2,643 research outputs found
Periodic compression of an adiabatic gas: Intermittency enhanced Fermi acceleration
A gas of noninteracting particles diffuses in a lattice of pulsating
scatterers. In the finite horizon case with bounded distance between collisions
and strongly chaotic dynamics, the velocity growth (Fermi acceleration) is well
described by a master equation, leading to an asymptotic universal
non-Maxwellian velocity distribution scaling as v ~ t. The infinite horizon
case has intermittent dynamics which enhances the acceleration, leading to v ~
t ln t and a non-universal distribution.Comment: 6 pages, 4 figures, to appear in EPL
(http://epljournal.edpsciences.org/
A bouncing ball model with two nonlinearities: a prototype for Fermi acceleration
Some dynamical properties of a bouncing ball model under the presence of an
external force modeled by two nonlinear terms are studied. The description of
the model is made by use of a two dimensional nonlinear measure preserving map
on the variables velocity of the particle and time. We show that raising the
straight of a control parameter which controls one of the nonlinearities, the
positive Lyapunov exponent decreases in the average and suffers abrupt changes.
We also show that for a specific range of control parameters, the model
exhibits the phenomenon of Fermi acceleration. The explanation of both
behaviours is given in terms of the shape of the external force and due to a
discontinuity of the moving wall's velocity.Comment: A complete list of my papers can be found in:
http://www.rc.unesp.br/igce/demac/denis
Thermodynamics of a bouncer model: a simplified one-dimensional gas
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.Comment: 36 pages, 10 figures. To appear in: Communications in Nonlinear
Science and Numerical Simulation, 201
A one-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator
A modification of the one-dimensional Fermi accelerator model is considered
in this work. The dynamics of a classical particle of mass , confined to
bounce elastically between two rigid walls where one is described by a
non-linear van der Pol type oscillator while the other one is fixed, working as
a re-injection mechanism of the particle for a next collision, is carefully
made by the use of a two-dimensional non-linear 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;
(ii) the case where collisions of the particle does 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
() controlling the non-linearity of the moving wall. For large
, a diffusion on the velocity is observed leading us to conclude 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 oscillation, 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 complicate organization
Corrugated waveguide under scaling investigation
Some scaling properties for classical light ray dynamics inside a
periodically corrugated waveguide are studied by use of a simplified
two-dimensional nonlinear area-preserving map. It is shown that the phase space
is mixed. The chaotic sea is characterized using scaling arguments revealing
critical exponents connected by an analytic relationship. The formalism is
widely applicable to systems with mixed phase space, and especially in studies
of the transition from integrability to non-integrability, including that in
classical billiard problems.Comment: A complete list of my papers can be found in:
http://www.rc.unesp.br/igce/demac/denis
Fermi acceleration and suppression of Fermi acceleration in a time-dependent Lorentz Gas
We study some dynamical properties of a Lorentz gas. We have considered both
the static and time dependent boundary. For the static case we have shown that
the system has a chaotic component characterized with a positive Lyapunov
Exponent. For the time-dependent perturbation we describe the model using a
four-dimensional nonlinear map. The behaviour of the average velocity is
considered in two situations (i) non-dissipative and (ii) dissipative. Our
results show that the unlimited energy growth is observed for the
non-dissipative case. However, when dissipation, via damping coefficients, is
introduced the senary changes and the unlimited engergy growth is suppressed.
The behaviour of the average velocity is described using scaling approach
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