Pade Approximation Technique Research Articles

The analysis of a reactive hydromagnetic internal heat generating poiseuille fluid flow through a channel.

In this paper, the analysis of a reactive hydromagnetic Poiseuille fluid flow under different chemical kinetics through a channel in the presence of a heat source is carried out. An exothermic reaction is assumed while the concentration of the material is neglected. The Adomian decomposition method together with Pade approximation technique are used to obtain the solutions of the governing nonlinear non-dimensional differential equations. Effects of various physical parameters on the velocity and temperature fields of the fluid flow are investigated. The entropy generation analysis, irreversibility distribution ratio, Bejan number and the conditions for thermal criticality for different chemical kinetics are also presented.

Improved Pade-Pole Clustering Approach using Genetic Algorithm for Model Order Reduction

Reducing the order of higher order systems by mixed approach is Improved Pade-Pole clustering based method to derive a reduced order approximation for a stable continuous time system is presented. In this method, the denominator polynomial of the reduced order model is derive by improved pole-clustering approach and the numerator polynomial are obtain through Pade approximation technique and by parameter optimization by minimizing the mean square error between the time responses of the original and reduced system element through genetic algorithm. The reduced order model so obtained by improved clustering algorithm guaranteed the stability in the reduced model.

Numerical solutions of nonlinear biochemical model using a hybrid numerical-analytical technique

In this paper, a hybrid numerical-analytical technique resulting from the combination of the differential transformation method and the Pade approximation technique; hereby referred to as differential transformation-Pade approximation technique (DTPAT) is introduced and applied for numerical solutions to the nonlinear biochemical reaction model. The obtained numerical results via the DTPAT are in excellent agreement with those obtained using ADM, PIM, RK4, HPM, and MPHM. The DTPAT increases the convergent rate of the series solutions obtained via the DTM, is showed to be very effective; it requires less computational work, and hence a promising technique for both linear and nonlinear systems in other areas of medical and biomedical sciences.

Ultrasonic scattering from poroelastic materials using a mixed displacement-pressure formulation

In this work, a numerical technique suitable for evaluating the ultrasonic scattering from a three-dimensional poroelastic material is presented. Following Biot’s derivation of the macroscopic governing equations for a fluid saturated poroelastic material, the predicted two propagating wave equations are formulated in terms of displacement and pressure. Assuming that porosity variations on a microscopic scale have a cumulative effect in generating a scattered field, the scattering attenuation coefficient of a Biot medium can be determined. The scattered fields of the wave equations are numerically evaluated as Neumann series solutions of the Kirchhoff-Helmholtz integral equation. A Pade approximant technique is employed to extrapolate beyond the Neumann series’ radius of convergence (weak scattering regime). In the case of bovine trabecular bone, the relationship between the scattering attenuation coefficient and the structural and mechanical properties of the trabecular bone is of particular interest. The results demonstrate the validity of the linear frequency-dependent assumption of attenuation coefficient n the low frequency range. Further comparisons, between measured observations and the numerical results will be discussed.

Hydromagnetic Effects on Fluid Flow and Internal Flow Separation in a Linearly Diverging Channel

In this paper, we investigated the hydromagnetic steady flow of a viscous conducting fluid in a twodimensional uniform width linearly diverging channel. For this investigation the effect of an externally applied homogeneous magnetic field on the development of velocity profiles and internal flow separation in the diverging channel are observed. The solution for the flow governing non-linear differential equation is found using perturbation method together with Pade approximation technique. The investigation results reveal that the requirement of flow Reynolds number for the development of internal flow separation increases with an increase in magnetic field intensity. Furthermore, the behavior of velocity profiles under the effect of magnetic field is discussed.

Thermal Stability of a Reactive Hydromagnetic Poiseuille Fluid Flow through a Channel

This study is conducted to investigate the thermal stability of a reactive Hydromagnetic Poiseuille fluid flow through a channel. It is assumed that the reaction is exothermic under different chemical kinetics: Sensitized, Arrhenius and Bimolecular neglecting the concentration of the material. The analytical solutions of the nonlinear dimensionless equations governing the fluid flow are obtained using Adomian Decomposition Method (ADM) together with Pade Approximation technique to determine the thermal stability of the fluid flow and important properties of temperature fields including bi-furcations and thermal criticality conditions are discussed.

Output tracking control for a velocity-sensorless VTOL aircraft with measurement delays

In this paper, we develop a non-linear controller to achieve output tracking for a velocity-sensorless vertical take-off and landing (VTOL) aircraft in the presence of measurement delays. By applying the Pade approximation technique, the original controlled system is transformed into an augmented dimension system without any time delay. After constructing full-order observers, error coordinate transformation, and system decomposition, the tracking problem of the newly transformed system is changed into the stabilisation problem of two non-minimum phase subsystems and one minimum phase subsystem. The resulting controller not only forces the VTOL aircraft to asymptotically track the desired trajectories, but also drives the unstable internal dynamics, which stands for the non-minimum property of VTOL aircraft, to follow the causal ideal internal dynamics (IID) solved via the stable system centre (SSC) method. Numerical simulation results illustrate the effectiveness of the proposed controller.

Stable Time-Domain Beam Propagation Method for Modeling Ultrashort Pulse Propagation in Dispersive Optical Structures

In this letter, the time-domain beam propagation method has been formulated and verified to model ultrashort optical pulse propagation in structures containing material dispersion. The nonparaxial time-domain wave equation was used to march the pulsed beams using Pade approximant technique. The method has been tested using three different Lorentzian dispersive profiles. It has been observed that the new technique is very stable, accurate, and efficient in modeling ultrashort pulse propagation in long dispersive optical structures.

A new solution for natural convection about a vertical cone embedded in porous media prescribed wall temperature using, power series - Pade

The combination of any series solutions with the Pade approximants provides a powerful tool for handling initial or boundary value problems on infinite or semi-infinite domains. This study apply an integrated Power series- Pade approximants technique (PS - Pade) to solve a system of nonlinear differential equations arising from the similarity solution for the natural convection of Darcian fluid about a vertical full cone embedded in porous media prescribed wall temperature. The results of present method are compared with numerical results as well as other resalts reported in literature. The obtained results in comparison with the numerical ones represent remarkable accuracy. Finally, Nusselt number, as an important parameter in heat transfer, is calculated by obtained analytical solution using Power series- Pade approximants technique.

Chemical potential and internal energy of the noninteracting Fermi gas in fractional-dimensional space

Chemical potential and internal energy of a noninteracting Fermi gas at low temperature are evaluated using the Sommerfeld method in the fractional-dimensional space. When temperature increases, the chemical potential decreases below the Fermi energy for any dimension equal to 2 and above due to the small entropy, while it increases above the Fermi energy for dimensions below 2 as a result of high entropy. The ranges of validity of the truncated series expansions of these quantities are extended from low to intermediate temperature regime as well as from high to relatively low density regime by using the Pade approximant technique.

Bit error rate analysis of diversity M-phase-shift keying receivers in Weibull fading with cochannel interference

In this study, the effect of introducing cochannel interference (CCI) on the performance of diversity receivers operating over the Weibull fading channel is thoroughly investigated. More specifically, the authors derive novel bit error rate (BER) expressions for the dual-branch selection combining (SC) and post-detection equal gain combining (EGC) diversity M-PSK receivers with possibly correlated branches operating over Weibull fading channels in presence of CCI. A characteristic function (CF)-based approach is used to achieve this goal. For the EGC correlated branches case, because of lack of existence of a closed-form expression for the CF of the sum of two Weibull random variables (RVs), the authors revert to using the Pade approximation (PA) technique to approximate this CF by a rational function and hence an approximate BER expression is obtained. Various results pertaining to the effect of fading severity of both the desired signal and the interferers, the effect of the number of interferers and the effect of correlation between diversity branches for different M-PSK modulations are presented. The obtained results are verified by comparison with Monte Carlo simulations and excellent agreement is observed.

On the performance analysis of wireless receiver using generalized-gamma fading model

In this paper, we provide a unified analysis for wireless system over generalized fading channels that is modeled by the two parameter generalized gamma model. This model is versatile enough to represent short-term fading such as Weibull, Nakagami-m, or Rayleigh as well as shadowing. The performance measures such as the amount of fading, average bit error rate, and signal outage are considered for analysis. With the aid of moment generating function (MGF) approach and Pade approximation (PA) technique, outage probability and average bit error rate have been evaluated for a variety of modulation formats. We first use the PA technique to find a simple way to evaluate compact rational expressions for the MGF of output signal-to-noise ratio, unlike previously derived intricate expressions in terms of Fox’s H and MeijerG functions. Using these rational expressions, we evaluate the performance of wireless receivers under a range of representative channel fading conditions. Our results are validated through computer simulations, which shows perfect match.

Clustering Method for Reducing Order of Linear System using Pade Approximation

A mixed method is proposed for finding stable reduced order models of single-input- single-output large-scale systems using Pade approximation and the clustering technique. The denominator polynomial of the reduced order model is determined by forming the clusters of the poles of the original system, and the coefficients of numerator polynomial are obtained by using the Pade approximation technique. This method guarantees stability of the reduced order model when the original high order system is stable. The methodology of the proposed method is illustrated with the help of examples from literature.

On the Use of Padé Approximation for Performance Evaluation of Maximal Ratio Combining Diversity over Weibull Fading Channels

We use the Pade approximation (PA) technique to obtain closed-form approximate expressions for the moment-generating function (MGF) of the Weibull random variable. Unlike previously obtained closed-form exact expressions for the MGF, which are relatively complicated as being given in terms of the Meijer G-function, PA can be used to obtain simple rational expressions for the MGF, which can be easily used in further computations. We illustrate the accuracy of the PA technique by comparing its results to either the existing exact MGF or to that obtained via Monte Carlo simulations. Using the approximate expressions, we analyze the performance of digital modulation schemes over the single channel and the multichannels employing maximal ratio combining (MRC) under the Weibull fading assumption. Our results show excellent agreement with previously published results as well as with simulations.

Automated Discovery of Numerical Approximation Formulae via Genetic Programming

This paper describes the use of genetic programming to perform automated discovery of numerical approximation formulae. We present results involving rediscovery of known approximations for Harmonic numbers, discovery of rational polynomial approximations for functions of one or more variables, and refinement of existing approximations through both approximation of their error function and incorporation of the approximation as a program tree in the initial GP population. Evolved rational polynomial approximations are compared to Pade approximations obtained through the Maple symbolic mathematics package. We find that approximations evolved by GP can be superior to Pade approximations given certain tradeoffs between approximation cost and accuracy, and that GP is able to evolve approximations in circumstances where the Pade approximation technique cannot be applied. We conclude that genetic programming is a powerful and effective approach that complements but does not replace existing techniques from numerical analysis.

Padé approximation for extended boundary condition method in electromagnetic scattering analysis

AbstractThe Padé approximation technique in conjunction with the extended boundary condition method (EBC) is implemented to solve the scattering problem over a finite frequency interval. The algorithm is based on expanding the system equations in their power series, and then finding a recurrence relation for the series coefficients. Fairly good results are obtained. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 100–101, 2002.

A study on the effects of active suspension upon vehicle handling

This paper develops a 7 DOF vehicle model to study the effects of the active suspension on ride. The model is used to derive a control law for the active suspension using a full state linear optimal control technique. A wheelbase preview type active suspension is also considered in the control law derivation. The time delay between wheelbases is approximated using Pade approximation technique. The ride model is extended to a 14 DOF handling model. The 14 DOF handling model includes lateral, longitudinal, yaw and four wheel spin motions in addition to the 7 DOF ride model. A control law which is derived considering only ride related parameters is used to study the effects of the active suspension on a vehicle handling. J-turn maneuver simulation results show that the active suspension has a slower response in lateral acceleration and yaw rate, a bigger steady state lateral acceleration and an oversteer tendency. Lane changing maneuver simulation results show that the active suspension has a little bigger lateral acceleration but a much smaller roll angle and roll motion. Braking maneuver simulation results show that the active suspension has a much smaller pitch angle and pitch motion.

A Tractable Class of Maximal Hedging Policies in Multi-PartManufacturing Systems

The flow control problem in multi-part failure prone manufacturing systems is considered. While computationnaly attractive, the near optimal controllers of Caramanis and Sharifnia, suffer from the drawback that the production capacity set must be approximated via a very restricted set of inscribed hypercubes, namely those for which a componentwise feasibility requirement is satisfied. Also, due to the completely decoupled nature of production along each component, utilization of the restricted capacity set is suboptimal. A class of capacity set incribed hypercube policies called simple maximal hedging (SMH) policies is introduced. In SMH policies production levels along the various components of the capacity set are coupled, the componentwise feasibility requirement is lifted, and there is no underutilization of production capacity if needed. In a p part types manufacturing system, for partwise additive cost functionals, it is shown that performance evaluation of a given SMH policy reduces to the analysis of p decoupled (fictitious) semi-Markovian machines. The machines are Markovianized via first passage-time analysis and a Pade approximants technique. Numerical optimization over the class of SMH policies in a sample manufacturing system indicates that their performance can come close to that of the optimal control.

Hydro-pneumatic Slow-active Suspension with Preview Control

SUMMARY In this work, the preview control problem is considered for fully active and hydro-pneumatic slow-active systems. Based on the quarter car model, linear optimal control theory is used to derive the control laws. The Pade approximation technique is used to represent the preview time resulting from a preview sensor mounted at the front bumper to measure the road irregularities ahead of the front wheels. The results for the slow-active system with preview showed that there is 15% improvement in ride comfort compared to slow-active without preview and 28.5% improvement over passive system at similar root mean square (r.m.s) dynamic tyre load and suspension working space. The performance gains are, however, lower by about 15% than those obtainable with the theoretically ideal, fully active system with preview. The power results for slow active with and without preview showed that a 2kW fixed displacement hydraulic pump is enough for full vehicle requirements.

Effect of Non-Linear Components on the Performance of a Hydro -Pneumatic Slow-Active Suspension System

In this work, the effects of component non-linearities on the ride performance of a hydro-pneumatic slow-active suspension system are studied theoretically. Based on the quarter car linear model, linear optimal control theory is used to calculate the feedback and feedforward gains. These gains are used in both linear and non-linear models with and without preview control. The Pade approximation technique is used to represent the preview time resulting from a preview sensor mounted on the vehicle front bumper to measure the road irregularities ahead of the front wheel. The results on a typical major road showed that at similar r.m.s. values of suspension working space, the non-linear slow-active system with preview provided a 28 per cent improvement in ride comfort and a 17 per cent reduction in dynamic tyre load compared with a passive system. However, the inclusion of non-linear effects of the components increases the ride comfort acceleration by 10 per cent and suspension working space by 12 per cent compared to the equivalent linear model at approximately equal values of r.m.s. dynamic tyre load.