249 research outputs found
Rotating potential of a stochastic parametric pendulum
The parametric pendulum is a fruitful dynamical system manifesting some of the
most interesting phenomena of nonlinear dynamics, well-known to exhibit rather
complex motion including period doubling, fold and pitchfork bifurcations, let alone
the global bifurcations leading to chaotic or rotational motion. In this thesis, the
potential of establishing rotational motion is studied considering the bobbing motion
of ocean waves as the source of excitation of a
oating pendulum. The challenge
within this investigation lies on the fact that waves are random, as well as their
observed low frequency, characteristics which pose a broader signi cance within the
study of vibrating systems. Thus, a generic study is conducted with the parametric
pendulum being excited by a narrow-band stochastic process and particularly,
the random phase modulation is utilized. In order to explore the dynamics of the
stochastic system, Markov-chain Monte-Calro simulations are performed to acquire
a view on the in
uence of randomness onto the parameter regions leading to rotational
response. Furthermore, the Probability Density Function of the response
is calculated, applying a numerical iterative scheme to solve the total probability
law, exploiting the Chapman-Kolmogorov equation inherent to Markov processes. A
special case of the studied structure undergoing impacts is considered to account for
extreme weather conditions and nally, a novel design is investigated experimentally,
aiming to set the ground for future development
Probabilistic response and rare events in Mathieu׳s equation under correlated parametric excitation
We derive an analytical approximation to the probability distribution function (pdf) for the response of Mathieu׳s equation under parametric excitation by a random process with a spectrum peaked at the main resonant frequency, motivated by the problem of large amplitude ship roll resonance in random seas. The inclusion of random stochastic excitation renders the otherwise straightforward response to a system undergoing intermittent resonances: randomly occurring large amplitude bursts. Intermittent resonance occurs precisely when the random parametric excitation pushes the system into the instability region, causing an extreme magnitude response. As a result, the statistics are characterized by heavy-tails. We apply a recently developed mathematical technique, the probabilistic decomposition-synthesis method, to derive an analytical approximation to the non-Gaussian pdf of the response. We illustrate the validity of this analytical approximation through comparisons with Monte-Carlo simulations that demonstrate our result accurately captures the strong non-Gaussianinty of the response. Keywords: Mathieu׳s equationColored stochastic excitationHeavy-tailsIntermittent instabilitiesRare eventsStochastic roll resonanceUnited States. Office of Naval Research (Grant ONR N00014- 14-1-0520)Massachusetts Institute of Technology. Naval Engineering Education Center (Grant 3002883706
Harnessing optical micro-combs for microwave photonics
In the past decade, optical frequency combs generated by high-Q
micro-resonators, or micro-combs, which feature compact device footprints, high
energy efficiency, and high-repetition-rates in broad optical bandwidths, have
led to a revolution in a wide range of fields including metrology, mode-locked
lasers, telecommunications, RF photonics, spectroscopy, sensing, and quantum
optics. Among these, an application that has attracted great interest is the
use of micro-combs for RF photonics, where they offer enhanced functionalities
as well as reduced size and power consumption over other approaches. This
article reviews the recent advances in this emerging field. We provide an
overview of the main achievements that have been obtained to date, and
highlight the strong potential of micro-combs for RF photonics applications. We
also discuss some of the open challenges and limitations that need to be met
for practical applications.Comment: 32 Pages, 13 Figures, 172 Reference
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