Phase-response analysis of synchronization for periodic flows

We apply phase-reduction analysis to examine synchronization properties of periodic fluid flows. The dynamics of unsteady flows is described in terms of the phase dynamics, reducing the high-dimensional fluid flow to its single scalar phase variable. We characterize the phase response to impulse perturbations, which can in turn quantify the influence of periodic perturbations on the unsteady flow. These insights from phase-based analysis uncover the condition for synchronization. In the present work, we study as an example the influence of periodic external forcing on an unsteady cylinder wake. The condition for synchronization is identified and agrees closely with results from direct numerical simulations. Moreover, the analysis reveals the optimal forcing direction for synchronization. Phase-response analysis holds potential to uncover lock-on characteristics for a range of periodic flows.

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Phase-reduction analysis of periodic thermoacoustic oscillations in a Rijke tube

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.1093 ◽

2021 ◽

Vol 933 ◽

Author(s):

Calum S. Skene ◽

Kunihiko Taira

Keyword(s):

Optimal Placement ◽

External Forcing ◽

Frequency Locking ◽

Rijke Tube ◽

Thermoacoustic Instability ◽

Phase Dynamics ◽

Sustained Oscillations ◽

Phase Reduction ◽

Efficient Route ◽

Thermoacoustic Oscillations

Phase-reduction analysis captures the linear phase dynamics with respect to a limit cycle subjected to weak external forcing. We apply this technique to study the phase dynamics of the self-sustained oscillations produced by a Rijke tube undergoing thermoacoustic instability. Through the phase-reduction formulation, we are able to reduce these dynamics to a scalar equation for the phase, which allows us to efficiently determine the synchronisation properties of the system. For the thermoacoustic system, we find the conditions for which $m:n$ frequency locking occurs, which sheds light on the mechanisms behind asynchronous and synchronous quenching. We also reveal the optimal placement of pressure actuators that provide the most efficient route to synchronisation.

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Interleukin–6 plays a central role in the hepatic erythropoietin expression during acute phase response: Analysis of two murine models

Zeitschrift für Gastroenterologie ◽

10.1055/s-0029-1246365 ◽

2010 ◽

Vol 48 (01) ◽

Author(s):

P Ramadori ◽

G Ahmad ◽

G Ramadori

Keyword(s):

Acute Phase ◽

Interleukin 6 ◽

Acute Phase Response ◽

Phase Response ◽

Response Analysis ◽

Murine Models

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Effects of spontaneous swallows on breathing in awake goats

Journal of Applied Physiology ◽

10.1152/japplphysiol.01079.2000 ◽

2002 ◽

Vol 92 (5) ◽

pp. 1923-1935 ◽

Cited By ~ 32

Author(s):

Thom R. Feroah ◽

H. V. Forster ◽

Carla G. Fuentes ◽

Ivan M. Lang ◽

David Beste ◽

...

Keyword(s):

Electrical Activity ◽

Tidal Volume ◽

Onset Time ◽

Phase Response ◽

Response Analysis ◽

Dependent Effect ◽

Pharyngeal Muscle ◽

Awake State ◽

Respiratory Phase

The effects of spontaneous swallows on breathing before, during, and after solitary swallows were investigated in 13 awake goats. Inspiratory (Ti) and expiratory (Te) time and respiratory output were determined from inspiratory airflow [tidal volume (Vt)] and peak diaphragmatic activity (Diapeak). The onset time for 1,128 swallows was determined from pharyngeal muscle electrical activity. During inspiration, the later the swallowing onset, the greater increase in Ti and Vt, whereas there was no significant effect on Te and Diapeak. Swallows in early expiration increased the preceding Ti and reduced Te, whereas later in expiration swallows increased Te. After expiratory swallows, Ti and Vt were reduced whereas minimal changes in Diapeak were observed. Phase response analysis revealed a within-breath, phase-dependent effect of swallowing on breathing, resulting in a resetting of the respiratory oscillator. However, the shift in timing in the breaths after a swallow was not parallel, further demonstrating a respiratory phase-dependent effect on breathing. We conclude that, in the awake state, within- and multiple-breath effects on respiratory timing and output are induced and/or required in the coordination of breathing and swallowing.

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Phase response analysis during in vivo-like high conductance states; dendritic SK determines the mean and variance of responses to dendritic excitation

BMC Neuroscience ◽

10.1186/1471-2202-11-s1-o12 ◽

2010 ◽

Vol 11 (S1) ◽

Author(s):

Nathan W Schultheiss ◽

Jeremy R Edgerton ◽

Dieter Jaeger

Keyword(s):

Phase Response ◽

Response Analysis ◽

Mean And Variance ◽

The Mean ◽

Conductance States ◽

High Conductance

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Control of three-dimensional phase dynamics in a cylinder wake

Experiments in Fluids ◽

10.1007/bf00209358 ◽

1994 ◽

Vol 18-18 (1-2) ◽

pp. 26-35 ◽

Cited By ~ 51

Author(s):

G. D. Miller ◽

C. H. K. Williamson

Keyword(s):

Three Dimensional ◽

Cylinder Wake ◽

Phase Dynamics

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Theoretical analysis of the zigzag instability of a vertical columnar vortex pair in a strongly stratified fluid

Journal of Fluid Mechanics ◽

10.1017/s0022112000001166 ◽

2000 ◽

Vol 419 ◽

pp. 29-63 ◽

Cited By ~ 48

Author(s):

PAUL BILLANT ◽

JEAN-MARC CHOMAZ

Keyword(s):

Froude Number ◽

Evolution Equations ◽

Vortex Pair ◽

Horizontal Velocity ◽

Phase Variable ◽

Two Dimensional ◽

Stratified Turbulence ◽

Periodic Patterns ◽

Phase Dynamics ◽

Columnar Vortex

A general theoretical account is proposed for the zigzag instability of a vertical columnar vortex pair recently discovered in a strongly stratified experiment.The linear inviscid stability of the Lamb–Chaplygin vortex pair is analysed by a multiple-scale expansion analysis for small horizontal Froude number (Fh = U/LhN, where U is the magnitude of the horizontal velocity, Lh the horizontal lengthscale and N the Brunt–Väisälä frequency) and small vertical Froude number (Fv = U/LvN, where Lv is the vertical lengthscale) using the scaling of the equations of motion introduced by Riley, Metcalfe & Weissman (1981). In the limit Fv = 0, these equations reduce to two-dimensional Euler equations for the horizontal velocity with undetermined vertical dependence. Thus, at leading order, neutral modes of the flow are associated, among others, to translational and rotational invariances in each horizontal plane. To each broken invariance is related a phase variable that may vary freely along the vertical. Conservation of mass and potential vorticity impose at higher order the evolution equations governing the phase variables that we derive for Fh [Lt ] 1 and Fv [Lt ] 1 in the spirit of phase dynamics techniques established for periodic patterns. In agreement with the experimental observations, this asymptotic analysis shows the existence of an instability consisting of a vertically modulated rotation and a translation of the columnar vortex pair perpendicular to the travelling direction. The dispersion relation as well as the spatial eigenmode of the zigzag instability are determined. The analysis predicts that the most amplified vertical wavelength should scale as U/N and the maximum growth rate as U/Lh.Our main finding is thus that the typical thickness of the ensuing layers will be such that Fv = O(1) and not Fv [Lt ] 1 as assumed by Riley et al. (1981) and Lilly (1983). This implies that such strongly stratified flows are not described by two- dimensional horizontal equations. These results may help to understand the layering commonly observed in stratified turbulence and the fundamental differences with strictly two-dimensional turbulence.

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