scholarly journals Self-consistent method to extract non-linearities from pulsating star light curves – I. Combination frequencies

2020 ◽  
Vol 498 (1) ◽  
pp. 1194-1204
Author(s):  
M Lares-Martiz ◽  
R Garrido ◽  
J Pascual-Granado
Keyword(s):  
Transfer Functions ◽  
Volterra Series ◽  
Power Spectra ◽  
Light Curves ◽  
Stellar Structure ◽  
Mode Identification ◽  
Driving Mechanisms ◽  
Non Linear ◽  
Linear Behaviour ◽  
Combination Frequencies

ABSTRACT Stellar pulsation is a common phenomenon and is sustained because of coherent driving mechanisms. When pulsations are driven by heat or convective mechanisms, it is usual to observe combination frequencies in the power spectra of the stellar light-curves. These combination frequencies are not solutions of the perturbed stellar structure equations. In dense power spectra from a light-curve of a given multiperiodic pulsating star, they can compromise the mode identification in asteroseismic analyses, and hence they must be treated as spurious frequencies and removed. In this paper, a method based on fitting the set of frequencies that best describes a general non-linear model, like the Volterra series, is presented. The method allows these frequencies to be extracted from the power spectrum, thereby improving the frequency analysis and enabling hidden frequencies to emerge from what was initially considered as noise. Moreover, the method yields frequencies with uncertainties several orders of magnitude smaller than the Rayleigh dispersion, which is sometimes used as if it were an error when identifying combination frequencies. Furthermore, it is compatible with the classical counting cycles method, the so-called O-C method, which is valid only for mono-periodic stars. The method creates the possibility of characterizing the non-linear behaviour of a given pulsating star by studying in detail the complex generalized transfer functions on which the model is based.

scholarly journals The occurrence of non-pulsating stars in the γ Dor and δ Sct instability regions

2013 ◽  
Vol 9 (S301) ◽  
pp. 63-66 ◽  
Author(s):  
Joyce A. Guzik ◽  
Paul A. Bradley ◽  
Jason Jackiewicz ◽  
Katrien Uytterhoeven ◽  
Karen Kinemuchi
Keyword(s):  
Effective Temperature ◽  
Power Spectra ◽  
Light Curves ◽  
The Other ◽  
Pulsating Stars ◽  
Driving Mechanisms ◽  
Other Hand ◽  
Instability Regions ◽  
Physical Reasons ◽  
Ppm Level

AbstractWe examine the light curves of over 2700 stars observed in long cadence by the Kepler spacecraft as part of the Guest Observer program. Most of these stars are faint (Kepler magnitude > 14), and fall near or within the effective temperature and log g range of the γ Dor and δ Sct instability strips. We find that the pulsating stars are obvious from inspection of the light curves and power spectra, even for these faint stars. However, we find that a large number of stars are ‘constant’, i.e. show no frequencies in the 0.2 to 24 d−1 range above the 20 ppm level. We discuss the statistics for the constant stars, and some possible physical reasons for lack of pulsations. On the other hand, γ Dor and δ Sct candidates have been found in the Kepler data spread throughout and even outside of the instability regions of both types that were established from pre-Kepler ground-based observations. We revisit mechanisms to produce g- or p-mode pulsations in conditions when these modes are not expected to be unstable via the He-ionization κ effect (δ Sct) or convective blocking (γ Dor) pulsation driving mechanisms.

Analysis of an aerodynamic grooved journal bearing with plain sleeve

2006 ◽  
Vol 220 (1) ◽  
pp. 51-60 ◽  
Author(s):  
C-C Wang
Keyword(s):  
Reynolds Equation ◽  
Dynamic Behaviour ◽  
Journal Bearing ◽  
Power Spectra ◽  
Operating Conditions ◽  
Complex Dynamic ◽  
Non Linear ◽  
Linear Behaviour ◽  
Bearing Number ◽  
Rotor Mass

This article studies the non-linear behaviour of a herringbone-grooved rigid rotor supported by a gas film bearing. A numerical method is employed to a time-dependent mathematical model for herringbone-grooved gas journal bearings. The finite difference method with successive over-relation method is employed to solve the Reynolds equation. The system state trajectory, Poincaré maps, power spectra, and bifurcation diagrams are used to analyse the dynamic behaviour of the rotor centre in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behaviour comprising periodic and quasi-periodic responses of the rotor centre. This article shows how the dynamic behaviour of this type of system varies with changes in rotor mass and bearing number. The results of this study contribute to a further understanding of the non-linear dynamics of aerodynamic-grooved journal bearing systems.

scholarly journals The Effect Of Unsteady Stretch On Laminar Premixed Curved Flames

2021 ◽  
Author(s):  
Meysam Sahafzadeh
Keyword(s):  
Time Scales ◽  
Equivalence Ratio ◽  
Transfer Functions ◽  
Premixed Flames ◽  
Scalar Fields ◽  
Individual Species ◽  
Response Analysis ◽  
Stretch Rate ◽  
Non Linear ◽  
Linear Behaviour

Laminar flamelets are often used to model premixed turbulent combustion. The libraries of rates of conversion from chemical to thermal enthalpies used for flamelets are typically based on counter-flow, strained laminar planar flames under steady conditions. The significance of transient strain has been discussed in the literature with most assertions being that their chemical time scales are sufficiently short compared to the turbulent time scales to treat them as quasi-steady. Less discussed is the unsteady motion of a curved flame front component of stretch rate. This thesis seeks further understanding of the effect of stretch rate on premixed flames by developing and validating a model for use with transient premixed laminar flame dynamics in a cylindrically-symmetric outward radial flow geometry (i.e., inwardly propagating flame). A FORTRAN code is developed and validated which models a laminar premixed flame exposed to an oscillating mass flowrate. This code solves transient equations of continuity, momentum, energy, and individual species in radial coordinates. In this model, flame response is studied when the flow and scalar fields remain aligned (i.e., no strain). The model is applied to conditions in which the flame expands (positive stretch) and contracts (negative stretch) radially by the addition of the externally-defined oscillating mass flow rate. The transient response of laminar premixed flames results in amplitude decrease and phase shift increase with increasing frequency. In order to implement the transient behaviour of flamelets in turbulent modelling more efficiently, a frequency response analysis is applied as a process characterization tool to simplify the complex non-linear behaviour using flame transfer functions. It is shown that with increasing frequency of the perturbation, when equivalence ratio is kept constant, or with decreasing equivalence ratio in the same frequency, non-linear behaviour of the flame becomes prominent. Therefore, linear models can only predict the flame behaviour with accuracy below the threshold of when the fluid and chemistry time scales are the same order of magnitude. Various nonlinear models are studied in order to find the most appropriate flame transfer function for higher frequencies to extend the predictive capabilities of these models.

scholarly journals Mode Identification of the β Cephei star BW Vulpeculae

1995 ◽  
Vol 155 ◽  
pp. 56-57
Author(s):  
C. Aerts ◽  
T. Van Hoolst ◽  
P. Mathias
Keyword(s):  
Moment Method ◽  
Radial Pulsation ◽  
Mode Identification ◽  
Pulsation Mode ◽  
Non Linear ◽  
Linear Behaviour ◽  
The Moment

AbstractWe identify the pulsation mode of BW Vul by means of both the moment method and the method of photometric amplitudes and find a radial pulsation. We briefly study the non-linear behaviour of BW Vul.

THE PULSATING WHITE DWARF G 185-32

2004 ◽  
Vol 13 (07) ◽  
pp. 1213-1216
Author(s):  
BÁRBARA GARCIA CASTANHEIRA ◽  
S. O. KEPLER
Keyword(s):  
White Dwarf ◽  
White Dwarfs ◽  
Light Curves ◽  
Stellar Structure ◽  
Dwarf Stars ◽  
White Dwarf Stars ◽  
Non Linear ◽  
Linear Effects

We study the structure of pulsating white dwarf stars, which present multi-periodic light variations with periods around minutes, defining instability strips along their cooling sequence. We analyze the ultraviolet (HST) and optical (WET) light curves of the pulsating white dwarf G185-32. Among all pulsating white dwarfs, this star has the shortest periodicity so far observed. We detected 18 periodicities, including non-linear effects, which can be used to study the stellar structure, constraining the physics of the degenerate matter.

Modelling the Heave Response of Tension Leg Platforms Using the Volterra Series

2003 ◽  
Author(s):  
Scott Taylor ◽  
Nicholas Haritos ◽  
Krish Thiagarajan
Keyword(s):  
Natural Frequency ◽  
Transfer Functions ◽  
Volterra Series ◽  
Wave Spectrum ◽  
Vertical Plane ◽  
Fatigue Cracking ◽  
Gas Production ◽  
Linear Wave ◽  
Non Linear ◽  
Volterra Method

Tension Leg Platforms (TLPs) are predominately used for deep water oil and gas production. The use of tendons creates a small amplitude, high cyclic response in the vertical plane (heave, roll and pitch). Under these conditions fatigue cracking becomes an important consideration. The amplitude of the vertical motion is minimised by ensuring the natural frequency of the TLP lies above the energetic part of the wave spectrum. However, due to non-linear wave loading effects, it is possible for waves to create an output at their sum-frequency, which may consequently equal the natural frequency of the platform. This phenomenon is more commonly known as ‘springing’. The Volterra method [1] is a technique used to model the behaviour of TLPs under these conditions. This approach quantifies the linear and non-linear (quadratic, cubic, etc) responses separately using transfer functions, which are determined from the input and output of the system. In this paper an orthogonalised Volterra series for use with both Gaussian and non-Gaussian input data is presented. The data used in the Volterra modelling was collected from tests conducted on a model TLP. The wave height and platform motion were measured at wave frequencies around one, a half and a third of the model’s heave natural frequencies. Both regular and irregular wave tests were performed to varying wave heights and frequencies. Using the Volterra method, the transfer functions were calculated up to the third order. Difficulties encountered due to the use of discrete data were identified and where possible their effects minimized. The results demonstrate clear evidence of springing, with dynamic amplification present at sum-frequencies close to the natural frequency of the platform for the non-linear responses.

scholarly journals The Effect Of Unsteady Stretch On Laminar Premixed Curved Flames

2021 ◽  
Author(s):  
Meysam Sahafzadeh
Keyword(s):  
Time Scales ◽  
Equivalence Ratio ◽  
Transfer Functions ◽  
Premixed Flames ◽  
Scalar Fields ◽  
Individual Species ◽  
Response Analysis ◽  
Stretch Rate ◽  
Non Linear ◽  
Linear Behaviour

Laminar flamelets are often used to model premixed turbulent combustion. The libraries of rates of conversion from chemical to thermal enthalpies used for flamelets are typically based on counter-flow, strained laminar planar flames under steady conditions. The significance of transient strain has been discussed in the literature with most assertions being that their chemical time scales are sufficiently short compared to the turbulent time scales to treat them as quasi-steady. Less discussed is the unsteady motion of a curved flame front component of stretch rate. This thesis seeks further understanding of the effect of stretch rate on premixed flames by developing and validating a model for use with transient premixed laminar flame dynamics in a cylindrically-symmetric outward radial flow geometry (i.e., inwardly propagating flame). A FORTRAN code is developed and validated which models a laminar premixed flame exposed to an oscillating mass flowrate. This code solves transient equations of continuity, momentum, energy, and individual species in radial coordinates. In this model, flame response is studied when the flow and scalar fields remain aligned (i.e., no strain). The model is applied to conditions in which the flame expands (positive stretch) and contracts (negative stretch) radially by the addition of the externally-defined oscillating mass flow rate. The transient response of laminar premixed flames results in amplitude decrease and phase shift increase with increasing frequency. In order to implement the transient behaviour of flamelets in turbulent modelling more efficiently, a frequency response analysis is applied as a process characterization tool to simplify the complex non-linear behaviour using flame transfer functions. It is shown that with increasing frequency of the perturbation, when equivalence ratio is kept constant, or with decreasing equivalence ratio in the same frequency, non-linear behaviour of the flame becomes prominent. Therefore, linear models can only predict the flame behaviour with accuracy below the threshold of when the fluid and chemistry time scales are the same order of magnitude. Various nonlinear models are studied in order to find the most appropriate flame transfer function for higher frequencies to extend the predictive capabilities of these models.

scholarly journals An extensive photometric study of the Blazhko RR Lyrae star RZ Lyr*

2012 ◽  
Vol 423 (2) ◽  
pp. 993-1005 ◽  
Author(s):  
J. Jurcsik ◽  
Á. Sódor ◽  
G. Hajdu ◽  
B. Szeidl ◽  
Á. Dózsa ◽  
...  
Keyword(s):  
Light Curve ◽  
Light Curves ◽  
Stellar Structure ◽  
Time Base ◽  
Photometric Method ◽  
Physical Parameters ◽  
Component Solution ◽  
Rr Lyrae ◽  
Curve Variation ◽  
Type Variable

Abstract The analysis of recent, extended multicolour CCD and archive photoelectric, photographic and visual observations has revealed several important properties of RZ Lyr, an RRab-type variable exhibiting large-amplitude Blazhko modulation. On the time base of ∼110 yr, a strict anticorrelation between the pulsation- and modulation-period changes is established. The light curve of RZ Lyr shows a remarkable bump on the descending branch in the small-amplitude phase of the modulation, similarly to the light curves of bump Cepheids. We speculate that the stellar structure temporally suits a 4:1 resonance between the periods of the fundamental and one of the higher order radial modes in this modulation phase. The light-curve variation of RZ Lyr can be correctly fitted with a two-modulation-component solution; the 121-d period of the main modulation is nearly but not exactly four times longer than the period of the secondary modulation component. Using the inverse photometric method, the variations in the pulsation-averaged values of the physical parameters in different phases of both modulation components are determined.

scholarly journals Interaction of equivalence ratio fluctuations and flow fluctuations in acoustically forced swirl flames

2021 ◽  
pp. 175682772110155
Author(s):  
Vincent Kather ◽  
Finn Lückoff ◽  
Christian O. Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Equivalence Ratio ◽  
Transfer Functions ◽  
Transport Model ◽  
Mode Conversion ◽  
Fuel Injector ◽  
One Dimensional ◽  
Flow Fluctuations ◽  
Non Linear ◽  
Non Local ◽  
Acoustic Forcing

The generation and turbulent transport of temporal equivalence ratio fluctuations in a swirl combustor are experimentally investigated and compared to a one-dimensional transport model. These fluctuations are generated by acoustic perturbations at the fuel injector and play a crucial role in the feedback loop leading to thermoacoustic instabilities. The focus of this investigation lies on the interplay between fuel fluctuations and coherent vortical structures that are both affected by the acoustic forcing. To this end, optical diagnostics are applied inside the mixing duct and in the combustion chamber, housing a turbulent swirl flame. The flame was acoustically perturbed to obtain phase-averaged spatially resolved flow and equivalence ratio fluctuations, which allow the determination of flux-based local and global mixing transfer functions. Measurements show that the mode-conversion model that predicts the generation of equivalence ratio fluctuations at the injector holds for linear acoustic forcing amplitudes, but it fails for non-linear amplitudes. The global (radially integrated) transport of fuel fluctuations from the injector to the flame is reasonably well approximated by a one-dimensional transport model with an effective diffusivity that accounts for turbulent diffusion and dispersion. This approach however, fails to recover critical details of the mixing transfer function, which is caused by non-local interaction of flow and fuel fluctuations. This effect becomes even more pronounced for non-linear forcing amplitudes where strong coherent fluctuations induce a non-trivial frequency dependence of the mixing process. The mechanisms resolved in this study suggest that non-local interference of fuel fluctuations and coherent flow fluctuations is significant for the transport of global equivalence ratio fluctuations at linear acoustic amplitudes and crucial for non-linear amplitudes. To improve future predictions and facilitate a satisfactory modelling, a non-local, two-dimensional approach is necessary.

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