3,204 research outputs found
Stable integrated hyper-parametric oscillator based on coupled optical microcavities
We propose a flexible scheme based on three coupled optical microcavities
which permits to achieve stable oscillations in the microwave range, the
frequency of which depends only on the cavity coupling rates. We find the
different dynamical regimes (soft and hard excitation) to affect the
oscillation intensity but not their period. This configuration may permit to
implement compact hyper-parametric sources on an integrated optical circuit,
with interesting applications in communications, sensing and metrology.Comment: 4 pages, 5 figure
Metabifurcation analysis of a mean field model of the cortex
Mean field models (MFMs) of cortical tissue incorporate salient features of
neural masses to model activity at the population level. One of the common
aspects of MFM descriptions is the presence of a high dimensional parameter
space capturing neurobiological attributes relevant to brain dynamics. We study
the physiological parameter space of a MFM of electrocortical activity and
discover robust correlations between physiological attributes of the model
cortex and its dynamical features. These correlations are revealed by the study
of bifurcation plots, which show that the model responses to changes in
inhibition belong to two families. After investigating and characterizing
these, we discuss their essential differences in terms of four important
aspects: power responses with respect to the modeled action of anesthetics,
reaction to exogenous stimuli, distribution of model parameters and oscillatory
repertoires when inhibition is enhanced. Furthermore, while the complexity of
sustained periodic orbits differs significantly between families, we are able
to show how metamorphoses between the families can be brought about by
exogenous stimuli. We unveil links between measurable physiological attributes
of the brain and dynamical patterns that are not accessible by linear methods.
They emerge when the parameter space is partitioned according to bifurcation
responses. This partitioning cannot be achieved by the investigation of only a
small number of parameter sets, but is the result of an automated bifurcation
analysis of a representative sample of 73,454 physiologically admissible sets.
Our approach generalizes straightforwardly and is well suited to probing the
dynamics of other models with large and complex parameter spaces
Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators
Many engineering structures are composed of weakly coupled sectors assembled
in a cyclic and ideally symmetric configuration, which can be simplified as
forced Duffing oscillators. In this paper, we study the emergence of localized
states in the weakly nonlinear regime. We show that multiple spatially
localized solutions may exist, and the resulting bifurcation diagram strongly
resembles the snaking pattern observed in a variety of fields in physics, such
as optics and fluid dynamics. Moreover, in the transition from the linear to
the nonlinear behaviour isolated branches of solutions are identified.
Localization is caused by the hardening effect introduced by the nonlinear
stiffness, and occurs at large excitation levels. Contrary to the case of
mistuning, the presented localization mechanism is triggered by the
nonlinearities and arises in perfectly homogeneous systems
Structure, dynamics and bifurcations of discrete solitons in trapped ion crystals
We study discrete solitons (kinks) accessible in state-of-the-art trapped ion
experiments, considering zigzag crystals and quasi-3D configurations, both
theoretically and experimentally. We first extend the theoretical understanding
of different phenomena predicted and recently experimentally observed in the
structure and dynamics of these topological excitations. Employing tools from
topological degree theory, we analyze bifurcations of crystal configurations in
dependence on the trapping parameters, and investigate the formation of kink
configurations and the transformations of kinks between different structures.
This allows us to accurately define and calculate the effective potential
experienced by solitons within the Wigner crystal, and study how this
(so-called Peierls-Nabarro) potential gets modified to a nonperiodic globally
trapping potential in certain parameter regimes. The kinks' rest mass (energy)
and spectrum of modes are computed and the dynamics of linear and nonlinear
kink oscillations are analyzed. We also present novel, experimentally observed,
configurations of kinks incorporating a large-mass defect realized by an
embedded molecular ion, and of pairs of interacting kinks stable for long
times, offering the perspective for exploring and exploiting complex collective
nonlinear excitations, controllable on the quantum level.Comment: 25 pages, 10 figures, v2 corrects Fig. 2 and adds some text and
reference
Synchronization framework for modeling transition to thermoacoustic instability in laminar combustors
We, herein, present a new model based on the framework of synchronization to
describe a thermoacoustic system and capture the multiple bifurcations that
such a system undergoes. Instead of applying flame describing function to
depict the unsteady heat release rate as the flame's response to acoustic
perturbation, the new model considers the acoustic field and the unsteady heat
release rate as a pair of nonlinearly coupled damped oscillators. By varying
the coupling strength, multiple dynamical behaviors, including limit cycle
oscillation, quasi-periodic oscillation, strange nonchaos, and chaos can be
captured. Furthermore, the model was able to qualitatively replicate the
different behaviors of a laminar thermoacoustic system observed in experiments
by Kabiraj et al.~[Chaos 22, 023129 (2012)]. By analyzing the temporal
variation of the phase difference between heat release rate oscillations and
pressure oscillations under different dynamical states, we show that the
characteristics of the dynamical states depend on the nature of synchronization
between the two signals, which is consistent with previous experimental
findings.Comment: 18 pages, 7 figure
Analysis of nonlinear oscillators using volterra series in the frequency domain Part I : convergence limits
The Volterra series representation is a direct generalisation of the linear convolution integral and has been widely applied in the analysis and design of
nonlinear systems, both in the time and the frequency domain. The Volterra series is associated with the so-called weakly nonlinear systems, but even within the
framework of weak nonlinearity there is a convergence limit for the existence of a valid Volterra series representation for a given nonlinear differential equation.
Barrett(1965) proposed a time domain criterion to prove that the Volterra series converges with a given region for a class of nonlinear systems with cubic stiffness
nonlinearity. In this paper this time-domain criterion is extended to the frequency domain to accommodate the analysis of nonlinear oscillators subject to harmonic
excitation
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