855 research outputs found
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
Metric for attractor overlap
We present the first general metric for attractor overlap (MAO) facilitating
an unsupervised comparison of flow data sets. The starting point is two or more
attractors, i.e., ensembles of states representing different operating
conditions. The proposed metric generalizes the standard Hilbert-space distance
between two snapshots to snapshot ensembles of two attractors. A reduced-order
analysis for big data and many attractors is enabled by coarse-graining the
snapshots into representative clusters with corresponding centroids and
population probabilities. For a large number of attractors, MAO is augmented by
proximity maps for the snapshots, the centroids, and the attractors, giving
scientifically interpretable visual access to the closeness of the states. The
coherent structures belonging to the overlap and disjoint states between these
attractors are distilled by few representative centroids. We employ MAO for two
quite different actuated flow configurations: (1) a two-dimensional wake of the
fluidic pinball with vortices in a narrow frequency range and (2)
three-dimensional wall turbulence with broadband frequency spectrum manipulated
by spanwise traveling transversal surface waves. MAO compares and classifies
these actuated flows in agreement with physical intuition. For instance, the
first feature coordinate of the attractor proximity map correlates with drag
for the fluidic pinball and for the turbulent boundary layer. MAO has a large
spectrum of potential applications ranging from a quantitative comparison
between numerical simulations and experimental particle-image velocimetry data
to the analysis of simulations representing a myriad of different operating
conditions.Comment: 33 pages, 20 figure
Kick control: using the attracting states arising within the sensorimotor loop of self-organized robots as motor primitives
Self-organized robots may develop attracting states within the sensorimotor
loop, that is within the phase space of neural activity, body, and
environmental variables. Fixpoints, limit cycles, and chaotic attractors
correspond in this setting to a non-moving robot, to directed, and to irregular
locomotion respectively. Short higher-order control commands may hence be used
to kick the system from one self-organized attractor robustly into the basin of
attraction of a different attractor, a concept termed here as kick control. The
individual sensorimotor states serve in this context as highly compliant motor
primitives.
We study different implementations of kick control for the case of simulated
and real-world wheeled robots, for which the dynamics of the distinct wheels is
generated independently by local feedback loops. The feedback loops are
mediated by rate-encoding neurons disposing exclusively of propriosensoric
inputs in terms of projections of the actual rotational angle of the wheel. The
changes of the neural activity are then transmitted into a rotational motion by
a simulated transmission rod akin to the transmission rods used for steam
locomotives.
We find that the self-organized attractor landscape may be morphed both by
higher-level control signals, in the spirit of kick control, and by interacting
with the environment. Bumping against a wall destroys the limit cycle
corresponding to forward motion, with the consequence that the dynamical
variables are then attracted in phase space by the limit cycle corresponding to
backward moving. The robot, which does not dispose of any distance or contact
sensors, hence reverses direction autonomously.Comment: 17 pages, 9 figure
Dynamical indicators for the prediction of bursting phenomena in high-dimensional systems
Drawing upon the bursting mechanism in slow-fast systems, we propose
indicators for the prediction of such rare extreme events which do not require
a priori known slow and fast coordinates. The indicators are associated with
functionals defined in terms of Optimally Time Dependent (OTD) modes. One such
functional has the form of the largest eigenvalue of the symmetric part of the
linearized dynamics reduced to these modes. In contrast to other choices of
subspaces, the proposed modes are flow invariant and therefore a projection
onto them is dynamically meaningful. We illustrate the application of these
indicators on three examples: a prototype low-dimensional model, a body forced
turbulent fluid flow, and a unidirectional model of nonlinear water waves. We
use Bayesian statistics to quantify the predictive power of the proposed
indicators
Controlling Multistability in a Vibro-Impact Capsule System
This is the final version of the article. Available from Springer Verlag via the DOI in this record.This work concerns the control of multistability in a vibro-impact capsule system driven by a harmonic excitation. The capsule is able to move forward and backward in a rectilinear direction, and the main objective of this work is to control such motion in the presence of multiple coexisting periodic solutions. A position feedback controller is employed in this study, and our numerical investigation demonstrates that the proposed control method gives rise to a dynamical scenario with two coexisting solutions, corresponding to forward and backward progression. Therefore, the motion direction of the system can be controlled by suitably perturbing its initial conditions, without altering the system parameters. To study the robustness of this control method, we apply numerical continuation methods in order to identify a region in the parameter space in which the proposed controller can be applied. For this purpose, we employ the MATLAB-based numerical platform COCO, which supports the continuation and bifurcation detection of periodic orbits of non-smooth dynamical systems.The second author has been supported by a Georg Forster Research Fellowship granted by the Alexander von Humboldt Foundation, Germany. The authors would like to thank Dr. Haibo Jiang for stimulating discussions and comments on this work
- âŠ