A consistent approach for the treatment of Fermi acceleration in time-dependent billiards

Karlis, A. K.; Diakonos, F. K.; Constantoudis, Vassilios

doi:10.1063/1.3697399

Cited by 13 publications

(14 citation statements)

References 38 publications

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“…One must first realize that the addition of the last term in ( 7) is (only and again) a diffusive approximation; see e.g. [14][15][16]. In particular one should not be forced to think that the true origin of the nonequilibrium condition is literally the connection (through the test particle) of the finite temperature dynamics (first two terms in (7)) with an infinite temperature reservoir (last term in ( 7)).…”

Section: Diffusive Accelerationmentioning

confidence: 99%

Producing suprathermal tails in the stationary velocity distribution

Demaerel

Roeck

Maes

2020

Physica A: Statistical Mechanics and its Applications

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We revisit effective scenarios for the origin of heavy tails in stationary velocity distributions. A first analysis combines localization with diffusive acceleration. That gets realized in space plasmas to find the so-called kappa-distributions having powerlaw decay at high speeds. There, localization at high energy already takes place for the reversible dynamics, but becomes effective by an active diffusion in velocity space. A model for vibrating granular gases and giving rise to stretched exponential tails is also briefly discussed, where negative friction is the energizer. In all cases, the resulting nonMaxwellian velocity distributions are frenetically caused by the dependence on the speed of kinetic parameters.Dedicated to the memory of Christian Van den Broeck.

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Section: Diffusive Accelerationmentioning

confidence: 99%

Producing suprathermal tails in the stationary velocity distribution

Demaerel

Roeck

Maes

2020

Physica A: Statistical Mechanics and its Applications

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“…Boltzmann equations and generalisations have been used to study the distribution of velocities, which typically has an exponential rather than normal tail [136]. Recent work in this direction has included periodically oscillating billiards [137], a Lorentz gas with stochastically moving scatterers [138,139], and more general stochastic processes [140].…”

Section: Vibratingmentioning

confidence: 99%

Diffusion in the Lorentz Gas

Dettmann¹

2014

Commun. Theor. Phys.

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. The Lorentz gas, a point particle making mirror-like reflections from an extended collection of scatterers, has been a useful model of deterministic diffusion and related statistical properties for over a century. This survey summarises recent results, including periodic and aperiodic models, finite and infinite horizon, external fields, smooth or polygonal obstacles, and in the Boltzmann-Grad limit. New results are given for several moving particles and for obstacles with flat points. Finally, a variety of applications are presented.

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“…The traditional approach to describe Fermi acceleration developing in such types of time-dependent systems is generally given in terms of a diffusion process which takes place in momentum space. The evolution of the probability density function for the magnitude of particle velocities as a function of the number of collisions is determined by the Fokker-Planck equation, and results for the one-dimensional case consider either static wall approximation or moving boundary description [9][10][11]. The phenomenon, however, seems not to be robust since dissipation is assumed to be a mechanism to suppress Fermi acceleration [12].…”

Section: Introductionmentioning

confidence: 99%

One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

Botari

Leonel

2013

Phys. Rev. E

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A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ ) controlling the nonlinearity of the moving wall. For large χ , a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization.

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A consistent approach for the treatment of Fermi acceleration in time-dependent billiards

Cited by 13 publications

References 38 publications

Producing suprathermal tails in the stationary velocity distribution

Producing suprathermal tails in the stationary velocity distribution

Diffusion in the Lorentz Gas

One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

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