High-order approximate solutions of strongly nonlinear cubic-quintic Duffing oscillator based on the harmonic balance method

In this paper, a new reliable analytical technique has been introduced based on the Harmonic Balance Method (HBM) to determine higher-order approximate solutions of the strongly nonlinear cubicquintic Duffing oscillator. The application of the HBM leads to very complicated sets of nonlinear algebraic equations. In this technique, the high-order nonlinear algebraic equations are approximated in the form of a power series solution, and this solution produces desired results even for small as well as large amplitudes of oscillation. Moreover, a suitable truncation formula is found in which the solution measures better results than existing results and it saves a lot of calculation. It is highly noteworthy that using the proposed technique, the third-order approximate solutions gives an excellent agreement as compared with the numerical solutions (considered to be exact). The proposed technique is applied to the strongly nonlinear cubic-quintic Duffing oscillator to reveals its novelty, reliability and wider applicability

Exact solution for linear and nonlinear systems of PDEs by homotopy-perturbation method

In this paper, the homotopy-perturbation method (HPM)proposed by J.-H. He is adopted for solving linear and nonlinear systems of partial differential equations (PDEs). In this method, a homotopy parameter p, which takes the values from 0 to 1, is introduced. When p = 0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p gradually increases to 1, the system goes through a sequence of ‘deformations’, the solution of each of which is ‘close’ to that at the previous stage of ‘deformation’. Eventually at p = 1,the system takes the original form of the equation and the final stage of ‘deformation’ gives the desired solution. Some examples are presented to demonstrate the efficiency and simplicity of the method

An analytical technique to obtain higher-order approximate periods for nonlinear oscillator

ABSTRACT: This paper presents simulation results of the influence of wide range modulation index values ( ) in carrier-based PWM strategy for application in generating the stepped waveform. The waveform is tested for application in single-phase half-bridge modular multilevel converters (MMCs) topology. The results presented in this paper include a variation of the fundamental component (50 Hz) in the voltage output.  It also studies total harmonic distortion of the output voltage (THDv) and the output current (THDi) when the modulation index is changed over the linear-modulation region, 0 < < 1. It also explores the effect of a modulation index greater than 1. Moreover, different output voltage shapes, as a consequence of varied on MMCs, are also illustrated for showing the effect of varying the value of on sub-module of MMCs. ABSTRAK: Penulisan ini berkenan simulasi pengaruh pelbagai nilai indeks modulasi     ( ) dalam strategi PWM berasaskan aplikasi dalam menghasilkan bentuk gelombang yang bertingkat. Bentuk gelombang ini diuji untuk aplikasi dalam topologi MMCs. Penilaian dan hasil dari artikle ini termasuk variasi komponen asas (50 Hz) dalam voltan keluar. Ia juga meneliti jumlah penyelarasan harmonik voltan keluar (THDv) dan arus keluaran (THDi) apabila indeks modulasi ditukar dalam rantau modulasi linear, 0 < <1. Ia juga meneroka kesan indeks modulasi lebih daripada 1. Selain itu, bentuk voltan keluar yang berbeza sebagai akibat dari pelbagai  pada MMCs juga digambarkan untuk menunjukkan kesan berbeza-beza nilai  pada sub-modul MMCs

An analytical approximation technique for the duffing oscillator based on the energy balance method

In this paper, an analytical approximation technique has been presented of obtaining higher-order approximate solutions for highly nonlinear Duffing oscillator based on the energy balance method (EBM). Higher-order approximate natural frequencies have been obtained in a novel analytical way. The accuracy of the solution method is evaluated within as error analysis. It is highly remarkable that using the presented technique, the approximation solutions produces desired results even for large oscillation as compared with the exact ones. Moreover, the solution method yields much better results than existing solutions after using a suitable truncation formula. The presented technique is applied to well-known Duffing oscillator to illustrate its novelty, reliability and wider applicabilit

Metabolite profiling at the cellular and subcellular level reveals metabolites associated with salinity tolerance in sugar beet

Hossain MS, Persicke M, ElSayed AI, Kalinowski J, Dietz K-J. Metabolite profiling at the cellular and subcellular level reveals metabolites associated with salinity tolerance in sugar beet. Journal of Experimental Botany. 2017;68(21-22):5961-5976.Sugar beet is among the most salt-tolerant crops. This study aimed to investigate the metabolic adaptation of sugar beet to salt stress at the cellular and subcellular levels. Seedlings were grown hydroponically and subjected to stepwise increases in salt stress up to 300 mM NaCl. Highly enriched fractions of chloroplasts were obtained by nonaqueous fractionation using organic solvents. Total leaf metabolites and metabolites in chloroplasts were profiled at 3 h and 14 d after reaching the maximum salinity stress of 300 mM NaCl. Metabolite profiling by gas chromatography- mass spectrometry (GC-MS) resulted in the identification of a total of 83 metabolites in leaves and chloroplasts under control and stress conditions. There was a lower abundance of Calvin cycle metabolites under salinity whereas there was a higher abundance of oxidative pentose phosphate cycle metabolites such as 6-phosphogluconate. Accumulation of ribose-5-phosphate and ribulose-5-phosphate coincided with limitation of carbon fixation by ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco). Increases in glycolate and serine levels indicated that photorespiratory metabolism was stimulated in salt-stressed sugar beet. Compatible solutes such as proline, mannitol, and putrescine accumulated mostly outside the chloroplasts. Within the chloroplast, putrescine had the highest relative level and probably assisted in the acclimation of sugar beet to high salinity stress. The results provide new information on the contribution of chloroplasts and the extra-chloroplast space to salinity tolerance via metabolic adjustment in sugar beet

Comparing numerical methods for the solution of Cauchy reaction-diffusion problems

In this paper, the solution of Cauchy reaction-diffussion problems is presented by homotopy-perturbation method (HPM). Reaction-difussion equations have special importance in engineering and sciences and constitute a good model for many systems in various fields. The HPM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparison between the solutions of HPM and the Adomian decomposition solutions, variational iteration solutions, homotopy analysis solutions and the exact solutions are made. The results reveals that the HPM is a powerful and efficient tool for PDEs

Analytical treatment of system of linear and nonlinear PDEs by Homotopy-Perturbation method

In this paper, the homotopy-perturbation method (HPM) is employed to obtain approximate analytical solution to the linear and nonlinear systems of partial di®erential equations (PDEs). HPM yields solutions in convergent series forms with easily computable terms. Generally, the closed form of the exact solution or its expansion is obtained without any noise terms. Test examples demonstrate the e±ciency of HPM

Solving linear system of partial differential equations by homotopy-pertubation method

In this paper, the homotopy-perturbation method (HPM) is employed to obtain approximate analytical solution to the linear systems of partial differential equations (PDEs). HPM yields solutions in convergent series forms with easily computable terms, and in linear cases, yields exact solutions. Comparisons with the exact solutions show the potential of HPM in solving linear systems of PDEs

A modified algorithm for the homotopy perturbation method with applications to Lotka-Volterra systems

In this paper, the homotopy-perturbation method (HPM) is modified in order to obtain the approximate solutions of the nonlinear differential equation response in a sequence of time intervals. The modified method provides a solution close to the exact one within a certain error. The accuracy of this method is examined by comparison with the Adomian decomposition method (ADM). The results prove that the modified HPM is a powerful tool for the solution of nonlinear equations

Exploratory Study of Separation of Sulphidised Chrome Spinels from Reduced Ilmenite

The removal of chromium-containing impurities, such as chrome spinel (ZCr2O4 where Z = Fe, Mg, Mn) from ilmenite (FeTiO3) concentrates through selective sulphidation, has been investigated by the authors. Laboratory experimental studies using sulphur added to ilmenite concentrates under Becher-type reduction conditions showed it is possible to selectively sulphidise chrome spinels from different ilmenite deposits. In this paper, processes to remove the sulphidised chrome spinels from the bulk ilmenite concentrates were investigated using flotation and magnetic separation techniques. Clustering or fusing of the reduced ilmenite (RI) and sulphidised chrome spinel grains was found to have a detrimental effect on flotation performance and made it difficult to have clear separation. A light wet grind was effective for breaking the clustering, but it caused the sulphide rim to spall off from chrome spinel surfaces, which reduces flotation efficiency. The preliminary results obtained after a magnetic separation (0.7 A) of a demetallised sulphidised RI sample show that the sulphidised chrome spinels preferentially report to the magnetic fraction. Additional magnetic separation of the non-magnetic fraction at a lower current (0.3 A) improved the recovery of sulphidised chrome spinels. The demetallisation process followed by a magnetic separation provided insights into a potential route for the removal of chrome spinels from reduced ilmenite concentrates. These two steps simulate the aeration stage of the Becher process. Further studies are required to optimise the process parameters