Fractional dynamics in the light scattering intensity fluctuation in dusty plasma

Muniandy, S. V.; Chew, Wei-Xiang; Wong, C. S.

doi:10.1063/1.3533905

Cited by 21 publications

(8 citation statements)

References 50 publications

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“…and also exhibits short memory with rate of decay slower compared to the standard exponential form of OU process. 17 As one may expect in the limit of !1=2 or b!1, by setting Next, we show the applicability of fractional charging dynamical model by demonstrating how the fOU can provide a better match between theory and experimental measurements of the dust charge. Experimental determination of particle charge in a bulk dc discharge shows some discrepancies between experiments and orbital motion limited (OML) theory, especially at high pressure.…”

Section: Theoretical Model and Resultsmentioning

confidence: 87%

Stochastic dynamics of charge fluctuations in dusty plasma: A non-Markovian approach

2011

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Dust particles in typical laboratory plasma become charged largely by collecting electrons and=or ions. Most of the theoretical studies in dusty plasma assume that the grain charge remains constant even though it fluctuates due to the discrete nature of the charge. The rates of ions and electrons absorption depend on the grain charge, hence its temporal evolution. Stochastic charging model based on the standard Langevin equation assumes that the underlying process is Markovian. In this work, the memory effect in dust charging dynamics is incorporated using fractional calculus formalism. The resulting fractional Langevin equation is solved to obtain the amplitude and correlation function for the dust charge fluctuation. It is shown that the effects of ion-neutral collisions can be interpreted in phenomenological sense through the nonlocal fractional order derivative. V

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Section: Theoretical Model and Resultsmentioning

confidence: 87%

Stochastic dynamics of charge fluctuations in dusty plasma: A non-Markovian approach

2011

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“…The authors in [33] present light scattering intensity fluctuation in dusty plasma; they considered the scattered electric field as a stationary stochastic process. The FC is used to model the fractional kinetic for polydisperse particles and show that the correlation based on fractional Ornstein-Uhlenbeck process may provide a novel insight into the complex transport behaviors in dusty plasma.…”

Section: Introductionmentioning

confidence: 99%

Description of the Dynamics of Charged Particles in Electric Fields: An Approach Using Fractional Calculus

Gómez-Aguilar

Alvarado‐Méndez

2015

Springer Series in Optical Sciences

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The Free Electron Lasers (FEL) uses a beam of electrons accelerated to relativistic velocities as the active medium to laser generation; these electrons are bound to atoms, but move freely in a magnetic field. The efficiency of FEL depends on several parameters such as relaxation time, longitudinal effects and transverse variations of the optical field. Moreover, the electron dynamics in a magnetic field undulator serves as a means of radiation source for coupling to the electric field. The transverse motion of the electrons leads to either a gain or loss energy from or to the field; this depends on the position of the particle regarding the phase of the external radiation field. On the other hand, optical tweezers are noninvasive tools that use a laser beam to generate powerful forces enough to manipulate microscopic matter by using electric and magnetic fields. In this work, we described the fractional dynamics of charged particles in electric fields to know their displacement. Fractional Newton's second law is considered and the order of the fractional differential equation is 0 < ≤ 1. We use the Laplace transform of the fractional derivative in Caputo sense. Dissipative effects are observed in the study cases of the particle dynamics due to the order of the derivative, and the standard electrodynamics is recovered by taking the limit when = 1.

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“…Fractional calculus gains increase interests in processing biomedical signals; see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The fractional integral of the Riemann-Liouville type is widely used in the field; see, for example, [17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Essay on Fractional Riemann-Liouville Integral Operator versus Mikusinski’s

Zhao

2013

Mathematical Problems in Engineering

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This paper presents the representation of the fractional Riemann-Liouville integral by using the Mikusinski operators. The Mikusinski operators discussed in the paper may yet provide a new view to describe and study the fractional Riemann-Liouville integral operator. The present result may be useful for applying the Mikusinski operational calculus to the study of fractional calculus in mathematics and to the theory of filters of fractional order in engineering.

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Fractional dynamics in the light scattering intensity fluctuation in dusty plasma

Cited by 21 publications

References 50 publications

Stochastic dynamics of charge fluctuations in dusty plasma: A non-Markovian approach

Stochastic dynamics of charge fluctuations in dusty plasma: A non-Markovian approach

Description of the Dynamics of Charged Particles in Electric Fields: An Approach Using Fractional Calculus

Essay on Fractional Riemann-Liouville Integral Operator versus Mikusinski’s

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