New method for solving strong conservative odd parity nonlinear oscillators: Applications to plasma physics and rigid rotator

This study proposes a new modification of the homotopy perturbation method. A new parameter alpha is introduced into the homotopy equation in order to improve the results and accuracy. An optimal analysis identifies the parameter alpha, aimed at improving the solutions. A comparative analysis of the proposed method reveals that the new method presents results with higher degree of accuracy and precision than the classic homotopy perturbation method. Absolute error analysis shows the convenience of the proposed method, providing much smaller errors. Two examples are presented: Duffing and Van der pol’s nonlinear oscillators to demonstrate the efficiency, accuracy, and applicability of the new method.

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Accurate numerical solutions of conservative nonlinear oscillators

Nonlinear Engineering ◽

10.1515/nleng-2014-0009 ◽

2014 ◽

Vol 3 (4) ◽

Author(s):

Najeeb Alam Khan ◽

Khan Nasir Uddin ◽

Khan Nadeem Alam

Keyword(s):

Differential Equation ◽

Plasma Physics ◽

Nonlinear Oscillator ◽

Numerical Solutions ◽

Arbitrary Order ◽

Nonlinear Oscillators ◽

Higher Order ◽

Algebraic Equations ◽

Restoring Force ◽

Arbitrary Power

AbstractThe objective of this paper is to present an investigation to analyze the vibration of a conservative nonlinear oscillator in the form u" + lambda u + u^(2n-1) + (1 + epsilon^2 u^(4m))^(1/2) = 0 for any arbitrary power of n and m. This method converts the differential equation to sets of algebraic equations and solve numerically. We have presented for three different cases: a higher order Duffing equation, an equation with irrational restoring force and a plasma physics equation. It is also found that the method is valid for any arbitrary order of n and m. Comparisons have been made with the results found in the literature the method gives accurate results.

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A new method based on the harmonic balance method for nonlinear oscillators

Physics Letters A ◽

10.1016/j.physleta.2007.04.025 ◽

2007 ◽

Vol 368 (5) ◽

pp. 371-378 ◽

Cited By ~ 37

Author(s):

Y.M. Chen ◽

J.K. Liu

Keyword(s):

Harmonic Balance ◽

Harmonic Balance Method ◽

Nonlinear Oscillators ◽

Balance Method ◽

New Method

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Meteor velocity determination with plasma physics

Atmospheric Chemistry and Physics Discussions ◽

10.5194/acpd-4-1247-2004 ◽

2004 ◽

Vol 4 (1) ◽

pp. 1247-1268 ◽

Cited By ~ 1

Author(s):

L. P. Dyrud ◽

K. Denney ◽

S. Close ◽

M. Oppenheim ◽

L. Ray ◽

...

Keyword(s):

Plasma Physics ◽

Radar Data ◽

New Method ◽

Altitude Range ◽

Meteor Trail ◽

Radar Reflection ◽

Head Echo ◽

Meteor Trails ◽

Plasma Reflection ◽

Field Aligned Irregularities

Abstract. Understanding the global meteor flux at Earth requires the measurement of meteor velocities. While several radar methods exist for measuring meteor velocity, they may be biased by plasma reflection mechanisms. This paper presents a new method for deriving meteoroid velocity from the altitudinal extent of non-specular trails. This method employs our recent discoveries on meteor trail plasma instability. Dyrud et al. (2002) demonstrated that meteor trails are unstable over a limited altitude range, and that the precise altitudes of instability are dependent on the meteoroid velocity that generated the trail. Since meteor trail instability results in field aligned irregularities (FAI) that allow for radar reflection, non-specular trail observations may be used to derive velocity. We use ALTAIR radar data of combined head echos and non-specular trails to test non-specular trail derived velocity against head echo velocities. Meteor velocities derived from non-specular trail altitudinal width match to within 5 km/s when compared with head echo range rates from the same meteor. We apply this technique to Piura radar observations of hundreds of non-specular trails to produce histograms of occurrence of meteor velocity based solely on this non-specular trails width criterion. The results from this study show that the most probable velocity of meteors seen by the Piura radar is near 50 km/s which is comparable with modern head echo studies.

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Meteor velocity determination with plasma physics

Atmospheric Chemistry and Physics ◽

10.5194/acp-4-817-2004 ◽

2004 ◽

Vol 4 (3) ◽

pp. 817-824 ◽

Cited By ~ 8

Author(s):

L. P. Dyrud ◽

K. Denney ◽

S. Close ◽

M. Oppenheim ◽

J. Chau ◽

...

Keyword(s):

Plasma Physics ◽

Radar Data ◽

New Method ◽

Altitude Range ◽

Meteor Trail ◽

Radar Reflection ◽

Head Echo ◽

Meteor Trails ◽

Plasma Reflection ◽

Field Aligned Irregularities

Abstract. Understanding the global meteor flux at Earth requires the measurement of meteor velocities. While several radar methods exist for measuring meteor velocity, they may be biased by plasma reflection mechanisms. This paper presents a new method for deriving meteoroid velocity from the altitudinal extent of non-specular trails. This method employs our recent discoveries on meteor trail plasma instability. Dyrud et al. (2002) demonstrated that meteor trails are unstable over a limited altitude range, and that the precise altitudes of instability are dependent on the meteoroid that generated the trail. Since meteor trail instability results in field aligned irregularities (FAI) that allow for radar reflection, non-specular trail observations may be used to derive velocity. We use ALTAIR radar data of combined head echos and non-specular trails to test non-specular trail derived velocity against head echo velocities. Meteor velocities derived from non-specular trail altitudinal width match to within 5 km/s when compared with head echo range rates from the same meteor. We apply this technique to Piura radar observations of hundreds of non-specular trails to produce histograms of occurrence of meteor velocity based solely on this non-specular trails width criterion. The results from this study show that the most probable velocity of meteors seen by the Piura radar is near 50 km/s, which is comparable with modern head echo studies.

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Selective Sampling and Orientation of Non-Homogeneous Tissues

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100100238 ◽

1968 ◽

Vol 26 ◽

pp. 98-99

Author(s):

C. C. Clawson ◽

L. W. Anderson ◽

R. A. Good

Keyword(s):

Electron Microscopy ◽

Electron Microscope ◽

Light Microscopy ◽

Random Sampling ◽

New Method ◽

Microscope Examination ◽

Small Areas ◽

Selective Sampling ◽

Large Numbers ◽

Specific Orientation

Investigations which require electron microscope examination of a few specific areas of non-homogeneous tissues make random sampling of small blocks an inefficient and unrewarding procedure. Therefore, several investigators have devised methods which allow obtaining sample blocks for electron microscopy from region of tissue previously identified by light microscopy of present here techniques which make possible: 1) sampling tissue for electron microscopy from selected areas previously identified by light microscopy of relatively large pieces of tissue; 2) dehydration and embedding large numbers of individually identified blocks while keeping each one separate; 3) a new method of maintaining specific orientation of blocks during embedding; 4) special light microscopic staining or fluorescent procedures and electron microscopy on immediately adjacent small areas of tissue.

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