257 research outputs found
Synchronization by Nonlinear Frequency Pulling
We analyze a model for the synchronization of nonlinear oscillators due to
reactive coupling and nonlinear frequency pulling motivated by the physics of
arrays of nanoscale oscillators. We study the model for the mean field case of
all-to-all coupling, deriving results for the onset of synchronization as the
coupling or nonlinearity increase, and the fully locked state when all the
oscillators evolve with the same frequency
Synchronization by Reactive Coupling and Nonlinear Frequency Pulling
We present a detailed analysis of a model for the synchronization of
nonlinear oscillators due to reactive coupling and nonlinear frequency pulling.
We study the model for the mean field case of all-to-all coupling, deriving
results for the initial onset of synchronization as the coupling or
nonlinearity increase, and conditions for the existence of the completely
synchronized state when all the oscillators evolve with the same frequency.
Explicit results are derived for Lorentzian, triangular, and top-hat
distributions of oscillator frequencies. Numerical simulations are used to
construct complete phase diagrams for these distributions
Basin stability approach for quantifying responses of multistable systems with parameters mismatch
Acknowledgement This work is funded by the National Science Center Poland based on the decision number DEC-2015/16/T/ST8/00516. PB is supported by the Foundation for Polish Science (FNP).Peer reviewedPublisher PD
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
Solitons in a double pendulums chain model, and DNA roto-torsional dynamics
It was first suggested by Englander et al to model the nonlinear dynamics of
DNA relevant to the transcription process in terms of a chain of coupled
pendulums. In a related paper [q-bio.BM/0604014] we argued for the advantages
of an extension of this approach based on considering a chain of double
pendulums with certain characteristics. Here we study a simplified model of
this kind, focusing on its general features and nonlinear travelling wave
excitations; in particular, we show that some of the degrees of freedom are
actually slaved to others, allowing for an effective reduction of the relevant
equations
Analysis of Collective Neutrino Flavor Transformation in Supernovae
We study the flavor evolution of a dense gas initially consisting of pure
mono-energetic and . Using adiabatic invariants and the
special symmetry in such a system we are able to calculate the flavor evolution
of the neutrino gas for the cases with slowly decreasing neutrino number
densities. These calculations give new insights into the results of recent
large-scale numerical simulations of neutrino flavor transformation in
supernovae. For example, our calculations reveal the existence of what we term
the ``collective precession mode''. Our analyses suggest that neutrinos which
travel on intersecting trajectories subject to destructive quantum interference
nevertheless can be in this mode. This mode can result in sharp transitions in
the final energy-dependent neutrino survival probabilities across all
trajectories, a feature seen in the numerical simulations. Moreover, this
transition is qualitatively different for the normal and inverted neutrino mass
hierarchies. Exploiting this difference, the neutrino signals from a future
galactic supernova can potentially be used to determine the actual neutrino
mass hierarchy.Comment: 18 pages, 6 figures, retex4 forma
Guidance of the resonance energy flow in the mechanism of coupled magnetic pendulums
This paper presents a methodology of controlling the resonance energy
exchange in mechanical system consisting of two weakly coupled magnetic
pendulums interacting with the magnetic field generated by coils placed
underneath. It is shown that properly guided magnetic fields can effectively
change mechanical potentials in a way that the energy flow between the
oscillators takes the desired direction. Studies were considered by using a
specific set of descriptive functions characterizing the total excitation
level, its distribution between the pendulums, and the phase shift. The
developed control strategies are based on the observation that, in the case of
antiphase oscillation, the energy is moving from the pendulum subjected to the
repelling magnetic field, to the oscillator under the attracting field. In
contrast, during the inphase oscillations, the energy flow is reversed.
Therefore, closed-loop controller requires only the information about phase
shift, which is easily estimated from dynamic state signals through the
coherency index. Advantage of suggested control strategy is that the temporal
rate of inputs is dictated by the speed of beating, which is relatively slow
compared to the carrying oscillations
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