Quasi-periodic Research Articles

SALT observation of X-ray pulse reprocessing in 4U 1626−67

We investigate optical reprocessing of X-rays in the LMXB pulsar 4U 1626-67 in its current spin-up phase using observations with Southern African Large Telescope (SALT), near-simultaneous observations with Swift-XRT and non-simultaneous RXTE-PCA observations and present the results of timing analysis. Using SALT observations carried out on 5th and 6th March, 2014, we detect some interesting reprocessing signatures. We detect a weak optical Quasi Periodic Oscillation (QPO) in the power density spectrum on March 5th at 48 mHz with a fractional rms of 3.3% in spite of the fact that source shows no corresponding X-ray QPO in the spin-up phase. In the light curve obtained on March 5th, we detect a coherent pulsation at the spin period of ~7.677 s. A previously known, slightly down-shifted side-band is also detected at 129.92 mHz. The frequency spacing between main pulse and this side-band is different from earlier observations, though the statistical significance of the difference is limited. The light curve of 6th March displays short time-scale variability in the form of flares on timescales of a few minutes. Folded pulse profiles resulting from data of this night show an interesting trend of pulse peak drifting. This drift could be due to i) rapid changes in the reprocessing agent, like orbital motion of an accretion disk warp around the neutron star or ii) intrinsic pulse phase changes in X-rays. We also examine some X-ray light curves obtained with RXTE-PCA during 2008-2010 for pulse shape changes in short time scales during X-ray flares.

On the quasi-periodic response in the delayed forced Duffing oscillator

We explore the quasi-periodic (QP) vibrations in a delayed Duffing equation submitted to periodic forcing. The second-step perturbation method is applied on the slow flow of the oscillator to derive the slow–slow flow near the primary resonance. The QP solution corresponding to the nontrivial equilibrium of the slow–slow flow as well as its modulation envelope is predicted analytically. The influence of different system parameters on the QP response is reported and discussed. The analytical results show that for weak nonlinearity and small damping large-amplitude QP vibration induced by destabilization of limit cycle via Neimark–Sacker bifurcation occurs in a broadband of the excitation frequency and in large range of delay parameters.

Energy harvesting in a delayed and excited Duffing harvester device

We explore quasi-periodic (QP) vibration-based energy harvesting (EH) in a forced nonlinear oscillator under time delay. The energy harvesting system consists in a delayed Duffing oscillator subject to harmonic excitation coupled to an electric circuit through an electromechanical coupling mechanism.We consider the case of primary resonance for which the frequency of the excitation is near the natural frequency of the oscillator. Application of the double-step perturbation method enables the approximation of the amplitude of the QP vibrations used to extract the average powers from the harvester device. Results shown that for a small value of delay amplitude, the periodic vibration-based EH can be extracted in a narrow range near the resonance, while QP vibration-based EH can be extracted over broad ranges of excitation. For relatively increasing value of the delay amplitude, only QP vibration-based EH can be extracted.

Madden Julian Oscillations in Total Column Ozone, Air Temperature and Surface Pressure Measured over Cochin during Summer Monsoon 2015

The intra-seasonal variability plays a major role in the inter-annual variability of weather parameters such as rainfall, temperature and pressure which lead to extreme weather events in certain years. The active (more rainy days) and break (less rainy days) periods of Indian summer monsoon heavily depend on the intra-seasonal variability of weather parameters such as wind, pressure and temperature oscillations during the monsoon season. In the present analysis daily total column ozone, surface temperature and surface pressure measured over Cochin using Microtop II Ozonometer (sun Photometer) were used to study the Intra-Seasonal Variations (ISV) of the above parameters during the monsoon season, 2015. The dominant and significant intra-seasonal oscillations (ISOs) were identified using an advanced statistical method called the Discrete Mayer’s Wavelet (DMW) analysis. Two major ISOs such as Madden Julian Oscillations (MJO, 30 - 60 days) and quasi-bi weekly (12 - 16 days) oscillations were found in TCO, surface temperature and pressure. In TCO an additional mode of ISO with quasi tri-weekly periodicity was also found (16 - 22 day). It is observed that MJO mode is the dominant among all other modes and its positive and negative phases correlate with positive and negative anomalies of the above parameters. The ISO mode in the surface pressure shows an out of phase relation with the Indian summer monsoon rainfall which indicates the active and break periods of Indian summer monsoon. The contribution of MJO mode is dominant in the tropical atmosphere, which modulates the intra-seasonal variability. It is found that for the year 2015 total column ozone, surface pressure and surface temperature show an annual range of 30 DU, 4 hPa and 1°C, respectively.

On self-excited oscillations of the Earth

Recently, Izvestiya, Physics of the Solid Earth has published the empirical results certainly indicating the influence of the free oscillations of the Earth on earthquake activity. It is known that free oscillations are excited by the earthquakes. Therefore, we may hypothesize that the Earth experiences self-excited oscillations. In this paper, it is shown that the very fact that free oscillations affect global seismicity does not necessarily mean that resonant self-excited oscillations of the Earth do exist. At the same time, the signs of selfexcited relaxation oscillations are in some cases probably observed in the form of hidden periodicity with a quasi period of ~3 h in the aftershock sequences from the strong earthquakes. The further research on this subject appears to be promising.

Strong correlation between quasiperiodic echoes and plasma drift in the E region

AbstractSimultaneous observations of quasiperiodic (QP) echoes and plasma drift in the ionospheric E region were conducted in Fuke (19.5°N, 109.1°E), Hainan province, China, to investigate the QP striation tilts under varying plasma drift conditions. The E region field‐aligned irregularities (FAIs), observed using the Hainan VHF radar, and the drift velocities of the plasma blobs in the Es layer, recorded by the Hainan Digisonde operating in drift mode, are reported. The QP echoes and drift data recorded during the entire year of 2013 were analyzed and compared. A surprising consistency between the striation tilt of the QP echoes and the drift direction of the plasma blobs was discovered. A negative echo striation of the QP FAIs was recorded when the measured drift direction of the plasma blobs was southward, whereas a positive echo striation was observed during the northward drift. Furthermore, the echo trace was continuous, whereas the QP striation changed from negative to positive, and vice versa. Thus, it can be concluded that the morphology of the QP echoes may be controlled by the background wind fields in the E region. The northward/southward‐drifting striated FAIs in the observation region of a coherent scatter radar might induce the positive/negative QP echo striation in the range‐time‐intensity plots.

Islands of stability and recurrence times in AdS

We study the stability of anti-de Sitter (AdS) spacetime to spherically symmetric perturbations of a real scalar field in general relativity. Further, we work within the context of the "two time framework" (TTF) approximation, which describes the leading nonlinear effects for small amplitude perturbations, and is therefore suitable for studying the weakly turbulent instability of AdS---including both collapsing and non-collapsing solutions. We have previously identified a class of quasi-periodic (QP) solutions to the TTF equations, and in this work we analyze their stability. We show that there exist several families of QP solutions that are stable to linear order, and we argue that these solutions represent islands of stability in TTF. We extract the eigenmodes of small oscillations about QP solutions, and we use them to predict approximate recurrence times for generic non-collapsing initial data in the full (non-TTF) system. Alternatively, when sufficient energy is driven to high-frequency modes, as occurs for initial data far from a QP solution, the TTF description breaks down as an approximation to the full system. Depending on the higher order dynamics of the full system, this often signals an imminent collapse to a black hole.

Study of structural break points in global and hemispheric temperature series by piecewise regression

The study of climate trends taking into consideration possible structural changes is important for understanding climate development characterized by a stochastic trend or by a determined one.In the paper global and hemisphere temperature anomalies are modeled by piecewise linear regression and break points in the temperature evolution are found. It was demonstrated that the used method allowed finding of breaks characterized by long time trends (low frequency processes) as well as abrupt changes (fast frequency processes). The obtained break points for slow temperature change are close to the ones found by other authors however additional conditions (as segment length, gradient and others) are not used here. The results for higher break point numbers are like the ones of step slope models. It was demonstrated that the successive phases of warming and cooling and most of the break points subdividing these periods in the Northern Hemisphere are introduced by the Atlantic multidecadal oscillation. Because the strong quasi periodicity of the Atlantic multidecadal oscillation the authors recommend the removal of its influence on the temperature from the temperature series before studies of trends or structural changes. The Northern Hemisphere temperature data after the removal of the Atlantic multidecadal oscillation influence show structures like the Southern Hemisphere temperatures. Model selection by the Schwarz–Bayesian Information Criterion developed by Liu, Wu and Zidek (LWZ criterion) shows that models with only one break point are to be preferred.

Stellar rotation period inference with Gaussian processes

The light curves of spotted, rotating stars are often non-sinusoidal and Quasi-Periodic (QP) and a strictly periodic sinusoid is therefore not a representative generative model. Ideally, a physical model of the stellar surface would be conditioned on the data, however the parameters of such models can be highly degenerate.

Algebro-geometric Constructions of Quasi Periodic Flows of the Discrete Self-dual Network Hierarchy and Applicationsℰ

In this paper we obtain the discrete integrable self-dual network hierarchy associated with a discrete spectral problem. On the basis of the theory of algebraic curves, the continuous flow and discrete flow related to the discrete self-dual network hierarchy are straightened using the Abel-Jacobi coordinates. The meromorphic function and the Baker-Akhiezer function are introduced on the hyperelliptic curve. Quasi-periodic solutions of the discrete self-dual network hierarchy are constructed with the help of the asymptotic properties and the algebra-geometric characters of the meromorphic function, the Baker-Akhiezer function and the hyperelliptic curve.

Analysis of the Quasi Periodic Scenario Leading to Chaos in a Square Cavity

Analysis of the Quasi Periodic Scenario Leading to Chaos in a Square Cavity

Equatorial noise emissions with quasiperiodic modulation of wave intensity

AbstractEquatorial noise (EN) emissions are electromagnetic wave events at frequencies between the proton cyclotron frequency and the lower hybrid frequency observed in the equatorial region of the inner magnetosphere. They propagate nearly perpendicular to the ambient magnetic field, and they exhibit a harmonic line structure characteristic of the proton cyclotron frequency in the source region. However, they were generally believed to be continuous in time. We investigate more than 2000 EN events observed by the Spatio‐Temporal Analysis of Field Fluctuations and Wide‐Band Data Plasma Wave investigation instruments on board the Cluster spacecraft, and we show that this is not always the case. A clear quasiperiodic (QP) time modulation of the wave intensity is present in more than 5% of events. We perform a systematic analysis of these EN events with QP modulation of the wave intensity. Such events occur usually in the noon‐to‐dawn magnetic local time sector. Their occurrence seems to be related to the increased geomagnetic activity, and it is associated with the time intervals of enhanced solar wind flow speeds. The modulation period of these events is on the order of minutes. Compressional ULF magnetic field pulsations with periods about double the modulation periods of EN wave intensity and magnitudes on the order of a few tenths of nanotesla were identified in about 46% of events. We suggest that these compressional magnetic field pulsations might be responsible for the observed QP modulation of EN wave intensity, in analogy to formerly reported VLF whistler mode QP events.

Statistical investigation of VLF quasiperiodic emissions measured by the DEMETER spacecraft

AbstractWe present a survey of quasiperiodic (QP) ELF/VLF emissions detected onboard the DEMETER (Detection of Electro‐Magnetic Emissions Transmitted from Earthquake Regions) satellite (altitude of about 700 km, nearly Sun‐synchronous orbit at 10:30/22:30 LT). Six years of data have been visually inspected for the presence of QP emissions with modulation periods higher than 10 s and with frequency bandwidths higher than 200 Hz. It is found that these QP events occur in about 5% of daytime half orbits, while they are basically absent during the night. The events occur predominantly during quiet geomagnetic conditions following the periods of enhanced geomagnetic activity. Their occurrence and properties are systematically analyzed. QP emissions occur most often at frequencies from about 750 Hz to 2 kHz, but they may be observed at frequencies as low as 500 Hz and as high as 8 kHz. Modulation periods of QP events may range from about 10 to 100 s, with typical values of 20 s. Frequency drifts of the identified events are generally positive, but they are lower for events with larger modulation periods. The events are usually limited to higher L values (L > 2). The upper L shell boundary of their occurrence could not be identified using the DEMETER data, but they are found to extend up to at least L ~ 6. The occurrence rate of the events is significantly lower at the longitudes of the South Atlantic anomaly (by a factor of more than 2).

Analytic Study on Chaotic Characteristics of Viscoelastic Beams Based on the Evolution of Nonlinear Stiffness

So far there exist deficiencies on monitoring methods of structures' stiffness among bridges' health monitoring. This paper introduces viscoelastic beams with nonlinear stiffness, explains physical nonlinear factors of beams through the sum of linear and cubic terms, and thus establishes a dynamic model of the viscoelastic beam with nonlinear stiffness under forced vibration. When the numerical simulation methods are applied, it studies systems of the bridge on nonlinear dynamic behaviors resulting from the variation of stiffness. The results prove that the bigger the coefficient of nonlinear stiffness is, the stronger the sensitivity of the beam's vibration against the initial conditions is. Since the beginning of periodic motion of the beam's vibration, there gradually appears quasi periodicity and period doubling bifurcation, then chaotic motion at last. The stronger the nonlinearity of the viscoelastic beam with nonlinear stiffness is, the stronger the sensitivity of the vibration against the initial ...

Ground‐based ELF/VLF chorus observations at subauroral latitudes—VLF‐CHAIN Campaign

AbstractWe report observations of very low frequency (VLF) and extremely low frequency (ELF) chorus waves taken during the ELF/VLF Campaign observation with High‐resolution Aurora Imaging Network (VLF‐CHAIN) of 17–25 February 2012 at subauroral latitudes at Athabasca (L=4.3), Canada. ELF/VLF waves were measured continuously with a sampling rate of 100 kHz to monitor daily variations in ELF/VLF emissions and derive their detailed structures. We found quasiperiodic (QP) emissions whose repetition period changes rapidly within a period of 1 h without corresponding magnetic pulsations. QP emissions showed positive correlation between amplitude and frequency sweep rate, similarly to rising‐tone elements. We found an event of nearly simultaneous enhancements of QP emissions and Pc1/electromagnetic ion cyclotron wave intensities, suggesting that the temperature anisotropy of electrons and ions developed simultaneously at the equatorial plane of the magnetosphere. We also found QP emissions whose intensity suddenly increased in association with storm sudden commencement without changing their frequency. Falling‐tone ELF/VLF emissions were observed with their rate of frequency change varying from 0.7 to 0.05 kHz/s over 10 min. Bursty‐patch emissions in the lower and upper frequency bands are often observed during magnetically disturbed periods. Clear systematic correlation between these various ELF/VLF emissions and cosmic noise absorption was not obtained throughout the campaign period. These observations indicate several previously unknown features of ELF/VLF emissions in subauroral latitudes and demonstrate the importance of continuous measurements for monitoring temporal variations in these emissions.

Wake transition in the flow around a circular cylinder with a splitter plate

AbstractA simple way to decrease the drag and oscillating lift forces in the flow around a circular cylinder consists of positioning a splitter plate in the wake, parallel to the flow. In this paper, the effect of the splitter plate on the wake dynamics, more specifically on the wake transition, is described in detail. First, two-dimensional and three-dimensional direct numerical simulations (DNS) using the spectral element method were used to observe the behaviour of the wake in the presence of the splitter plate. Then, a linear stability analysis based on the Floquet theory was performed in order to obtain information on how the splitter plate changes the instabilities that lead to wake transition. Simulations were carried out for several gaps between the splitter plate and the cylinder, with the Reynolds number varying in the range between 100 and 350, which corresponds to the wake transition in the flow around a circular cylinder. The results of the simulations showed a discontinuity in the Strouhal number curve that is consistent with the results available in the literature. The stability analysis showed how the splitter plate modifies the transition of the flow to a three-dimensional configuration. The splitter plate has a stabilizing effect on the flow for small gaps, delaying the appearance of three-dimensional structures to higher Reynolds numbers. Mode A and a quasi-periodic (QP) mode are observed for such small gaps. As the gap is increased the discontinuity in the Strouhal number curve also caused a clear change in the characteristics of the neutral stability curve, and the existence of an unstable period-doubling mode was observed. The onset characteristics of the unstable modes are analysed and discussed in depth.

The Dynamics of a Class of Quasi-Periodic Schrödinger Cocycles

Let $${f:\mathbb{T} \to\mathbb{R}}$$ be a Morse function of class C 2 with exactly two critical points, let $${\omega \in \mathbb{T}}$$ be Diophantine, and let λ > 0 be sufficiently large (depending on f and ω). For any value of the parameter $${E\in \mathbb{R}}$$ , we make a careful analysis of the dynamics of the skew-product map $$\Phi_E(\theta,r)=\left(\theta+\omega, {\rm \lambda} f(\theta)-E-1/r\right),$$ acting on the “torus” $${\mathbb{T} \times \widehat{\mathbb{R}}}$$ . Here, $${\widehat{\mathbb{R}}}$$ denotes the projective space $${\mathbb{R} \cup\{\infty\}}$$ . The map Φ E is intimately related to the quasi-periodic Schrodinger cocycle $${(\omega, A_E): \mathbb{T}\times \mathbb{R}^2 \to \mathbb{T}\times \mathbb{R}^2,\, (\theta,x)\mapsto (\theta+\omega, A_E(\theta)\cdot x)}$$ , where $${A_E:\mathbb{T}\to {\rm SL}(2,\mathbb{R})}$$ is given by $$A_{E}(\theta)=\left( \begin{array}{ll}0 \quad \quad \quad 1 -1 \quad {\rm \lambda} f(\theta)-E \\\end{array}\right),\quad E \in \mathbb{R}.$$ More precisely, (ω, A E ) naturally acts on the space $${\mathbb{T} \times \widehat{\mathbb{R}}}$$ , and Φ E is the map thus obtained. The cocycle (ω, A E ) arises when investigating the eigenvalue equation H θ u = Eu, where H θ is the quasi-periodic Schrodinger operator $$(H_\theta u)_n=-(u_{n+1}+u_{n-1}) + {\rm \lambda} f(\theta+(n-1)\omega)u_n,$$ acting on the space $${l^2(\mathbb{Z})}$$ . It is well known that the spectrum of $${H_\theta,\, \sigma(H)}$$ , is independent of the phase $${\theta \in \mathbb{T}}$$ . Under our assumptions on f, ω and λ, Sinai (in J Stat Phys 46(5–6):861–909, 1987) has shown that σ(H) is a Cantor set, and the operator H θ has a pure-point spectrum, with exponentially decaying eigenfunctions, for a.e. $${\theta \in \mathbb{T}}$$ The analysis of Φ E allows us to derive three main results:

Quasiperiodic VLF emissions with short‐period modulation and their relationship to whistlers: A case study

AbstractWe study properties of quasiperiodic (QP) VLF emissions recorded on 24 December 2011 during the VLF campaign in northern Finland. The main attention is paid to interrelationships between different characteristic periods in the QP spectra. In particular, we analyze regular variations in the QP repetition intervals (1–10 min) during the event from 15:30 to 22 UT, their changes during substorms, and short periodic (several second) modulation observed within separate QP elements. We explained the variations of periods of QP emissions in terms of the model of auto‐oscillation regime of the cyclotron instability in the magnetosphere. During the considered event lasting about 7 h we observed a regular increase in the time intervals between the QP elements. We relate this increase with weakening of the magnetospheric source of energetic electrons. Significant variations in the QP period occurred during substorms. These variations can be due to a substorm‐related increase in the energetic‐electron flux and/or due to the precipitation of these electrons into the ionosphere which changes the reflection coefficient of VLF waves. We analyze the fine structure of QP element spectra and reveal the periods related to the time scales of guided propagation of whistler mode waves along the magnetic field line, which suggests that ducted propagation regime took place for the QP emissions. The periods were about 6–9 s for frequencies 1.2–4 kHz, respectively, which was similar to the period of almost simultaneously observed two‐hop whistlers. In the low‐frequency part of QP spectra periodic emissions with shorter periods of about 3 s were observed. Analysis of fine structure of QP elements shows that their formation is affected by both linear effects (i.e., group‐velocity dispersion) and quasi‐linear effects related to the modification of the energetic electron distribution function. It allows us to observe the transition from purely linear to quasi‐linear regime of wave‐particle interactions in the spectra of these short periodic emissions. The nonlinear regime can be understood in terms of passive mode locking in magnetospheric cyclotron maser.

Detection of quasi-periodic processes in repeated measurements: New approach for the fitting and clusterization of different data

Many experimentalists were accustomed to think that any independent measurement forms a non-correlated measurement that depends weakly from others. We are trying to reconsider this conventional point of view and prove that similar measurements form a strongly-correlated sequence of random functions with memory. In other words, successive measurements “remember” each other at least their nearest neighbors. This observation and justification on real data help to fit the wide set of data based on the Prony’s function. The Prony’s decomposition follows from the quasi-periodic (QP) properties of the measured functions and includes the Fourier transform as a partial case. New type of decomposition helps to obtain a specific amplitude–frequency response (AFR) of the measured (random) functions analyzed and each random function contains less number of the fitting parameters in comparison with its number of initial data points. Actually, the calculated AFR can be considered as the generalized Prony’s spectrum (GPS), which will be extremely useful in cases where the simple model pretending on description of the measured data is absent but vital necessity of their quantitative description is remained. These possibilities open a new way for clusterization of the initial data and new information that is contained in these data gives a chance for their detailed analysis. The electron paramagnetic resonance (EPR) measurements realized for empty resonator (pure noise data) and resonator containing a sample (CeO2 in our case) confirmed the existence of the QP processes in reality. But we think that the detection of the QP processes is a common feature of many repeated measurements and this new property of successive measurements can attract an attention of many experimentalists.

The first observation of memory effects in the infrared (FT-IR) measurements: do successive measurements remember each other?

Over the past couple of decades there have been major advances in the field of nanoscience and nanotechnology. Many applications have sprouted from these fields of research. It is essential, given the scale of the materials, to attain accurate, valid and reproducible measurements. Material properties have shown to be a function of their size and composition. Physiochemical properties of the nanomaterials can significantly alter material behavior compared to bulk counterparts. For example, metal oxide nanoparticles have found broad applications ranging from photo-catalysis to antibacterial agents. In our study, we synthesized CuO nanoparticles using well established sol-gel based methods with varying levels of Ni doping. However, upon analysis of measured infrared data, we discovered the presence of quasi-periodic (QP) processes. Such processes have previously been reported to be tightly associated with measurement memory effects. We were able to detect the desired QP process in these measurements from three highly accurate repetitive experiments performed on each Ni (1–7%) doped CuO sample. In other words, successive measurements performed in a rather short period of time remember each other at least inside a group of neighboring measurements.