A simplified Fermi Accelerator Model under quadratic frictional force

Tavares, Danila F.; Leonel, Edson D.

doi:10.1590/s0103-97332008000100011

Cited by 9 publications

(4 citation statements)

References 17 publications

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“…Hence, it is possible to observe a variety of different behaviours when the damping is varied. Examples of dissipative dynamical systems related to a variety of fields of physics that are treated by the use of discrete mappings can be found in [14][15][16][17][18][19][20][21][22][23][24][25] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Dissipation and its consequences in the scaling exponents for a family of two-dimensional mappings

Oliveira¹,

Leonel²

2012

J. Phys. A: Math. Theor.

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The effects and consequences of dissipation in the scaling exponents describing the behaviour of average properties over the chaotic dynamics for a family of two-dimensional mappings are studied. The mapping is parametrized by an exponent γ in one of the dynamical variables and by a parameter δ ∈ [0, 1], which denotes the amount of the dissipation. The Lyapunov exponents are obtained for different values of γ and δ in the range 0 < δ < 1. The behaviour of the approaching orbits to the chaotic attractors is described analytically to be of exponential type. The deviation around the average action for chaotic orbits was described by a single set of scaling exponents obtained for different γ leading the model to fall into the same universality class as that of the dissipative bouncer model.

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Section: Introductionmentioning

confidence: 99%

Dissipation and its consequences in the scaling exponents for a family of two-dimensional mappings

Oliveira¹,

Leonel²

2012

J. Phys. A: Math. Theor.

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“…The unlimited diffusion in velocity generated due to collisions of a particle with a massive and time moving boundary is known in the literature as Fermi acceleration [25]. Robustness is not a characteristic of the phenomenon since inelastic collision [48,49,50,51] as well as dissipation introduced by the drag-type force [52,53] suppresses the unlimited diffusion.…”

Section: Stadium Billiard As Model the Mapping And Chaotic Propertiesmentioning

confidence: 99%

Separation of particles leading either to decay or unlimited growth of energy in a driven stadium-like billiard

Livorati

Palmero

Dettmann

et al. 2014

J. Phys. A: Math. Theor.

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Abstract. A competition between decay and growth of energy in a time-dependent stadium billiard is discussed giving emphasis in the decay of energy mechanism. A critical resonance velocity is identified for causing of separation between ensembles of high and low energy and a statistical investigation is made using ensembles of initial conditions both above and below the resonance velocity. For high initial velocity, Fermi acceleration is inherent in the system. However for low initial velocity, the resonance allies with stickiness hold the particles in a regular or quasi-regular regime near the fixed points, preventing them from exhibiting Fermi acceleration. Also, a transport analysis along the velocity axis is discussed to quantify the competition of growth and decay of energy and making use distributions of histograms of frequency, and we set that the causes of the decay of energy are due to the capture of the orbits by the resonant fixed points.

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“…For dissipative systems [12] the structure of the phase space commonly has attractors [13] that can be periodic [14] or chaotic [15].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of a bouncer model: A simplified one-dimensional gas

Leonel

Livorati

2015

Communications in Nonlinear Science and Numerical Simulation

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Some dynamical properties of non interacting particles in a bouncer model are described. They move under gravity experiencing collisions with a moving platform. The evolution to steady state is described in two cases for dissipative dynamics with inelastic collisions: (i) for large initial energy; (ii) for low initial energy. For (i) we prove an exponential decay while for (ii) a power law marked by a changeover to the steady state is observed. A relation for collisions and time is obtained and allows us to write relevant observables as temperature and entropy as function of either number of collisions and time.

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A simplified Fermi Accelerator Model under quadratic frictional force

Cited by 9 publications

References 17 publications

Dissipation and its consequences in the scaling exponents for a family of two-dimensional mappings

Dissipation and its consequences in the scaling exponents for a family of two-dimensional mappings

Separation of particles leading either to decay or unlimited growth of energy in a driven stadium-like billiard

Thermodynamics of a bouncer model: A simplified one-dimensional gas

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