Quasi-periodic Modes Research Articles

Experimental investigation on the mode transition characteristics of a phase-change thermofluidic oscillator with external loads

Phase-change thermofluidic oscillator has drawn significant attention thanks to its low operating temperature, which is beneficial for recovering low-grade heat. The vapor–liquid coupling oscillation in the thermofluidic oscillator leads to complex non-linear mode transition phenomenon that affects the steady operation. In this work, the mode transition characteristics of a thermofluidic oscillator with external loads (i.e., a needle valve and a load reservoir) are experimentally investigated through bifurcation analysis. A low-order van der Pol model is employed to examine the effect of acoustic resistance on mode transition. Experimental results demonstrate that modifying the valve opening and load volume under a constant temperature difference can trigger bifurcation, resulting in high-frequency limit cycle, low-frequency limit cycle and quasi-periodic modes. The non-linear features of each mode are revealed through phase space and Poincaré section, with Neimark-Sacker bifurcation, second bifurcation and inverse Neimark-Sacker bifurcation observed. Steady-state performance of oscillator is then characterized under different oscillation modes. The maximum pressure amplitudes measured are 11.54 kPa during the high-frequency oscillation and 1.35 kPa during the low-frequency oscillation, while the maximum displacement amplitudes obtained are 45.5 mm during the high-frequency oscillation and 91.4 mm during the low-frequency oscillation. The oscillation modes can be adjusted by external load to maximize output performance. This study offers comprehensive guidelines for constructing phase-change thermofluidic oscillators.

Identifying quasi-periodic variability using multivariate empirical mode decomposition: a case of the tropical Pacific

Abstract. A variety of statistical tools have been used in climate science to gain a better understanding of the climate system's variability on various temporal and spatial scales. However, these tools are mostly linear, stationary, or both. In this study, we use a recently developed nonlinear and nonstationary multivariate time series analysis tool – multivariate empirical mode decomposition (MEMD). MEMD is a powerful tool for objectively identifying (intrinsic) timescales of variability within a given spatio-temporal system without any timescale pre-selection. Additionally, a red noise significance test is developed to robustly extract quasi-periodic modes of variability. We apply these tools to reanalysis and observational data of the tropical Pacific. This reveals a quasi-periodic variability in the tropical Pacific on timescales ∼ 1.5–4.5 years, which is consistent with El Niño–Southern Oscillation (ENSO) – one of the most prominent quasi-periodic modes of variability in the Earth’s climate system. The approach successfully confirms the well-known out-of-phase relationship of the tropical Pacific mean thermocline depth with sea surface temperature in the eastern tropical Pacific (recharge–discharge process). Furthermore, we find a co-variability between zonal wind stress in the western tropical Pacific and the tropical Pacific mean thermocline depth, which only occurs on the quasi-periodic timescale. MEMD coupled with a red noise test can therefore successfully extract (nonstationary) quasi-periodic variability from the spatio-temporal data and could be used in the future for identifying potential (new) relationships between different variables in the climate system.

Teleconnections link to summer heat extremes in the south-central U.S.: Insights from CMIP5 and CMIP6 simulations

This study examines the relationship between teleconnections, which represent quasiperiodic modes of large-scale atmospheric and oceanic variability, and extreme heatwaves in the south-central (SC) U.S. region, aiming to understand multiyear variability in the heat extremes. Observational data and model simulations reveal that soil water has a stronger influence on surface air temperature in the SC region than individual teleconnections, though not as strong as their combined influence. Particularly, the Pacific North America (PNA), North Atlantic Oscillation (NAO), and Pacific Decadal Oscillation (PDO) teleconnections have a substantial impact on surface air temperature in the region through anomalous anticyclonic circulation, during their negative phases. The wave-activity flux analysis shows that the wave train associated with the PNA teleconnection originates from the extratropical North Pacific Ocean, likely influenced by sea surface temperature (SST) forcing. Similarly, the wave packet linked to the PDO pattern originates from the central Pacific Ocean in the middle latitudes. In contrast, the wave train related to the NAO pattern exhibits little connection to SST forcing, originating from Greenland and propagating across Europe, Russia, the North Pacific, and North America. While climate models generally capture the PNA and PDO wave trains, they struggle to accurately simulate the NAO wave train across the North Pacific Ocean towards North America. This indicates the current generation of climate models face challenges in representing the complex dynamics underlying the NAO wave train.

Spatially quasi-periodic water waves of finite depth

We present a numerical study of spatially quasi-periodic gravity-capillary waves of finite depth in both the initial value problem and travelling wave settings. We adopt a quasi-periodic conformal mapping formulation of the Euler equations, where one-dimensional quasi-periodic functions are represented by periodic functions on a higher-dimensional torus. We compute the time evolution of free surface waves in the presence of a background flow and a quasi-periodic bottom boundary and observe the formation of quasi-periodic patterns on the free surface. Two types of quasi-periodic travelling waves are computed: small-amplitude waves bifurcating from the zero-amplitude solution and larger-amplitude waves bifurcating from finite-amplitude periodic travelling waves. We derive weakly nonlinear approximations of the first type and investigate the associated small-divisor problem. We find that waves of the second type exhibit striking nonlinear behaviour, e.g. the peaks and troughs are shifted non-periodically from the corresponding periodic waves due to the activation of quasi-periodic modes.

Close relative motion on distant retrograde orbits

Distant Retrograde Orbits (DROs) in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions. Thus, the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO missions. However, as the reference DROs are obtained through numerical methods, the close relative motions on DROs are non-analytical, which severely limits the design of relative trajectories. In this paper, a novel approach is proposed to construct the analytical solution of bounded close relative motion on DROs. The linear dynamics of relative motion on DRO is established at first. The preliminary forms of the general solutions are obtained based on the Floquet theory. And the general solutions are classified as different modes depending on their periodic components. A new parameterization is applied to each mode, which allows us to explore the geometries of quasi-periodic modes in detail. In each mode, the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier series. In this way, the analytical bounded relative motion on DRO is obtained. Based on the analytical expression, the characteristics of different modes are comprehensively analyzed. The natural periodic mode is always located on the single side of the target spacecraft on DRO and is appropriate to be the parking orbits of the rendezvous and docking. On the basis of quasi-periodic modes, quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per period. The fly-around formation can support observations to targets on DRO from multiple viewing angles. And the fly-around formation is validated in a more practical ephemeris model.

Bloch waves in high contrast electromagnetic crystals

Analytic representation formulas and power series are developed describing the band structure inside non-magnetic periodic photonic three-dimensional crystals made from high dielectric contrast inclusions. Central to this approach is the identification and utilization of a resonance spectrum for quasiperiodic source-free modes. These modes are used to represent solution operators associated with electromagnetic and acoustic waves inside periodic high contrast media. A convergent power series for the Bloch wave spectrum is recovered from the representation formulas. Explicit conditions on the contrast are found that provide lower bounds on the convergence radius. These conditions are sufficient for the separation of spectral branches of the dispersion relation for any fixed quasi-momentum.

Vortex shedding modes of a vibrating cylinder colliding with a rigid wall

We have conducted two-dimensional computations of vortex-induced vibration of an elastically mounted circular cylinder colliding with a rigid wall at a Reynolds number of 300. For wide ranges of reduced velocities, we have identified C (chaotic), P (periodic), and QP (quasi-periodic) vortex shedding modes at two gap and mass ratios. The deflected gap flow induced by the wall shear layer during the descending motion of the cylinder cause stretching of the vortex strands, while both the P and QP modes show the “S”-type shedding signature. The pathlines for the C-mode yield unstable hyperbolic behavior, whereas twisted knots and spirals are seen for the P-mode. Criss-cross interactions with the swirling pathlines are observed in the QP-mode.

Nonlinear Forced Vibrations of Plates with Oscillating Inclusions

These studies focus on the forced vibrations of rectangular plates incorporating oscillating inclusions uniformly distributed in the carrier elastic medium. Plate’s equations of motion consist of the Lamé equation for a carrier material and the equation for oscillators representing the inclusions. The oscillators are acted upon by the nonlinear friction force, described by Coulomb’s modified law, and a cubically nonlinear elastic force. The simply supported forced plate is considered. Using the Galerkin approximation, the problem of plate vibrations is reduced to the study of a system of ODEs. According to numerical and qualitative analyses, the application of harmonic forcing causes the appearance of periodic, quasiperiodic, and chaotic regimes in the system. In particular, the analytical expression is derived for the periodic regimes of the forcing frequency. The scenarios of vibration’s development is identified at the variation of forcing amplitude. The quasiperiodic and chaotic modes are studied by means of Poincaré section technique, and Fourier and Lyapunov spectra analyses. The statistical properties of the sequences of temporal intervals between maxima of system’s solutions are considered in more detail. The sequence extracted from the chaotic trajectory is shown to possess long-term correlations and approximately obeys the Weibull distribution.

Anishchenko-Astakhov quasiperiodic generator excited by external harmonic force

A harmonic effect on a modified Anishchenko-Astakhov generator capable of demonstrating two-frequency quasi-periodic oscillations in the autonomous mode is considered. The possibility of doubling the three-frequency tori in a non-autonomous system is shown. The possibility of the effect of chaos suppression by an external signal is demonstrated, which leads not only to periodic, but also to quasi-periodic modes when the influence amplitude exceeds a certain threshold. Keywords: torus doublings, suppression of chaos, quasiperiodic generator

Воздействие гармонического сигнала на генератор квазипериодических колебаний Анищенко-Астахова

A harmonic effect on a modified Anishchenko-Astakhov generator capable of demonstrating two-frequency quasi-periodic oscillations in the autonomous mode is considered. The possibility of doubling the three-frequency tori in a non-autonomous system is shown. The possibility of the effect of chaos suppression by an external signal is demonstrated, which leads not only to periodic, but also to quasi-periodic modes when the influence amplitude exceeds a certain threshold.

Ecological and Genetic Models in Population Biophysics

Complex causal relationships occur between population dynamics and a change in a population genetic structure. In our study, a simple model was used to show that the evolutionary process of density-independent natural selection depending on the fitnesses determined by a single diallelic locus can lead to a change in population growth parameters, thus changing the dynamic modes in a population. Possible mechanisms and direction of these changes are discussed. The results clearly demonstrate that the evolutionary change in allele frequencies, accompanied by an increase in the average fitness of the population, may result in the occurrence of cyclic, quasiperiodic, and chaotic modes of population dynamics. The effects observed in our models are largely due to the simple combination (superposition) of the two models: natural selection leads to an evolutionary increase in fitness, and density regulation with an increase in reproductive potential leads to bifurcations that provide various fluctuations in population abundance. However, these fluctuations occur (and manifest themselves) in the course of genetic evolution. At the same time, the combination of models leads to the occurrence of new dynamic modes that are not observed in each of the models separately (i.e., fluctuations in gene frequencies associated with the multimodality of the considered systems and the emergence of new stable attractors).

Side-mode suppression in ultraviolet quasi-semicircle microlaser cavity

We report a quasi-semicircle GaN ultraviolet microcavity laser. Poincaré map of the quasi-semicircle cavity shows periodic, quasi-periodic and chaotic optical trajectories. Finite-element-method optical near-field distribution patterns of the periodic optical modes agree with the optical loops in the quasi-semicircle cavity. Based on the numerical results, optically pumped lasing experiment shows that ultraviolet multimode lasing action from different optical resonance modes can be effectively stimulated at low pumping intensity in the quasi-semicircle GaN cavity, and the side-mode suppression phenomenon can be obtained at high pumping intensity. Because the possible period optical loops are quasi-periodic and unstable, the quasi-whispering-gallery mode lasing with higher quality factor prefer to dominate the lasing action under high pumping. The experimental and simulated lasing modes suggest that side-mode suppression phenomenon can be caused by the mode competition between quasi-whispering-gallery modes and other quasi-periodic modes.

Near and far field laminar flow structures in an axisymmetric zero-net-mass-flux jet

Numerical simulations have been performed to study the near and far fields of an axisymmetric zero-net-mass flux (ZNMF) jet in the laminar-transitional regime, before the three-dimensional vortex breakdown that promotes transition to turbulence. The main frequencies driving the flow and their associated spatial modes have been calculated using the iterative, multidimensional higher order dynamic mode decomposition algorithm. The results show that the flow is periodic in the near field, but it is quasi-periodic in the far field, where two additional high frequency traveling modes appear. One of them is localized downstream a saddle point (a topology pattern characteristic of the suction phase defining the jet flow oscillations) and seems to be responsible for a shear layer instability. The second high frequency traveling mode, instead, extends further downstream and is associated with the overall wake of the ZNMF jet, which behaves in this sense as continuous jet. Evidence of non-linear coupling between the different spatio-temporal modes is presented in this work, which suggests the existence of a mechanism of energy transition between the periodic modes in the near field and the quasi-periodic modes in the far field previous to transition.

Terahertz emission from a weakly-coupled GaAs/AlGaAs superlattice biased into three different modes of current self-oscillations

Radio-frequency modulated terahertz (THz) emission power from weakly-coupled GaAs/AlGaAs superlattice (SL) has been increased by parallel connection of several SL mesas. Each SL mesa is a self-oscillator with its own oscillation frequency and mode. In coupled non-identical SL mesas biased at different voltages within the hysteresis loop the chaotic, quasiperiodic and frequency-locked modes of self-oscillations of current arise. THz emission was detected when three connected in parallel SL mesas were biased into the frequency-locked and quasiperiodic modes of self-oscillations of current, while in the chaotic mode of those it falls to the noise level.

Nonlinear power-dependent effects in exchange-coupled magnetic bilayers

We investigate the dynamics of exchange-coupled ferromagnetic films in the nonlinear limit and find a number of interesting features. The introduction of asymmetries in the magnetic driving field can produce a power-dependent localization of the magnetization oscillations, in one film or the other, by way of the optic mode frequency shifting in the large field limit. A nonlinear mixing of the acoustic and optic modes in the antiferromagnetically coupled system leads to quasiperiodic and multiperiodic composite modes. Numerical ferromagnetic resonance experiments will show additional absorption peaks (in the 20--50 GHz range) which have a rapid increase in strength with input power. The results are calculated through linearization techniques and numerical solutions of the Landau-Lifshitz-Gilbert equation. The nonlinear (and linear) behavior is illustrated through Poincar\'e section bifurcation diagrams.

Tracking microparticle motions in three-dimensional flow around a microcubic array fabricated on the wall surface

This paper describes the application of a microscopic defocusing image system to track 3D particle motions in microflow around a microcubic array near a microchannel wall surface. The measurement principle and calibration method were evaluated to provide accurate 3D microparticle location. Particle trajectories were measured in two microchannels. Measured velocity profiles of Hele–Shaw flows for two Reynolds numbers agreed well with theoretical profiles. Three-dimensional particle tracking in fluid flow around a microcubic array exhibited quasi-periodic and non-periodic trajectory modes. The experimental results indicated that 3D particle motions are spatially and time dependent even when the flow rate is constant, and microparticle trajectories may deviate from steady flow streamlines.

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.

Bloch waves in crystals and periodic high contrast media

Analytic representation formulas and power series are developed describing the band structure inside periodic photonic and acoustic crystals made from high contrast inclusions. Central to this approach is the identification and utilization of a resonance spectrum for quasi-periodic source free modes. These modes are used to represent solution operators associated with electromagnetic and acoustic waves inside periodic high contrast media. Convergent power series for the Bloch wave spectrum is recovered from the representation formulas. Explicit conditions on the contrast are found that provide lower bounds on the convergence radius. These conditions are sufficient for the separation of spectral branches of the dispersion relation.

Multi-frequency tori in wide-aperture lasers

A distributed model of wide-aperture laser based on Maxwell−Bloch equations in onedimensional approximation is considered. It is shown that an increase in the pumping parameter in the system gives rise to a cascade of bifurcations of periodic and quasi-periodic dynamic modes, as a result of which attractors in the form of three-frequency tori can be observed.

Climatic and geologic controls on the piezometry of the Querença-Silves karst aquifer, Algarve (Portugal)

Karst aquifers in semi-arid regions, like Querenca-Silves (Portugal), are particularly vulnerable to climate variability. For the first time in this region, the temporal structure of a groundwater-level time series (1985–2010) was explored using the continuous wavelet transform. The investigation focused on a set of four piezometers, two at each side of the S. Marcos-Quarteira fault, to demonstrate how each of the two sectors of the aquifer respond to climate-induced patterns. Singular spectral analysis applied to an extended set of piezometers enabled identification of several quasi-periodic modes of variability, with periods of 6.5, 4.3, 3.2 and 2.6 years, which can be explained by low-frequency climate patterns. The geologic forcing accounts for ~15 % of the differential variability between the eastern and western sectors of the aquifer. The western sector displays spatially homogenous piezometric variations, large memory effects and low-pass filtering characteristics, which are consistent with relatively large and uniform values of water storage capacity and transmissivity properties. In this sector, the 6.5-year mode of variability accounts for ~70 % of the total variance of the groundwater levels. The eastern sector shows larger spatial and temporal heterogeneity, is more reactive to short-term variations, and is less influenced by the low-frequency components related to climate patterns.