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 $\nu_e$ and $\bar\nu_e$. 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