Fokker‐Planck equation with velocity‐dependent coefficients: Application to dusty plasmas and active particles

Trigger, S. A.; Ébeling, W.; Ignatov, A. M.; Ткаченко, И. М.

doi:10.1002/ctpp.200310050

Cited by 8 publications

(13 citation statements)

References 10 publications

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“…Of course, the realization of the negative value of the total friction coefficient in the physical experiment requires special conditions, since other mechanisms of positive friction exist. At the same time at the presence of ion flow there is an effective mechanism of negative friction due to the ion scattering by grains [21], which can be very important for dusty plasmas even when ion absorption is small.…”

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confidence: 99%

Brownian motion of grains and negative friction in dusty plasmas

Trigger¹,

Zagorodny²

2004

Condens. Matter Phys.

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Within the approximation of dominant charging collisions the explicit microscopic calculations of the Fokker-Planck kinetic coefficients for highlycharged grains moving in plasma are performed. It is shown that due to ion absorption by grain the friction coefficient can be negative and thus the appropriate threshold value of the grain charge is found. The stationary solutions of the Fokker-Planck equation with the velocity dependent kinetic coefficient are obtained and a considerable deviation of such solutions from the Maxwellian distribution is established. Lw, 52.20.Hv, 52.25.Fi Description of the Brownian motion in the systems with particle or energy fluxes still remains one of the key problems in the statistical physics of the open systems [1]. Starting from the classical Lord Rayleigh work [2] many studies of the nonequilibrium motion of Brownian particles with additional (inner or external) energy supply have been performed. In particular, such studies are of great importance for physical-chemical [3,4] and biological [5] systems in which non-equilibrium Brownian particle motion is referred to as the motion of active Brownian particles. Recently the dynamical and energetic aspects of motion for the active Brownian particles have been described based on the Langevin equation and the appropriate FokkerPlanck equation [6,7]. The possibility of negative friction (negative values of friction coefficient) of the Brownian particles was regarded as a result of energy pumping. *

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confidence: 99%

Brownian motion of grains and negative friction in dusty plasmas

Trigger¹,

Zagorodny²

2004

Condens. Matter Phys.

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“…We will also see how a more precise knowledge of f 0 from simulations of the stationary state may increase the accuracy of Eq. (9). Finally, we note that one expects a mean field description based on a Vlasov-Fokker-Planck equation to be accurate in the regimes explored numerically.…”

Section: Numerical Testmentioning

confidence: 81%

“…Thus, we shall compare the theory (9) to direct N -body simulations. We integrate the N Langevin equations using the EulerMaruyama method.…”

Section: Numerical Testmentioning

confidence: 99%

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Approximated center-of-mass motion for systems of interacting particles with space- and velocity-dependent friction and anharmonic potential

Olivetti

Labeyrie²,

Kaiser³

2014

Phys. Rev. E

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We study the center-of-mass motion in systems of trapped interacting particles with space and velocity dependent friction, and anharmonic traps. Our approach, based on a dynamical ansatz assuming a fixed density profile, allows us to obtain information at once for a wide range of binary interactions and interaction strengths, at linear and non linear levels. Our findings are first tested on different simple models by comparison with direct numerical simulations. Then, we apply the method to characterize the motion of the center-of-mass of a magneto-optical trap, and its dependence on the number of trapped atoms. Our predictions are compared with experiments performed on a large Rb 85 magneto-optical trap.

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“…Under certain conditions (e.g., in the presence of an ion flow in the plasma), scattering of ions by grains may lead to negative friction as well [46]. In particular, it seems that this effect can be responsible for some observations in the experiments by Dahiya et al [19].…”

Section: Introductionmentioning

confidence: 99%

Active and passive Brownian motion of charged particles in two-dimensional plasma models

2004

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The dynamics of charged Coulomb grains in a plasma is numerically and analytically investigated. Analogous to recent experiments, it is assumed that the grains are trapped in an external parabolic field. Our simulations are based on a Langevin model, where the grain-plasma interaction is realized by a velocity-dependent friction coefficient and a velocity-independent diffusion coefficient. In addition to the ordinary case of positive (passive) friction between grains and plasma, we also discuss the effects of negative (active) friction. The latter case seems particularly interesting, since recent analytical calculations have shown that friction coefficients with negative parts may appear in some models of ion absorption by grains as well as in models of ion-grain scattering. Such negative friction may cause active Brownian motions of the grains. As our computer simulations show, the influence of negative friction leads to the formation of various stationary modes (rotations, oscillations), which, to some extent, can also be estimated analytically.

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Fokker‐Planck equation with velocity‐dependent coefficients: Application to dusty plasmas and active particles

Cited by 8 publications

References 10 publications

Brownian motion of grains and negative friction in dusty plasmas

Brownian motion of grains and negative friction in dusty plasmas

Approximated center-of-mass motion for systems of interacting particles with space- and velocity-dependent friction and anharmonic potential

Active and passive Brownian motion of charged particles in two-dimensional plasma models

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