Coupling of energy and harmonic balance method for solving a conservative oscillator with strong odd-nonlinearity

Razzak, Abdur

doi:10.24200/sci.2017.4258

Cited by 2 publications

(2 citation statements)

References 20 publications

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“…Ions with the same kinetic energy but different masses would acquire different velocities in applied fields. When injected into a field‐free drift spatial region, the ions will separate according to their mass‐to‐charge ratio; 1ighter ions will arrive at the end of the drift length before heavier ions. This is the operating principle of conventional time‐of‐flight mass spectrometry (TOF MS).…”

Section: Introductionmentioning

confidence: 99%

Time‐of‐flight mass spectrometers based on a wedge‐shaped electrostatic mirror with a two‐dimensional field

Spivak-Lavrov

Baisanov²,

Yakushev³

et al. 2020

Rapid Comm Mass Spectrometry

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Rationale: For most of the last two decades, a considerable effort has been made towards improving time-of-flight mass spectrometry (TOF MS), which has become an irreplaceable instrumental platform for the purposes of performing analytical measurements in life sciences, such as molecular biology, proteomics, medicine, etc.This can primarily be attributed to the ability of TOF MS to rapidly detect and identify nearly any targeted chemical trace with both high precision and accuracy.However, multi-span TOF MS experiments are limited due to aberrations arising from multiple reflection; our proposed scheme will minimize these aberrations. Methods:The inhomogeneous accelerating field is generated without using meshes by changing the potentials on the electrodes of the mirror. The ions are extracted from the ion source by short impulse activation of the accelerating electric field.Since the ions are extracted from various points of the source, even ions with identical masses acquire different velocities during acceleration. Results:We have shown that the "rear" ions of the packet catch up with the "front" ions, and packets of ions with identical masses are compressed in the direction of their movement. It is concluded that, by placing the detector in a plane with the greatest compression of ion packets, an enhanced performance of a time-of-flight mass spectrometer is achieved. Conclusions:We have shown that effective spatial-temporal focusing allows a small mass spectrometer to achieve high resolution and sensitivity. We also propose and numerically evaluate a new platform for designing multi-stage and multireflective time-of-flight analyzers with wedge-shaped mirrors. We applied the simulation results to the modernization of old equipment and showed that by simply replacing the electrostatic mirror with an optimized one, a significant increase in the analyzing power can be achieved.

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Section: Introductionmentioning

confidence: 99%

Time‐of‐flight mass spectrometers based on a wedge‐shaped electrostatic mirror with a two‐dimensional field

Spivak-Lavrov

Baisanov²,

Yakushev³

et al. 2020

Rapid Comm Mass Spectrometry

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“…Various versions of the approximate solution techniques have been used to find solutions of the nonlinear and conservative Duffing equation [6][7][8][9][10][11][12][13]. The homotopy analysis method [6], harmonic balance method [7], the homotopy Padé technique [8], energy balance method [9], coupled homotopy variational approach [10], the Newton harmonic balance method [11], parameter-expanding and max-min approach [12,13], coupling of energy and harmonic balance method [14], Jacobi elliptic functions [15], parameter based perturbation technique [16] have all been used to solve the nonlinear Duffing equation without damping effect. If the Duffing oscillator involves the damping effect, the amplitude of the oscillation decreases with time, then one obtains a nonconservative system.…”

Section: Introductionmentioning

confidence: 99%

A local differential transform approach for the cubic nonlinear Duffing oscillator with damping term

Tunc

Sarı

2018

Scientia Iranica

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Nonlinear behaviour of various problems is described by the Duffing model interpreted as a forced oscillator with a spring which has restoring force. In this paper, a new numerical approximation technique based on differential transform method has been introduced for the nonlinear cubic Duffing equation with and without damping effect. Since exact solutions of the corresponding equation for all initial guesses do not exist in the literature, we have first produced an exact solution for specific parameters by using the Kudryashov method to measure the accuracy of the currently suggested method. The innovative approach has been compared with the semi-analytic differential transform method and the fourth order RungeKutta method. Although the semi-analytic differential transform method is valid only for small time intervals, it has been proved that the innovative approach has ability to capture nonlinear behaviour of the process even in the long-time interval. In a comparison way, it has been shown that the present technique produces more accurate and computationally more economic results than the rival methods.

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Coupling of energy and harmonic balance method for solving a conservative oscillator with strong odd-nonlinearity

Cited by 2 publications

References 20 publications

Time‐of‐flight mass spectrometers based on a wedge‐shaped electrostatic mirror with a two‐dimensional field

Time‐of‐flight mass spectrometers based on a wedge‐shaped electrostatic mirror with a two‐dimensional field

A local differential transform approach for the cubic nonlinear Duffing oscillator with damping term

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