Quasi-periodic Mode Research Articles

Electromagnetic fields transformation in UWB infinite antenna arrays in the cluster excitation mode

Infinite ultra-wideband (UWB) arrays of TEM horns and Vivaldi antennas were considered. At the first stage we used an array model in the quasi-periodic excitation mode in the form of a Floquet channel. It was implemented in the HFSS electromagnetic modeling system. At the second stage the array parameters in the cluster excitation mode were determined using the calculated scattering matrix of the Floquet channel. Two clusters of TEM horns and Vivaldi antennas were analyzed. They were finite along one coordinate and infinite along the other. It was investigated how the cluster size, frequency, amplitude distribution of exciting waves, scanning in the sector of angles affect the shape of the amplitude-phase distribution of the field in the array aperture. It was shown that the field distribution in the emitting aperture may differ significantly from the distribution of exciting waves at the inputs of the array elements. An explanation of this effect based on the representation of the field in the array in the form of a superposition of its eigen waves was proposed.

A phase-resolvedFermi-LAT analysis of the mode-changing pulsar PSR J2021+4026 shows hints of a multipolar magnetosphere

Context.The radio-quietγ-ray pulsar PSR J2021+4026 is a peculiarFermi-LAT pulsar showing repeated and quasi-periodic mode changes. Itsγ-ray flux shows repeated variations between two states at intervals of ∼3.5 years. These events occur over timescales < 100 days and are correlated with sudden changes in the spin-down rate. Multiwavelength observations also revealed an X-ray phase shift relative to theγ-ray profile for one of the events. PSR J2021+4026 is currently the only known isolatedγ-ray pulsar showing significant variability, and thus it has been the object of thorough investigations.Aims.The goal of our work is to study the mode changes of PSR J2021+4026 with improved detail. By accurately characterizing variations in theγ-ray spectrum and pulse profile, we aim to relate theFermi-LAT observations to theoretical models. We also aim to interpret the mode changes in terms of variations in the structure of a multipolar dissipative magnetosphere.Methods.We continually monitored the rotational evolution and theγ-ray flux of PSR J2021+4026 using more than 13 years ofFermi-LAT data with a binned likelihood approach. We investigated the features of the phase-resolved spectrum and pulse profile, and from these we inferred the macroscopic conductivity, the electric field parallel to the magnetic field, and the curvature radiation cutoff energy. These physical quantities are related to the spin-down rate and theγ-ray flux and therefore are relevant to the theoretical interpretation of the mode changes. We introduced a simple magnetosphere model that combines a dipole field with a strong quadrupole component. We simulated magnetic field configurations to determine the positions of the polar caps for different sets of parameters.Results.We clearly detect the previous mode changes and confirm a more recent mode change that occurred around June 2020. We provide a full set of best-fit parameters for the phase-resolvedγ-ray spectrum and the pulse profile obtained in five distinct time intervals. We computed the relative variations in the best-fit parameters, finding typical flux changes between 13% and 20%. Correlations appear between theγ-ray flux and the spectral parameters, as the peak of the spectrum shifts by ∼10% toward lower energies when the flux decreases. The analysis of the pulse profile reveals that the pulsed fraction of the light curve is larger when the flux is low. Finally, the magnetosphere simulations show that some configurations could explain the observed multiwavelength variability. However, self-consistent models are required to reproduce the observed magnitudes of the mode changes.

Mode transition of a film fluttering in a circular cylinder wake

As a representative model in the investigation into fluid–structure coupling, a flexible film interacting with the wake of a circular cylinder involves intricate patterns of both solid motion and fluid evolution. Recent investigations have found that the interactions could be either periodic or aperiodic in experiments; the latter, however, is often overlooked. In this work, the irregular aperiodic flutter of a flexible film behind a circular cylinder is investigated experimentally. It is determined that the irregular flutter intermittently exhibits transient quasi-periodic mode and aperiodic mode. The former is accompanied by the large-scale vortices alternatively formed against the film surfaces, while the latter is associated with vortices formed downstream of the film's trailing edge, so that the whole film is enveloped by the extended shear layers. In order to separate the data individually pertaining to each of the two modes from the whole dataset, a motion-mode recognition method is proposed, and then conditional statistics of flow fields are achieved. The quasi-periodic mode corresponds to more intense velocity fluctuations in the wake, while in the aperiodic mode, the observed localized instability of shear layers induces an increase in the local streamwise velocity fluctuation.

A study of controlling the transverse vibration of a beam-plate system by utilizing a nonlinear coupling oscillator

In the engineering field, prolonged exposure of complex structures to high-strength vibration environments can lead to various engineering challenges. This underscores the importance of effectively managing the vibration of complex structures. Given the extensive utilization of beams and plates in the construction of intricate structures, this study incorporates a nonlinear coupling oscillator into the beam-plate system and formulates a vibration analysis model for this system. The governing equations of the system are derived theoretically and solved numerically using the Galerkin truncation method. This study focuses on the operational modes of the nonlinear coupling oscillator based on accurate numerical results. Meanwhile, the influence of parameters belonging to the nonlinear coupling oscillator on the transverse vibration responses of the beam-plate system is systemically studied. Upon meticulous examination of the numerical results, the operational states of the nonlinear coupling oscillator encompass the normal vibration suppression mode and the quasi-periodic vibration suppression mode. The alteration in the linear elastic coupling stiffness of the beam-plate system impacts the effectiveness of vibration suppression in the nonlinear coupling oscillator. This influence stems from the fact that changes in the linear elastic coupling stiffness directly affect the nonlinear forces exerted on the beam-plate system within a nonlinear coupling oscillator. Within a feasible range, the nonlinear stiffness and viscous damping can be chosen as the adjustable parameters for the nonlinear coupling oscillator to regulate the vibration of the beam-plate system by adjusting the motion mass of the nonlinear coupling oscillator, which presents a challenge. The appropriate utilization of the nonlinear coupling oscillator demonstrates favorable control effectiveness in managing the transverse vibration of the beam-plate system. The study presented in this work offers a method to simultaneously control the vibration of each component within beam-plate coupling systems.

Numerical Analysis of a Drop-Shaped Aquatic Robot

Finite-dimensional equations constructed earlier to describe the motion of an aquatic drop-shaped robot due to given rotor oscillations are studied. To study the equations of motion, we use the Poincaré map method, estimates of the Lyapunov exponents, and the parameter continuation method to explore the evolution of asymptotically stable solutions. It is shown that, in addition to the so-called main periodic solution of the equations of motion for which the robot moves in a circle in a natural way, an additional asymptotically stable periodic solution can arise under the influence of highly asymmetric impulsive control. This solution corresponds to the robot’s sideways motion near the circle. It is shown that this additional periodic solution can lose stability according to the Neimark–Sacker scenario, and an attracting torus appears in its vicinity. Thus, a quasiperiodic mode of motion can exist in the phase space of the system. It is shown that quasiperiodic solutions of the equations of motion also correspond to the quasiperiodic motion of the robot in a bounded region along a trajectory of a rather complex shape. Also, strange attractors were found that correspond to the drifting motion of the robot. These modes of motion were found for the first time in the dynamics of the drop-shaped robot.

Dynamics and stability of the wake behind a circular cylinder in the vicinity of a plane moving wall

This paper identifies and characterizes modes of the three-dimensional instability of the flow over a circular cylinder of diameter D near a plane moving wall with a gap height of G=0.1D beyond the onset of vortex shedding through the Floquet stability analysis. The associated effects of the transitions on the hydrodynamic forces of the cylinder are examined by performing direct numerical simulations. Six distinct three-dimensional modes are identified and their characteristics are discussed in detail. It is found that the physical mechanism responsible for the synchronous mode 1 appears to be associated to an elliptic instability. The quasi-periodic mode 4 is observed to transform to a synchronous mode (mode 6) on increasing the Reynolds number, indicating that they are likely to be resulted from the same physical mechanism. For mode 6, its physical nature seems to be a hyperbolic instability. Fully three-dimensional simulations show that the wake undergoes a rapid transition to complex chaotic flow state after the most dominant mode starts to saturate, due to the strongly nonlinear interactions of many modes with different spanwise wavelengths.

STREAMER MODE OF POSITIVE CORONA

One cycle of quasi-periodic streamer mode of positive corona at constant voltage is considered. The calculation results for the streamer propagation at a voltage near to threshold of the streamer mode and for the stage of partial release of the gap from the ions are presented. The simplified model of ionization development near the anode before the start of the next streamer is considered and it is estimated the ionized space size, from which the streamer propagation begins.

Nonlinear parametric vibration of spinning pipes conveying fluid with varying spinning speed and flow velocity

In this paper, a nonlinear parameter-excited model of spinning pipes conveying fluid is proposed by considering the spinning speed and flow velocity are perturbed periodically, and the stability and nonlinear parametric vibrations of such system are studied analytically and numerically. With taking the viscoelastic material and geometrical nonlinearity due to extensible pipe axis into account, the differential equations governing two transverse vibrations of the pipe are derived by the Hamilton principle. The system stability is then analyzed via the multiple scales method, and the nonlinear responses and spatial vibration shapes are investigated using numerical simulation. The contributions of some significant parameters on the vibrations of the system are discussed in detail. It is revealed that not any other motion but combination parametric resonance with quasi-periodic motion mode can occur in the present system, and it is induced fully by the periodically perturbed fluid. A perturbed spinning motion cannot result in any parametric resonance, however it has an opposite effect on the parametric vibrations as compared to that with constant spinning speed. The flow velocity, nonlinearity and viscoelastic damping all have significant impacts on the present parametric vibrations. Moreover, the pipe performs different aperiodic whirling motions in the first two modes, and the perturbed spinning speed will lead to a gentler motion of the pipe as compared to the case of constant spinning speed.

Double Functionality Concurrent Dual-Band Self-Oscillating Mixer

A concurrent dual-band self-oscillating mixer (SOM), based on a ring-shaped stepped-impedance resonator, is proposed and analyzed in detail. Taking advantage of the ring even and odd resonances, the circuit can operate in concurrent dual quasi-periodic mode and injection-locked mode. In the second case, it behaves as a dual-band zero-intermediate-frequency (IF) mixer. Initially, an analytical study of the SOM behavior in the two modes is presented. Then a variety of accurate numerical methods are used for an in-depth investigation of the main aspects of its performance, including stability, conversion gain, linearity, and phase noise. The recently proposed contour-intersection technique and the outer-tier perturbation analysis are suitably adapted to the SOM case. A method is also presented to distinguish the parameter intervals leading to heterodyne and to zero-IF operation at both the lower and upper frequency bands. In the zero-IF SOM, the possible instantaneous unlocking in the presence of modulated input signals is investigated and avoided. The methods have been applied to a dual mixer at the frequencies 2.4 and 4.1 GHz.

Transition to chaos in the wake of a circular cylinder near a moving wall at low Reynolds numbers

Floquet stability analysis has been employed to identify modes of three-dimensional (3D) instability in the flow over a circular cylinder of diameter D above a moving wall at a gap height of G = 0.2D, beyond the onset of two-dimensional vortex shedding. Two subharmonic modes (mode C1 and mode C2) and one long-wavelength quasi-periodic mode (mode QPL) are revealed. The characteristics of these 3D modes are discussed in detail. The results of 3D direct simulations show that it is the intensively nonlinear modal interactions that lead to a chaotic final flow state at higher Reynolds numbers, rather than the interference of the shear layer caused by the no-slip moving wall.

The overarching framework of core-collapse supernova explosions as revealed by 3D fornax simulations

ABSTRACT We have conducted 19 state-of-the-art 3D core-collapse supernova simulations spanning a broad range of progenitor masses. This is the largest collection of sophisticated 3D supernova simulations ever performed. We have found that while the majority of these models explode, not all do, and that even models in the middle of the available progenitor mass range may be less explodable. This does not mean that those models for which we did not witness explosion would not explode in Nature, but that they are less prone to explosion than others. One consequence is that the ‘compactness’ measure is not a metric for explodability. We find that lower-mass massive star progenitors likely experience lower-energy explosions, while the higher-mass massive stars likely experience higher-energy explosions. Moreover, most 3D explosions have a dominant dipole morphology, have a pinched, wasp-waist structure, and experience simultaneous accretion and explosion. We reproduce the general range of residual neutron-star masses inferred for the galactic neutron-star population. The most massive progenitor models, however, in particular vis à vis explosion energy, need to be continued for longer physical times to asymptote to their final states. We find that while the majority of the inner ejecta have Ye = 0.5, there is a substantial proton-rich tail. This result has important implications for the nucleosynthetic yields as a function of progenitor. Finally, we find that the non-exploding models eventually evolve into compact inner configurations that experience a quasi-periodic spiral SASI mode. We otherwise see little evidence of the SASI in the exploding models.

Transition to chaos in a cross-corrugated channel at low Reynolds numbers

The pressure-gradient driven flow in a three-dimensional cross-corrugated channel is investigated based on large eddy simulations. The channel geometry is highly tortuous so that the flow unsteadiness can be triggered at a moderate Reynolds number. The objective of this paper is to provide a better understanding of the laminar-to-chaotic transition in this type of channel. The transition from steady to chaos is found to occur at a low Reynolds number range between 77.4 and 113.1. The nonlinear dynamics is analyzed based on the power spectra of the velocity and reconstructed phase space. The route to chaos is identified, which favors the Ruelle-Takens-Newhouse scenario. Moreover, the transition from quasiperiodic mode to chaotic mode is accompanied with temporal intermittencies. The fluid dynamics is analyzed. It is found that the cross-corrugated geometry prompts a recirculating-and-rotating wake behind each contact corner. Each wake is enfolded by a pair of curved free shear layers. They are destabilized by the Kelvin-Helmholtz instability, leading to the periodic flow oscillation. Subsequently, the centrifugal instability sets in and promotes a type of primary vortex structures, forming streamwise “zig-zag” vortex streets. The competition between the adjacent vortex streets leads to a quasiperiodic flow. Temporal intermittencies emerge as the Reynolds number is increased. Finally, the periodicities in both the streamwise and spanwise directions are broken, and the flow becomes chaotic. When further increasing the Reynolds number to 343.1, Taylor-Görtler-like vortexes and necklace-like vortexes are formed in the channel.

Is the Madden–Julian Oscillation reliably detectable in Schumann Resonances?

The Madden–Julian Oscillation (MJO) is a quasi-periodic (∼30–90 days) eastward-moving atmospheric mode which primarily modifies rainfall patterns in the equatorial regions from Africa to the Pacific Ocean. It has been proposed that its signature is detectable within the intensity variations of the Schumann Resonances (SR) due to changes in the location and magnitude of the major lightning centres. Using six years of induction coil data recorded at the Eskdalemuir Observatory in the UK, we investigate whether the MJO is detectable in the first three Schumann Resonances. We extract the frequency and intensity values from each resonance every 10 min, averaged to a daily value and compare them to the Realtime Multivariate MJO (RMM) index. We use Empirical Mode Decomposition (EMD) to determine if certain modes correlate between the SR and RMM curves. We find that the EMD 30–70 day modes of the SR and RMM index occasionally beat in-phase during the La Niña periods of the El Niño Southern Oscillation (ENSO) but not El Niño periods. However, the relationship is not wholly consistent, implying that robust and reliable detection of the MJO in SR data remains challenging.

Nonlinear mode transition mechanisms of a self-excited Jet A-1 spray flame

Low-frequency combustion instabilities arise in an aero-engine gas turbine combustor under idle/sub-idle conditions, particularly when pilot-mode non-premixed combustion is sustained. Despite the fundamental importance of such instabilities, little is known about how they are initiated and grow in the system. Here, we present nonlinear mode transition processes using several analysis methods, including Fourier/Hilbert transforms, phase portraits, spectrograms, low-order analytic modeling, and high-speed flame visualization methods. Our results demonstrate that a non-premixed Jet A-1 spray flame yields an intermediate-amplitude, quasi-periodic L1 mode oscillation at 50 Hz for a low pilot equivalence ratio, and the frequency gradually increases with increasing fuel flowrates. Subsequent to a critical point (103 Hz), the system undergoes a discontinuous mode transition, giving rise to the formation of an extremely large pressure oscillation with an L2 mode structure at 244 Hz. Several key triggers were found to induce the mode shift: (i) generation of a high intensity pulse in the flame's heat release rate due to the spontaneous ignition of unburned reactant mixtures, (ii) emergence of a large-scale vortical structure and its interaction with a partially premixed flame front, and (iii) development of self-sustained limit cycle oscillations driven by periodic convection of a hot spot – a mechanism known as entropy wave propagation. Our study identifies the occurrence of a large-amplitude peak followed by a local minimum intensity, analogous to the activation energy concept, as an essential step for entry into a new state with large-amplitude limit cycle oscillations.

Numerico–Analytical Model of a Non-Planar Array of Horns

A non-planar array of strip horns is considered. A model of this structure is constructed in the form of a Floquet channel with smoothly varying parameters. The Floquet channel of an infinite array of coupled striplines is chosen as a reference waveguide. The scattering matrix of the Floquet channel in the quasi-periodic mode is found in the approximation of the theory of microwave transmission lines. Expressions are obtained for the elements of the scattering matrix in the mode of excitation of a single channel of a non-planar array. In this mode, the directional pattern of the radiation of the array into a planar waveguide is studied.

Patterns of variability in supercritical hadronic systems

A unique and often overlooked property of a source loaded with relativistic protons is that it can become supercritical, i.e. it can undergo an abrupt transition from a radiatively inefficient to a radiatively efficient state once its proton energy density exceeds a certain threshold. In this paper, we investigate the temporal variability of hadronic systems in this hardly explored regime. We show that there exists a range of proton densities that prevent the system from reaching a steady state, but drive it instead in a quasi-periodic mode. The escaping radiation then exhibits limit cycles, even if all physical parameters are held constant in time. We extend our analysis to cases where the proton injection rate varies with time and explore the variability patterns of escaping radiation as the system moves in and out from the supercritical regime. We examine the relevance of our results to the variability of the prompt gamma-ray burst emission and show that, at least on a phenomenological level, some interesting analogies exist.

Vibration influence on the onset of the longwave Marangoni instability in two-layer system

We study the longwave Marangoni convection in two-layer films under the influence of a low frequency vibration. A linear stability analysis is performed by means of the Floquet theory. A competition of subharmonic, synchronous, and quasiperiodic modes is considered. It has been found that the monotonic instability, which exists at constant gravity, is transformed into a synchronous instability, which is critical in a wide range of vibration amplitude. At parameters where oscillatory instability exists, the longwave quasiperiodic mode remains critical until a subharmonic mode becomes critical with the growth of the vibration amplitude.

Impact of Windings Configuration of Three-Phases Power Distribution Transformer on Ferroresonance

This paper dealt with the impact of ferroresonance on four common windings configurations of three-phases power distribution transformer, that were wye-wye (Y-Y), wye-delta (Y-∆), delta-delta (∆-∆), and delta-wye (∆-Y). The ferroresonance was initiated by the occurrence of open-phase faults of transformer primary windings, such as opened single-phase and opened two-phases (unbalanced system) as well as opened three-phases. The investigation of ferroresonance was based on simulation using ATPDraw. The results showed that the transformer windings configuration affected the ferroresonance responses. Subharmonic and quasi-periodic mode appeared on all configurations, whereas fundamental mode was only seen on Y-∆ configuration. The worst overvoltage on primary windings during opened single-phase and opened two-phases was observed on Y-Y configuration, that was about 554 % and 223 % at the R phase, respectively, while the worst overvoltage on primary windings during three-phases opened was obtained on Y-∆ configuration, that was about 150 % at the T phase. However, the primary three-phases voltage on Y-∆ configuration during opened single-phase and two-phases was generally the lowest compared to the other configurations. These results also revealed that Y-Y configuration was the most susceptible to overvoltage due to ferroresonance. On the other hand, Y-∆ configuration was the most robust to overvoltage due to ferroresonance.

Three-dimensional instabilities for the flow around a heaving foil.

This paper investigates the three-dimensional instabilities of the flow past a periodically heaving airfoil. By comparison with a pitching foil [Deng et al., Phys. Rev. E 92, 063013 (2015)PLEEE81539-375510.1103/PhysRevE.92.063013], here we present distinctive characteristics for the heaving foil, particulary regarding its Floquet modes. By increasing the frequency (Sr), or equivalently decreasing the amplitude (A_{D}) along the marginal stability curve in the (Sr,A_{D}) phase space, the critical Floquet mode emerges sequentially as A, quasiperiodic (QP), and B. It is interesting to note that both modes A and B are synchronous with the base flow, in contrast to the quasiperiodic mode QP. To further investigate the instability across the marginal curve, we fix the frequency at Sr=0.187, of which the critical Floquet mode is located in the synchronous regime, while varying A_{D} around the critical point. We find that the dominant mode switches from mode A to mode B, while mode QP never becomes critical as we increase A_{D}. We note that mode S, a subharmonic mode, can also be unstable, which, however, is not physically realizable, because the magnitude of its Floquet multiplier is always smaller than that of mode B. We have also studied the influence of various Reynolds numbers at the same critical point on the marginal stability curve, with the results resembling that by varying the amplitude A_{D}.

Blinding and Depolarization Effects in Vivaldi Antenna Arrays

The blinding and depolarization effects in a two-dimensional unipolarization Vivaldi antennas array are studied numerically. By the numerical electrodynamic simulation, it is shown that, in the quasiperiodic mode, the reflection coefficient in such an array has narrow-band peaks, which lead to a dramatic reduction in the transmission coefficient to free space. It is established that, when scanning beyond the main planes in a frequency band, significant changes in the polarization characteristics, which can change the polarization of the radiation field, are observed. An approximate model describing the electromagnetic processes in the array as an interaction of the eigenwaves of a system of coupled slot transmission lines is proposed. It is shown that the model proposed makes it possible to describe qualitatively and, in some cases, quantitatively the blinding and depolarization effects.