86 research outputs found
Efficient harmonic oscillator chain energy harvester driven by colored noise
We study the performance of an electromechanical harmonic oscillator chain as
an energy harvester to extract power from finite-bandwidth ambient random
vibrations, which are modelled by colored noise. The proposed device is
numerically simulated and its performance assessed by means of the net
electrical power generated and its efficiency in converting the external
noise-supplied power into electrical power. Our main result is a much enhanced
performance, both in the net electrical power delivered and in efficiency, of
the harmonic chain with respect to the popular single oscillator resonator. Our
numerical findings are explained by means of an analytical approximation, in
excellent agreement with numerics
Efficient time series detection of the strong stochasticity threshold in Fermi-Pasta-Ulam oscillator lattices
In this work we study the possibility of detecting the so-called strong
stochasticity threshold, i.e. the transition between weak and strong chaos as
the energy density of the system is increased, in anharmonic oscillator chains
by means of the 0-1 test for chaos. We compare the result of the aforementioned
methodology with the scaling behavior of the largest Lyapunov exponent computed
by means of tangent space dynamics, that has so far been the most reliable
method available to detect the strong stochasticity threshold. We find that
indeed the 0-1 test can perform the detection in the range of energy density
values studied. Furthermore, we determined that conventional nonlinear time
series analysis methods fail to properly compute the largest Lyapounov exponent
even for very large data sets, whereas the computational effort of the 0-1 test
remains the same in the whole range of values of the energy density considered
with moderate size time series. Therefore, our results show that, for a
qualitative probing of phase space, the 0-1 test can be an effective tool if
its limitations are properly taken into account.Comment: 5 pages, 2 figures; accepted for publication in Physical Review
Covariant hydrodynamic Lyapunov modes and strong stochasticity threshold in Hamiltonian lattices
We scrutinize the reliability of covariant and Gram-Schmidt Lyapunov vectors
for capturing hydrodynamic Lyapunov modes (HLMs) in one-dimensional Hamiltonian
lattices. We show that,in contrast with previous claims, HLMs do exist for any
energy density, so that strong chaos is not essential for the appearance of
genuine (covariant) HLMs. In contrast, Gram-Schmidt Lyapunov vectors lead to
misleading results concerning the existence of HLMs in the case of weak chaos.Comment: 4 pages, 4 figures. Accepted for publication in Physical Review
Macroscopic evidence of microscopic dynamics in the Fermi-Pasta-Ulam oscillator chain from nonlinear time series analysis
The problem of detecting specific features of microscopic dynamics in the
macroscopic behavior of a many-degrees-of-freedom system is investigated by
analyzing the position and momentum time series of a heavy impurity embedded in
a chain of nearest-neighbor anharmonic Fermi-Pasta-Ulam oscillators. Results
obtained in a previous work [M. Romero-Bastida, Phys. Rev. E {\bf69}, 056204
(2004)] suggest that the impurity does not contribute significantly to the
dynamics of the chain and can be considered as a probe for the dynamics of the
system to which the impurity is coupled. The () entropy, which measures
the amount of information generated by unit time at different scales of
time and of the observable, is numerically computed by methods of nonlinear
time-series analysis using the position and momentum signals of the heavy
impurity for various values of the energy density (energy per degree
of freedom) of the system and some values of the impurity mass . Results
obtained from these two time series are compared and discussed.Comment: 7 pages, 5 figures, RevTeX4 PRE format; to be published in Phys. Rev.
Unstable state decay in non-Markovian heat baths and weak signals detection
The statistics of the first passage and nonlinear relaxation times are used to characterize the decay process of an unstable state for an electrically charged Brownian particle embedded in non-Markovian heat baths under the action of an external electric field. The relaxation process is described, in the overdamped regime, by a Generalized Langevin Equation (GLE) characterized by an arbitrary friction memory kernel, and a bistable potential profile. By applying the quasideterministic approach, the statistics of the mean first passage time is calculated through the exact analytical solution of the GLE with arbitrary memory kernel in the linear regime of the bistable potential. To characterize the relaxation process including the nonlinear contributions of the bistable potential, we use the specific Ornstein–Uhlenbeck friction memory kernel to exactly calculate the nonlinear statistics of the mean first passage time as well as the nonlinear relaxation time. Both characteristic times are applied for possible detection of weak signals in the unstable state decay process.Peer ReviewedPreprin
Macroscopic detection of the strong stochasticity threshold in Fermi-Pasta-Ulam chains of oscillators
The largest Lyapunov exponent of a system composed by a heavy impurity
embedded in a chain of anharmonic nearest-neighbor Fermi-Pasta-Ulam oscillators
is numerically computed for various values of the impurity mass . A
crossover between weak and strong chaos is obtained at the same value
of the energy density (energy per degree of freedom)
for all the considered values of the impurity mass . The threshold \epsi
lon_{_T} coincides with the value of the energy density at which a
change of scaling of the relaxation time of the momentum autocorrelation
function of the impurity ocurrs and that was obtained in a previous work ~[M.
Romero-Bastida and E. Braun, Phys. Rev. E {\bf65}, 036228 (2002)]. The complete
Lyapunov spectrum does not depend significantly on the impurity mass . These
results suggest that the impurity does not contribute significantly to the
dynamical instability (chaos) of the chain and can be considered as a probe for
the dynamics of the system to which the impurity is coupled. Finally, it is
shown that the Kolmogorov-Sinai entropy of the chain has a crossover from weak
to strong chaos at the same value of the energy density that the crossover
value of largest Lyapunov exponent. Implications of this result
are discussed.Comment: 6 pages, 5 figures, revtex4 styl
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