21,316 research outputs found
Attractor reconstruction of an impact oscillator for parameter identification
Peer reviewedPreprin
Nonlinear dynamic analysis of an optimal particle damper
We study the dynamical behavior of a single degree of freedom mechanical
system with a particle damper. The particle (granular) damping was optimized
for the primary system operating condition by using an appropriate gap size for
a prismatic enclosure. The particles absorb the kinetic energy of the vibrating
structure and convert it into heat through the inelastic collisions and
friction. This results in a highly nonlinear mechanical system. Considering
linear signal analysis, state space reconstruction, Poincar\'e sections and the
determination of maximal Lyapunov exponents, the motion of the granular system
inside the enclosure is characterized for a wide frequency range. With the
excitation frequency as control parameter, either regular and chaotic motion of
the granular bed are found and their influence on the damping is analyzed.Comment: 18 pages, 8 figures. arXiv admin note: text overlap with
arXiv:1105.030
Nonlinear dynamical analysis of the Blazhko effect with the Kepler space telescope: the case of V783 Cyg
We present a detailed nonlinear dynamical investigation of the Blazhko
modulation of the Kepler RR Lyrae star V783 Cyg (KIC 5559631). We used
different techniques to produce modulation curves, including the determination
of amplitude maxima, the O-C diagram and the analytical function method. We
were able to fit the modulation curves with chaotic signals with the global
flow reconstruction method. However, when we investigated the effects of
instrumental and data processing artefacts, we found that the chaotic nature of
the modulation can not be proved because of the technical problems of data
stitching, detrending and sparse sampling. Moreover, we found that a
considerable part of the detected cycle-to-cycle variation of the modulation
may originate from these effects. According to our results, even the
four-year-long, unprecedented Kepler space photometry of V783 Cyg is too short
for a reliable nonlinear dynamical analysis aiming at the detection of chaos
from the Blazhko modulation. We estimate that two other stars could be suitable
for similar analysis in the Kepler sample and in the future TESS and PLATO may
provide additional candidates.Comment: 9 pages, 12 figures, accepted for publication in MNRA
The dynamics of laser droplet generation
We propose an experimental setup allowing for the characterization of laser
droplet generation in terms of the underlying dynamics, primarily showing that
the latter is deterministically chaotic by means of nonlinear time series
analysis methods. In particular, we use a laser pulse to melt the end of a
properly fed vertically placed metal wire. Due to the interplay of surface
tension, gravity force and light-metal interaction, undulating pendant droplets
are formed at the molten end, which eventually completely detach from the wire
as a consequence of their increasing mass. We capture the dynamics of this
process by employing a high-speed infrared camera, thereby indirectly measuring
the temperature of the wire end and the pendant droplets. The time series is
subsequently generated as the mean value over the pixel intensity of every
infrared snapshot. Finally, we employ methods of nonlinear time series analysis
to reconstruct the phase space from the observed variable and test it against
determinism and stationarity. After establishing that the observed laser
droplet generation is a deterministic and dynamically stationary process, we
calculate the spectra of Lyapunov exponents. We obtain a positive largest
Lyapunov exponent and a negative divergence, i.e., sum of all the exponents,
thus indicating that the observed dynamics is deterministically chaotic with an
attractor as solution in the phase space. In addition to characterizing the
dynamics of laser droplet generation, we outline industrial applications of the
process and point out the significance of our findings for future attempts at
mathematical modeling.Comment: 7 two-column pages, 8 figures; accepted for publication in Chaos
[supplementary material available at
http://www.matjazperc.com/chaos/laser.html
Forecasting high waters at Venice Lagoon using chaotic time series analisys and nonlinear neural netwoks
Time series analysis using nonlinear dynamics systems theory and multilayer neural networks models have been applied to the time sequence of water level data recorded every hour at 'Punta della Salute' from Venice Lagoon during the years 1980-1994. The first method is based on the reconstruction of the state space attractor using time delay embedding vectors and on the characterisation of invariant properties which define its dynamics. The results suggest the existence of a low dimensional chaotic attractor with a Lyapunov dimension, DL, of around 6.6 and a predictability between 8 and 13 hours ahead. Furthermore, once the attractor has been reconstructed it is possible to make predictions by mapping local-neighbourhood to local-neighbourhood in the reconstructed phase space. To compare the prediction results with another nonlinear method, two nonlinear autoregressive models (NAR) based on multilayer feedforward neural networks have been developed. From the study, it can be observed that nonlinear forecasting produces adequate results for the 'normal' dynamic behaviour of the water level of Venice Lagoon, outperforming linear algorithms, however, both methods fail to forecast the 'high water' phenomenon more than 2-3 hours ahead.Publicad
A Unified Approach to Attractor Reconstruction
In the analysis of complex, nonlinear time series, scientists in a variety of
disciplines have relied on a time delayed embedding of their data, i.e.
attractor reconstruction. The process has focused primarily on heuristic and
empirical arguments for selection of the key embedding parameters, delay and
embedding dimension. This approach has left several long-standing, but common
problems unresolved in which the standard approaches produce inferior results
or give no guidance at all. We view the current reconstruction process as
unnecessarily broken into separate problems. We propose an alternative approach
that views the problem of choosing all embedding parameters as being one and
the same problem addressable using a single statistical test formulated
directly from the reconstruction theorems. This allows for varying time delays
appropriate to the data and simultaneously helps decide on embedding dimension.
A second new statistic, undersampling, acts as a check against overly long time
delays and overly large embedding dimension. Our approach is more flexible than
those currently used, but is more directly connected with the mathematical
requirements of embedding. In addition, the statistics developed guide the user
by allowing optimization and warning when embedding parameters are chosen
beyond what the data can support. We demonstrate our approach on uni- and
multivariate data, data possessing multiple time scales, and chaotic data. This
unified approach resolves all the main issues in attractor reconstruction.Comment: 22 pages, revised version as submitted to CHAOS. Manuscript is
currently under review. 4 Figures, 31 reference
Phase-space reconstruction of an atomic chaotic system
We consider the dynamics of a single atom submitted to periodic pulses of a
far-detuned standing wave generated by a high-finesse optical cavity, which is
an atomic version of the well-known ``kicked rotor''. We show that the
classical phase-space map can be ``reconstructed'' by monitoring the
transmission of the cavity. We also studied the effect of spontaneous emission
on the reconstruction, and put limits to the maximum acceptable spontaneous
emission rate.Comment: 5 figures, submitted to PR
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