341 research outputs found
Recurrence-based time series analysis by means of complex network methods
Complex networks are an important paradigm of modern complex systems sciences
which allows quantitatively assessing the structural properties of systems
composed of different interacting entities. During the last years, intensive
efforts have been spent on applying network-based concepts also for the
analysis of dynamically relevant higher-order statistical properties of time
series. Notably, many corresponding approaches are closely related with the
concept of recurrence in phase space. In this paper, we review recent
methodological advances in time series analysis based on complex networks, with
a special emphasis on methods founded on recurrence plots. The potentials and
limitations of the individual methods are discussed and illustrated for
paradigmatic examples of dynamical systems as well as for real-world time
series. Complex network measures are shown to provide information about
structural features of dynamical systems that are complementary to those
characterized by other methods of time series analysis and, hence,
substantially enrich the knowledge gathered from other existing (linear as well
as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos
(2011
Chaotification as a Means of Broadband Vibration Energy Harvesting with Piezoelectric Materials
Computing advances and component miniaturization in circuits coupled with stagnating battery technology have fueled growth in the development of high efficiency energy harvesters. Vibration-to-electricity energy harvesting techniques have been investigated extensively for use in sensors embedded in structures or in hard-to-reach locations like turbomachinery, surgical implants, and GPS animal trackers. Piezoelectric materials are commonly used in harvesters as they possess the ability to convert strain energy directly into electrical energy and can work concurrently as actuators for damping applications. The prototypical harvesting system places two piezoelectric patches on both sides of the location of maximum strain on a cantilever beam. While efficient around resonance, performance drops dramatically should the driving frequency drift away from the beam\u27s fundamental frequency. To date, researchers have worked to improve harvesting capability by modifying material properties, using alternative geometries, creating more efficient harvesting circuits, and inducing nonlinearities. These techniques have partially mitigated the resonance excitation dependence for vibration-based harvesting, but much work remains. In this dissertation, an induced nonlinearity destabilizes a central equilibrium point, resulting in a bistable potential function governing the cantilever beam system. Depending on the environment, multiple stable solutions are possible and can coexist. Typically, researchers neglect chaos and assume that with enough energy in the ambient environment, large displacement trajectories can exist uniquely. When subjected to disturbances a system can fall to coexistent lower energy solutions including aperiodic, chaotic oscillations. Treating chaotic motion as a desirable behavior of the system allows frequency content away from resonance to produce motion about a theoretically infinite number of unstable periodic orbits that can be stabilized through control. The extreme sensitivity to initial conditions exhibited by chaotic systems paired with a pole placement control strategy pioneered by Ott, Grebogi, and Yorke permits small perturbations to an accessible system parameter to alter the system response dramatically. Periodic perturbation of the system trajectories in the vicinity of isolated unstable orbit points can therefore stabilize low-energy chaotic oscillations onto larger trajectory orbits more suitable for energy harvesting. The periodic perturbation-based control method rids the need of a system model. It only requires discrete displacement, velocity, or voltage time series data of the chaotic system driven by harmonic excitation. While the analysis techniques are not fundamentally limited to harmonic excitation, this condition permits the use of standard discrete mapping techniques to isolate periodic orbits of interest. Local linear model fits characterize the orbit and admit the necessary control perturbation calculations from the time series data. This work discusses the feasibility of such a method for vibration energy harvesting, displays stable solutions under various control algorithms, and implements a hybrid bench-top experiment using MATLAB and LabVIEW FPGA. In conclusion, this work discusses the limitations for wide-scale use and addresses areas of further work; both with respect to chaotic energy harvesting and parallel advances required within the field as a whole
The HARPS search for southern extra-solar planets. XXVII. Up to seven planets orbiting HD 10180: probing the architecture of low-mass planetary systems
Context. Low-mass extrasolar planets are presently being discovered at an
increased pace by radial velocity and transit surveys, opening a new window on
planetary systems. Aims. We are conducting a high-precision radial velocity
survey with the HARPS spectrograph which aims at characterizing the population
of ice giants and super-Earths around nearby solar-type stars. This will lead
to a better understanding of their formation and evolution, and yield a global
picture of planetary systems from gas giants down to telluric planets. Methods.
Progress has been possible in this field thanks in particular to the sub-m/s
radial velocity precision achieved by HARPS. We present here new high-quality
measurements from this instrument. Results. We report the discovery of a
planetary system comprising at least five Neptune-like planets with minimum
masses ranging from 12 to 25 M_Earth, orbiting the solar-type star HD 10180 at
separations between 0.06 and 1.4 AU. A sixth radial velocity signal is present
at a longer period, probably due to a 65-M_Earth object. Moreover, another body
with a minimum mass as low as 1.4 M_Earth may be present at 0.02 AU from the
star. This is the most populated exoplanetary system known to date. The planets
are in a dense but still well-separated configuration, with significant secular
interactions. Some of the orbital period ratios are fairly close to integer or
half-integer values, but the system does not exhibit any mean-motion
resonances. General relativity effects and tidal dissipation play an important
role to stabilize the innermost planet and the system as a whole. Numerical
integrations show long-term dynamical stability provided true masses are within
a factor ~3 from minimum masses. We further note that several low-mass
planetary systems exhibit a rather "packed" orbital architecture with little or
no space left for additional planets. (Abridged)Comment: 20 pages, 15 figures, accepted for publication in A&
Physics, Astrophysics and Cosmology with Gravitational Waves
Gravitational wave detectors are already operating at interesting sensitivity
levels, and they have an upgrade path that should result in secure detections
by 2014. We review the physics of gravitational waves, how they interact with
detectors (bars and interferometers), and how these detectors operate. We study
the most likely sources of gravitational waves and review the data analysis
methods that are used to extract their signals from detector noise. Then we
consider the consequences of gravitational wave detections and observations for
physics, astrophysics, and cosmology.Comment: 137 pages, 16 figures, Published version
<http://www.livingreviews.org/lrr-2009-2
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