a closed-form solution. To assess the veracity of the analytical findings, an algorithm based on the finite element (FE) method called the user-defined field (USDFLD) code is developed. In order to benchmark the present study, the dynamic response of VFGP annular plates is scrutinized under two types of excitations (impulsive and step), four different types of radial load profiles (such as constant, linear, parabolic, and sine distributions), and various asymmetric circumferential loads. Moreover, the influence of various geometrical and material characteristics on the dynamic response of VFGP annular plates is investigated.

On the nonlinear behaviour of the Rayleigh–Taylor instability with a tangential electric field for inviscid and perfect dielectric fluids

Fluid interfacial instability induced by gravity or external acceleration, known as the Rayleigh–Taylor instability, plays an important role in both scientific research and industrial application. How to control this instability is challenging. Researchers have been actively exploring the suppression method of applying electric fields parallel to dielectric fluid interfaces. The instability is characterized by the penetration of fingers at the interface. The velocities at the finger tips are the most important quantities since they characterize how fast the penetration occurs. The dynamics of the fingers is nonlinear. We present a nonlinear perturbation procedure for determining the amplitude and velocity of fingers at a Rayleigh–Taylor unstable interface between two incompressible, inviscid, immiscible and perfectly dielectric fluids in the presence of a horizontal electric field in two dimensions. The analytic formulas are displayed explicitly up to the third order of the initial disturbance. The comparison with the data from numerical simulations based on the vortex sheet method shows the theoretical formulas can capture well the nonlinear behaviour of the fingers. It is known that the interplay between the electric field and the fluids can lead to the suppression of interfacial instability. We further analyse the electrical force along the interface and show how this force leads to the instability suppression in our setting. It has been reported numerically in the literature that switching the electric permittivities of the fluids leads to quantitative differences in finger velocity. We show theoretically this phenomenon can only be explained by the nonlinear behaviour of the system.

Perturbation methodology for electromagnetic radiative fluxing of chemical reactive Casson fluid flow under heat source (sink) effectiveness

In this paper, magnetohydrodynamics of a Casson fluid flow is inspected with the presence of thermal radiation and chemical reaction. Employing the perturbation procedure, the modeling equations are tenacious; the graphs are acquired to illustrate the results. The Casson fluid velocity increases as the perturbation parameter increases. Grashof values for heat and mass transport enhanced Casson fluid velocity. Increasing Casson, magnetic, heat source, and radiation parameters reduce the flow velocity. Prandtl number, heat source, and radiation parameter all reduced the temperature profiles. Chemical reaction parameters lowered the concentration profiles. The skin friction enhances with Casson parameter impact. However, the skin-friction coefficient, Sherwood and Nusselt numbers reduce with an increment in the perturbation parameter. In certain cases, this study’s answers agreed well with the previous literature. Casson liquid with a magnetic region using mixed convection by an exponential vertical boundary layer is the novelty of the work.

Entropy generation on chemically reactive hydromagnetic oscillating flow of third grade nanofluid in a porous channel with Cattaneo-Christov heat flux

The heat and mass transfer characteristics along with Cattaneo-Christov heat flux on oscillating hydromagnetic flow of third grade nanofluid through a permeable channel under entropy generation analysis have been examined in this paper. The impacts of chemical reaction, Brownian motion, thermophoresis, Ohmic heating, and radiative heat have also been taken into consideration. The Buongiorno nanofluid model has been utilized for the present analysis.The investigation related to the present study is helpful in biomedical engineering, manufacturing industries as coolants, energy conservation, cancer treatments (like hyperthermia), dynamics of physiological fluids, biomedicines, and nano-drug suspension in pharmaceuticals. The system of nonlinear ordinary differential equations (ODEs) have been attained and solved by applying the Runge-Kutta 4th order method with the help of shooting process after the execution of the perturbation procedure on nondimensional partial differential equations (PDEs). The results of the present study have been deliberated by plotting graphs for the effects of various non-dimensional parameters on entropy, Bejan number, concentration, velocity, and temperature. The numerical values of heat and mass transfer rates for different physical parameters have been computed.

Rheology of peristaltic flow in couple stress fluid in an inclined tube: Heat and mass transfer analysis

The recent investigations ensure that the effect of an endoscope on the peristaltic flow is very important for medical diagnosis and it has many clinical applications such as gastric juice motion in the small intestine when an endoscope is inserted through it. Therefore, we have studied the problem of peristaltic flow with heat and mass transfer through the gap between coaxial inclined tubes where the inner tube is rigid and the outer tube has sinusoidal wave traveling down its wall. The inner tube fulfilled the slip condition while the outer tube has a no-slip condition. The lubrication approximation theory is utilized to simplify the normalized equations. The perturbation procedure is employed to concede the results for the pressure gradient and velocity field, whereas exact outcomes are established for the energy and concentration fields. Frictional forces and pressure rise per wavelength are calculated numerically. The impacts of embedded parameters are portrayed through graphs. It is found that fluid velocity reduces by increasing the couple stress parameter however the inverse effect is noted for the slip parameter. Furthermore, better pumping is viewed in the vertical tube as compared to the horizontal tube. A validity of perturbation solutions for velocity distribution is made with the finite element method and an admirable comparison is also noticed with previously published results.

Iterated hyperplane search for the budgeted maximum coverage problem

We present an iterated hyperplane search approach for the budgeted maximum coverage problem. Our algorithm relies on the idea of searching on specific areas identified by cardinality-constrained hyperplanes. It combines three complementary procedures: a tabu search procedure to identify a promising hyperplane, a hyperplane search procedure to examine candidate solutions on cardinality-constrained hyperplanes and a dedicated perturbation procedure to ensure the diversification of the search. We show the competitiveness of the algorithm on 30 benchmark instances and present experiments to study the key components of the algorithm.

Analysis of Fractional Thin Film Flow of Third Grade Fluid in Lifting and Drainage via Homotopy Perturbation Procedure

Analysis of thin film flows is an important topic in fluid dynamics due to the large number of industrial applications such as food processing, chip manufacturing, irrigation, oil refining process, painting finishing, etc. Analysis involves studying the effects of various parameters in absolute conditions. These parameters may be film thickness, volumetric flux, liquid velocity profile, viscosity, shear stress, gravity, density, and different boundary formations. We have expanded the formulations of non-Newtonian third grade fluid for lifting and draining in fractional space. Fractional calculus along with Homotopy Perturbation Method is used for the solution and analysis purposes. The suitability and consistency of the solutions is determined by detecting residuals in each case. Velocity profile, average velocity, and volume flow for lifting and drainage cases are calculated. To the best of authors knowledge, thin film flow of fractional third grade fluid is not attempted before in lifting and drainage. Investigation shows increase in value of fractional parameter that decreases the velocity profile in lifting while increases the velocity in drainage scenario. Also, the frictional parameter and the gravitational parameter have opposite, while material constant has direct relationship with the velocity profile in lifting case. All the parameters showed inverse effect on the velocity in drainage case.

Quasi-Periodic Solutions of a Damped Nonlinear Quasi-Periodic Mathieu Equation by the Incremental Harmonic Balance Method With Two Time Scales

Abstract Quasi-periodic (QP) solutions of a damped nonlinear QP Mathieu equation with cubic nonlinearity are investigated by using the incremental harmonic balance (IHB) method with two time scales. The damped nonlinear QP Mathieu equation contains two incommensurate harmonic excitation frequencies, one is a small frequency while the other nearly equals twice the linear natural frequency. It is found that Fourier spectra of QP solutions of the equation consist of uniformly spaced sidebands due to cubic nonlinearity. The IHB method with two time scales, which relates to the two excitation frequencies, is adopted to trace solution curves of the equation in an automatical way and find all frequencies of solutions and their corresponding amplitudes. Effects of parametric excitation are studied in detail. Based on approximation of QP solutions by periodic solutions with a large period, Floquet theory is used to study the stability of QP solutions. Three types of QP solutions can be obtained from the IHB method, which agree very well with results from numerical integration. However, the perturbation method using the double-step method of multiple scales (MMS) obtains only one type of QP solutions since the ratio of the small frequency to the linear natural frequency of the first reduced-modulation equation is nearly 1 in the second perturbation procedure, while the other two types of QP solutions from the IHB method with two time scales do not need the ratio. Furthermore, the results from the double-step MMS are different from those numerical integration and the IHB method with two time scales.

A coalitional game theoretic energy transaction algorithm for networked microgrids

With the large-scale application of microgrid technology in distribution networks, emerging energy transactions among multiple microgrids as well as between microgrids and the grid increase the operational burden to the power system. To coordinate these energy transactions, a coalitional game theoretic energy transaction algorithm for networked microgrids is developed in this paper to improve energy exchange efficiency. First, a distance-oriented method for maximizing coalition utilities is proposed to guide the order of transactions in a coalition, and the corresponding coalition utility would be fairly allocated by the Shapley value. Second, a modified coalition formation algorithm consisting of perturbation, merge and split procedures is designed to obtain a Dc-stable otherwise a better Dhp-stable partition on the network, in which no microgrid has an incentive to leave this partition, and the corresponding theoretical proof is given in this paper. Finally, relative to the non-cooperation mode and the Merge&Split procedure, simulation results show the advantages of the proposed algorithm in reducing costs and facilitating energy transactions in the network.

Combined effects of chemical reaction and variable thermal conductivity on MHD peristaltic flow of Phan-Thien-Tanner liquid through inclined channel

The paper investigates the blood flow analysis through a non-uniform inclined channel by treating blood as a non-Newtonian Phan-Thien-Tanner (PTT) liquid. The impact of the chemical reaction and convective boundary conditions are studied in the current formulation. The interaction referring to such constraints report supporting behavior to simulates the particles motion in surgical systems. The fluid movement is regulated through complictatd systems for which solution is enables via perturbation procedure. The influences of diverse emerging parameters over several physiological quantities are scrutinized explicitly. It is also detected that geometric parameters like amplitudes, non-uniform parameters, and inclination angles play a vital role in operating liquid transport phenomena. The obtained results reveal that controlling of velocity due to magnetic constants is observed while thermal determination of particles showing an enhancing trend. Hence magnetic field is used in blood flow analysis such as a catheter, drug delivery, etc. The objective of applicable pertialtic model provdes assistant in hemodialysis.

Pulsating Hydromagnetic Flow of Chemically Reactive Oldroyd-B Nanofluid in a Channel with Brownian Motion, Thermophoresis, and Joule Heating

In the present study, the magnetohydrodynamic pulsating flow of chemically reacting Oldroyd-B nanoliquid via channel with the impressions of Ohmic heating, radiative heat and viscous dissipation is studied. The ruling PDEs (partial differential equations) are changed into ODEs (Ordinary differential equations) by utilizing the perturbation procedure and numerically deciphered by adopting the 4th order Runge-Kutta approach with the aid of the shooting process. The novelty of the current work is to inspect the pulsating flow of Oldroyd-B nanoliquid via channel in the occurrence of an applied magnetic field by deploying the Buongiorno nanofluid model. The application of the proposed physical model is energy production, heating and cooling processes, thermoelectric devices, bio-medical applications like brain tumours, cancer treatment, drug targeting. Detailed analysis on the impacts of several pertinent parameters for velocity, temperature, nanoparticles concentration, rates of heat and mass transfer is done. The outcomes predict that the velocity of nanoliquid is improved with augmenting frequency parameter while it is reduced with acceleration in Hartmann number. The temperature rises with an improvement of thermophoresis, viscous dissipation, and Brownian motion while it falls for a given rise in Hartmann number and thermal radiation. Further, the nanoparticle concentration rises with an increasing Brownian motion while it falls over rising chemical reaction, thermophoresis, and Lewis number.

Entropy Generation on Pulsatile Hydromagnetic Flow of Jeffrey Nanofluid in a Porous Channel with Brownian Motion, Thermophoresis, and Heat Source/Sink Using Cattaneo-Christov Heat Flux

In this work, the entropy generation on MHD pulsatile flow of Jeffrey nanofluid in a porous channel with Cattaneo-Christov theory is investigated. Buongiorno nanofluid model is utilized to see the impact of thermophoresis and Brownian motion. The consequences of thermal radiation, heat source/sink, viscous dissipation, and Ohmic heating are considered. The governing equations are transformed to a system of ordinary differential equations by applying the perturbation procedure then numerically tackled with fourth-order Runge-Kutta scheme aided by shooting technique. The influences of different emerging parameters and variables on velocity, temperature, nanoparticles concentration, entropy generation, and Bejan number are presented graphically. The influence of emerging parameters on heat and mass transfer rates are prearranged in table. The temperature of nanofluid increases with an enhancement in Eckert number, thermophoretic, and Brownian movements, whereas it decelerates for the rising values of cross flow Reynolds number. The concentration of nanoparticles diminishes with an increment in the Lewis number, chemical reaction parameter, and Brownian motion parameter whereas it improves with a rise in thermophoresis parameter. The entropy generation is an increasing function of Eckert number and radiation parameter. Further, the Bejan number is enhanced for increasing the values of Hartmann number.

Cation Mixing and Capacity Loss in Li||Ni0.6Mn0.2Co0.2O2 Cells: Experimental Investigation and Application of the Multi-Site, Multi-Reaction Model

We clarify the degradation phenomena in a pouch cell that contains an insertion electrode (LizNi0.6Mn0.2Co0.2O2 or lithated NMC622) and a Li counter electrode. Greater than 500 cycles have been achieved in these cells employing 4 mAh/cm2 for both the initial Li metal negative and the NMC622 positive, and we find that cation mixing within the NMC622 is prevalent. That is, transition metals (Ni, and to a lesser extent, Mn and Co) in the transition-metal layer of NMC622 irreversibly exchange places with Li in the Li layer of NMC622, corresponding to a loss of Li sites and a concomitant loss of Coulombic capacity. The use of 1) a perturbation procedure of a recent publication employing the multi-site, multi-reaction model for the porous positive electrode and 2) a procedure to average the degradation phenomena over each cycle, which is shown to be consistent with slow degradation, simplifies the analysis of the experimental data and enables straightforward parameter regression. The resulting agreement between the model calculations and the experimental data is quite good, with the differences being similar to experiment-to-experiment variation.

Novel piezoelectric wind energy harvester based on coupled galloping phenomena with characterization and quantification of its dynamic behavior

In this study, a novel piezoelectric energy harvester is proposed based on coupled transverse and interference galloping to improve the energetic performance of the conventional transverse galloping-based piezoelectric energy harvester. To quantify the stochastic characteristics of the aerodynamic force under the coupled galloping effects, we developed a special approach that allowed us to successfully characterize the aerodynamic force obtained under a transient state and develop a set of coupled dynamic model system. An extensive investigation on the energetic state of the proposed system and its nonlinear behavior revealed the existence of an additional nonlinear damping mechanism. In particular, the associated nonlinear damping force was identified based on the energetic consideration of the proposed system. To the best knowledge of the authors, such a characterization process has not yet been reported. In addition, the dynamic model system was systematically designed by performing an eigen-analysis using the vector operator approach. Furthermore, a perturbation procedure was conducted to obtain the nonlinear limit-cycle behavior of the proposed system. The comparative analysis of the theoretical values derived using the proposed model system with those obtained from experiments revealed that they were consistent with each other, which validated the accuracy of the current modeling approach. When compared to the average electric power harvested from the conventional (transverse) galloping-based piezoelectric energy harvester, the proposed energy harvester generated 20 times more electric power.

Intensification-driven local search for the traveling repairman problem with profits

The Traveling Repairman Problem with Profits is to select a subset of nodes (customers) in a weighted graph to maximize the collected time-dependent revenues. We introduce an intensification-driven local search algorithm for solving this challenging problem. The key feature of the algorithm is an intensification mechanism that intensively investigates bounded areas around each very-high-quality local optimum encountered. As for its underlying local optimization, the algorithm employs an extended variable neighborhood search procedure which adopts for the first time a K-exchange sampling based neighborhood and a concise perturbation procedure to obtain high-quality solutions. Experimental results on 140 benchmark instances show a high performance of the algorithm by reporting 36 improved best-known results (new lower bounds) and equal best-known results for 95 instances. Additional experiments are conducted to investigate the usefulness of the key components of the algorithm.

Size-dependent frequency of simply supported elastic ultra-thin films with surface effect under periodic vibration

Although surface effects play an important role in the mechanical properties of ultra-thin films, the nonlinear vibrations of ultra-thin films influenced by surface effects have not been fully understood. This paper develops an analytical framework for studying the nonlinear vibrations of simply supported ultra-thin films with surface effects. The framework is based on the modified Kirchhoff plate theory. The surface stress effects are treated by the Gurtin–Murdoch surface elasticity model and the motion equations include the effects of curvature and classical inertia. The dimensionless frequency of forcibly vibrated ultra-thin films with a simple support and surface effects is explicitly deduced through a series of perturbation procedure. Finally, the surface effects are evaluated in two numerical examples. In these demonstrations, the surface effects significantly influenced the dimensionless frequency when the film thickness reduced to one micrometer or less.

A hybrid algorithm for the Vehicle Routing Problem with AND/OR Precedence Constraints and time windows

In this research, a new variant of the vehicle routing problem with time windows is studied where a given number of dispersed customers are related to each other through AND/OR precedence constraints.This generalization is necessary for problems like order picker routing models in which the target locations cannot be reached in any sequences, but AND/OR relations need to be taken into account in retrieving requested items. In such an application, a node cannot be visited before its AND-type predecessors, while at least one of its OR-type predecessors needs to be reached before that. We propose a Mixed Integer Linear Programming (MILP) model to formulate the problem. In addition, a meta-heuristic algorithm based on the hybridization of Iterated Local Search and Simulated Annealing approach is developed, which lead to reasonable results in terms of CPU time and solutions accuracy for a set of instances extended from the well-known Solomon benchmark. A different perturbation procedure and several simple and fast neighborhoods are applied to make a good balance between the diversification and intensification of the search. To improve the hybrid algorithm’s performance, Taguchi’s method (Peace, 1993) is used to tune the algorithm parameters. A comprehensive computational analysis is conducted to assess the performance of the developed algorithm.

Nonlinear surface waves on overdense plasma

Nonlinear perturbations have significant consequences on excitation of surface waves on overdense plasma. Linear surface modes on overdense plasma appear at specific frequencies of the incident wave. By nonlinear considerations, however, this phenomenon takes place for frequencies different from frequencies of the linear regime. Here, to study the nonlinear effects on the modifications of the proper frequencies of exciting the surface modes, we consider the framework of the warm electron-fluid model and Poisson equation. We apply a perturbation procedure to linearize the nonlinear set of magnetohydrodynamic equations. Obtaining the analytical solutions at the first- and second-order corrections provides a powerful tool to perform our study. By employing proper boundary conditions, we derive dispersion relations for both corrections. The range of the allowed frequency of the incident wave that leads to the stable surface plasma waves is determined at the linear approximation. Then, at the second-order corrections, we investigate the nonlinear modifications of the dispersion relation of the plasma surface waves and find a new proper frequency region. We also discuss the influences of the presence of the nonlinearities and the thermal effects on the involved physical quantities.

Overview of lattice calculations of the x-dependence of PDFs, GPDs and TMDs

For a long time, lattice QCD was unable to address the x-dependence of partonic distributions, direct access to which is impossible in Euclidean spacetime. Recent years have brought a breakthrough for such calculations when it was realized that partonic light-cone correlations can be accessed through spatial correlations computable on the lattice. Appropriately devised observables can be factorized into physical PDFs via a perturbative procedure called matching, analogous to the standard factorization of experimental cross sections. In this short review, aimed at a broader high-energy and nuclear physics community, we discuss the recent highlights of this research program. Key concepts are outlined, followed by a case study illustrating the typical stage of current lattice extractions and by a brief review of the most recent explorations. We finalize with a number of messages for the prospects of lattice determinations of partonic structure.