Oscillatory States Research Articles

Oscillatory Features of Fourth-Order Emden–Fowler Differential Equations with Sublinear Neutral Terms

This article examines the oscillatory characteristics of a fourth-order Emden–Fowler differential equation, specifically when it includes a sublinear neutral term. Our methodology centers on establishing multiple theorems that introduce innovative conditions to guarantee that there are no positive solutions to the examined equation. Due to the symmetry between non-oscillatory solutions, we obtain oscillation conditions by excluding only positive solutions. We employ the Riccati technique in various ways to achieve this objective. The criteria presented in this study complement and generalize many findings published in the literature. We support the efficiency of our findings by applying them to an example.

Sensitivity of Easterly QBO’s Boreal Winter Teleconnections and Surface Impacts to SSWs

Abstract The quasi-biennial oscillation (QBO) is thought to influence boreal winter surface conditions over Asia and around the North Atlantic. Confirming if these responses are robust is complicated by the QBO having multiple pathways to influence surface conditions as well as internal variability. The reanalysis record suggests that sudden stratospheric warmings (SSWs), breakdowns of the polar vortex that can elicit persistent surface impacts, are more frequent during easterly QBO (EQBO). Hence, this modulated frequency of SSWs may account for some of the EQBO surface responses. However, many climate models do not reproduce this QBO–SSW relationship, perhaps because it is noise or because the model QBOs are deficient. We circumvent these issues by using an ensemble of fixed boundary condition branched simulations in which a realistic EQBO is prescribed in control simulations previously devoid of a QBO, allowing us to isolate the transient atmospheric response to EQBO. Imposing EQBO accelerates the tropical upper-tropospheric wind, shifts the subtropical jet poleward, and attenuates the polar vortex. Interestingly, the latter is not entirely dependent on the statistically significant increase in SSW frequency due to EQBO. Corroborating observations, EQBO is associated with warmer surface temperatures over Asia and negative North Atlantic Oscillation (NAO) conditions. We then subsample the branched/control simulations based on which EQBO members have SSWs. The negative NAO response is primarily associated with more frequent SSWs, while the Asia warming develops irrespective of SSWs. These results have implications for wintertime predictability and clarify the pairing of particular QBO teleconnections with certain surface impacts. Significance Statement The QBO is one of the few parts of the Earth system that is predictable months in advance and that also elicits global effects on surface temperature, circulation, and precipitation. Unfortunately, climate models and operational forecast systems do not simulate the QBO well and it is not always clear how robust the global impacts of the QBO are. Here, we impose the QBO in idealized model simulations, which modulates wintertime surface temperature and precipitation over Asia, the North Atlantic, Europe, and Africa in a manner consistent with observations. This work substantiates the importance of climate and forecast models properly simulating the QBO.

Comparison Theorems for Oscillation of Higher-Order Neutral Delay Differential Equations

In this work, we study the oscillatory features of a class of neutral differential equations with multiple delays. We present novel oscillation conditions for this equation by using a comparison method. We create conditions that exclude the positive solution of the examined equation. Using the feature of symmetry between non-oscillatory solutions (positive and negative), these conditions also exclude negative solutions without adding additional restrictions. In our study, we take into account the even and odd cases of the order of the equation. Furthermore, we study the asymptotic properties in three different cases of functional coefficients. Our results are a fundamental extension and generalization of previous relevant findings, and this fact has been demonstrated through comparisons.

Quantized Microcavity Polariton Lasing Based on InGaN Localized Excitons.

Exciton-polaritons, which are bosonic quasiparticles with an extremely low mass, play a key role in understanding macroscopic quantum effects related to Bose-Einstein condensation (BEC) in solid-state systems. The study of trapped polaritons in a potential well provides an ideal platform for manipulating polariton condensates, enabling polariton lasing with specific formation in k-space. Here, we realize quantized microcavity polariton lasing in simple harmonic oscillator (SHO) states based on spatial localized excitons in InGaN/GaN quantum wells (QWs). Benefiting from the high exciton binding energy (90 meV) and large oscillator strength of the localized exciton, room-temperature (RT) polaritons with large Rabi splitting (61 meV) are obtained in a strongly coupled microcavity. The manipulation of polariton condensates is performed through a parabolic potential well created by optical pump control. Under the confinement situation, trapped polaritons are controlled to be distributed in the selected quantized energy sublevels of the SHO state. The maximum energy spacing of 11.3 meV is observed in the SHO sublevels, indicating the robust polariton trapping of the parabolic potential well. Coherent quantized polariton lasing is achieved in the ground state of the SHO state and the coherence property of the lasing is analyzed through the measurements of spatial interference patterns and g(2)(τ). Our results offer a feasible route to explore the manipulation of macroscopic quantum coherent states and to fabricate novel polariton devices towards room-temperature operations.

Dynamical states associated with the shift in whistling frequency in aeroacoustic system

Self-sustained aeroacoustic oscillations arising from the interactions between the hydrodynamic and acoustic fields are perceived as a whistle. Such whistling can lead to large amplitude acoustic oscillations that have disastrous consequences for engineering systems such as large segmented solid rocket motors and large gas pipelines. The whistling corresponds to the state of limit cycle oscillations (LCO) in dynamical systems theory. An aeroacoustic system exhibits different dynamical states when the bulk flow velocity is varied as a control parameter. Understanding the dynamical states and the transitions between them, as the control parameter is varied, is crucial in designing control strategies for such aeroacoustic oscillations. Previous studies have shown that as the control parameter varies, in an aeroacoustic system that has a flow through orifices, the whistling frequency shifts. We show that such a change in frequency occurs via three different scenarios— (1) direct transition between the two LCOs as an abrupt transition, (2) via a state of intermittency, and (3) via a state of aperiodicity. In the current aeroacoustic system, the abrupt transition between the LCOs is manifested as a bursting behaviour where the amplitude of the acoustic pressure fluctuations abruptly switches between the high and low-amplitude LCOs. Further, we show that the dynamical state and the transition between them during the frequency shift have a correlation with the magnitude of the frequency shift. Using recurrence theory we show that there is a change in the dynamical state of the system during the frequency shift. Further, we use synchronisation theory to investigate the coupled behaviour of the velocity (u′) and the acoustic pressure (p′) fluctuations during the different dynamical states. Our findings imply that u′ and p′ exhibit phase synchronisation (PS) during the state of LCO, corresponding to whistling. In contrast, u′ and p′ are desynchronised during the state of aperiodicity, corresponding to stable operation. Furthermore, the bursts of periodic oscillations during intermittency correspond to the phase-synchronised epochs of periodic u′ and p′, and the aperiodic epochs correspond to the desynchronised aperiodic u′ and p′.

The Effect of Liquid Saturation Transients on PEM Fuel Cell Impedance: Inductive Loop and Instability of Catalyst Layer Operation

We report a physics–based model for the electrochemical impedance of a PEM fuel cell cathode. The model takes into account the transient behavior of oxygen and proton transport in the cathode catalyst layer caused by a variation of the liquid saturation with cell current. Transients of the catalyst layer oxygen diffusivity result in a second capacitive arc in the Nyquist spectrum, while proton conductivity transients lead to the formation of an inductive loop. In the range of capillary pressures in which the liquid saturation in the catalyst layer is independent of the capillary pressures, the loop does not form. A stability analysis of a reduced system of equations reveals that the static limit of inductive loop is unstable with respect to spatial perturbations, implying that the post–oscillatory steady state is unattainable. Possible scenarios of instability development are discussed.

Oscillatory Active State of a Pd Nanocatalyst Identified by In Situ Capture of the Instantaneous Structure-Activity Change at the Atomic Scale.

Identifying the active phase with the highest activity, which is long-believed to be a steady state of the catalyst, is the basis of rational design of heterogeneous catalysis. In this work, we performed detailed in situ investigations, successfully capturing the instantaneous structure-activity change in oscillating Pd nanocatalysts during methane oxidation, which reveals an unprecedented oscillatory active state. Combining in situ quantitative environmental transmission electron microscopy and highly sensitive online mass spectrometry, we identified two distinct phases for the reaction: one where the Pd nanoparticles refill with oxygen, and the other, a period of abrupt pumping of oxygen and boosted methane oxidation within about 1 s. It is the rapid reduction process that shows the highest activity for total oxidation of methane, not a PdO or Pd steady state under the conditions applied here (methane:oxygen = 5:1). This observation challenges the traditional understanding of the active phase and requires a completely different strategy for catalyst optimization.

Impact of ENSO on the UTLS chemical composition in the Asian Summer Monsoon Anticyclone

The changes in the convection and background dynamics over the Asian Summer Monsoon (ASM) are mainly responsible for the changes in the concentrations of the tropospheric pollutants within the Asian Summer Monsoon Anticyclone (ASMA). In this study, we have investigated the structural and chemical composition changes of the ASMA during different El Niño–Southern Oscillation (ENSO) conditions by making use of reanalysis products and Microwave Limb Sounder (MLS) satellite observations. Our analysis mainly concentrates on the July and August months of 2015 (El Niño) and 2022 (La Niña), which are the cold (Nino Index 3.4 exceeding −0.5 in magnitude throughout the year) and warm (Nino Index exceeding +0.5 in magnitude throughout the year) phase of the ENSO. The ASMA structure during different phases of the ENSO is found to be different when compared with the long-term (2005–2023) mean. The ASMA is found to have a larger zonal extent during La Niña (2022), extending from 20° to 140° E compared to El Niño (2015), which is from 20° to 100–105°E. A significant decrease (increase) in the concentration of the tropospheric species (CO and WV) is noticed within the ASMA in El Niño (La Niña). The decrease in the tropospheric species is clearly evident throughout the upper troposphere. The northeastern edge of the ASMA at 100 hPa and 150 hPa showed quite distinct behaviour with an enhancement (reduction) in the tropospheric species during La Niña (El Niño). Interestingly, there is an increase in O3 concentrations over the northeastern edge of ASMA during 2015, which is attributed to the stratospheric intrusion. Our results also revealed the enhancement of the tropospheric species over the western Pacific region during 2015 but not in 2022. Current findings highlight dynamic shifts linked to varying ENSO phases, leading to notable alterations in both the ASMA structure and Upper Troposphere and Lower Stratosphere (UTLS) chemical composition.

A compensator design and stability margin monitor for digitally controlled DC-DC converters

ABSTRACT In this paper, an automatic direct digital design approach for compensators is presented to achieve a lookup table proportional – integral – derivative controller. Additionally, a correlation-based stability margin monitor with adaptive sliding window smoothing is proposed to increase the identifiable range for bandwidth detection. The proposed automatic compensator design approach meets the expected phase margin and crossover frequency and considers limit-cycle oscillation conditions throughout the design process. The digital controller with the direct digital design was implemented on a field programmable gate array to validate the approach and alternative design capabilities. Experimental results show that the direct digital design yields a higher crossover frequency than digital redesign. The best transient response performance can be obtained if a proper integral gain is designed. The digital controller with ASWS was fabricated using the TSMC 1P6M 0.18-μm standard CMOS process. Further experimental results show that the proposed ASWS provides a significantly more accurate identified frequency response by using narrow windows at low frequencies and expansive windows at high frequencies.

Optimal control of microgrid using ALO optimization MPPT with power quality enhancement

AbstractThe paper presents a normalized, varying step size-based least mean square-based control for a standalone microgrid and Ant Lion optimization-based maximum power point tracking. This modified version of the incremental conductance algorithm addresses issues like slow dynamic response, fixed step size issues, and steady state oscillations. Comparative analysis with well-known techniques shows that Ant Lion optimizes the tracking of maximum power points more accurately, with fewer oscillations and increased efficiency. Power management and power quality are maintained through proposed adaptive voltage source converter control. The proposed voltage control shows better performance under various dynamic and steady conditions.

Bubble thermodynamics in cryogenic fluids under ultrasonic field excitation: Theoretical analysis and numerical calculation

In the study of cavitation in room-temperature fluids, the heat transfer between gas and liquid in bubble oscillation is usually assumed to be an adiabatic process for simplification. However, this heat transfer and thermodynamic mechanism is not yet understood in cryogenic fluids, especially under small amplitude oscillation conditions excited by ultrasonic field. This article studies bubble thermodynamic model under an external ultrasonic field based on the heat transfer equation for cryogenic fluids. The temperature changes inside bubbles are calculated, and the heat transfer mechanism is briefly analyzed. The results indicate that the heat transfer mechanism of bubbles depends on the relationship between ultrasonic frequency and bubble resonance frequency. By analyzing two special cases of dual-bubble and high-pressure environment, it is believed that heat transfer can be approximated as an adiabatic process under high-pressure conditions with ultrasonic frequency far from the resonance frequency. This conclusion can provide a theoretical basis for subsequent accurate calculation of heat-transfer polytropic coefficient, or void faction measurement in cryogenic two-phase flow.

Explicit n-particle harmonic oscillator states in products of SU(1,1) representations

In this paper, we present a simple algorithm for the explicit construction of [Formula: see text]-particle harmonic oscillator states simultaneously belonging to irreducible representations of [Formula: see text] (or [Formula: see text]) and [Formula: see text]. For degenerate representations, the construction can be done using generating functions or hyperspherical harmonics. The cases with [Formula: see text] and [Formula: see text] are investigated at greater length. The analysis is extended to nondegenerate states, although the states are not so easily obtained as in the degenerate case. Finally, we briefly touch on the [Formula: see text] structure of Bell states.

A Survey on the Oscillation of First-Order Retarded Differential Equations

In this paper, a survey of the most interesting conditions for the oscillation of all solutions to first-order linear differential equations with a retarded argument is presented in chronological order, especially in the case when well-known oscillation conditions are not satisfied. The essential improvement and the importance of these oscillation conditions is also indicated.

Kuramoto model subject to subsystem resetting: How resetting a part of the system may synchronize the whole of it.

We introduce and investigate the effects of a new class of stochastic resetting protocol called subsystem resetting, whereby a subset of the system constituents in a many-body interacting system undergoes bare evolution interspersed with simultaneous resets at random times, while the remaining constituents evolve solely under the bare dynamics. Here, by reset is meant a reinitialization of the dynamics from a given state. We pursue our investigation within the ambit of the well-known Kuramoto model of coupled phase-only oscillators of distributed natural frequencies. Here, the reset protocol corresponds to a chosen set of oscillators being reset to a synchronized state at random times. We find that the mean ω_{0} of the natural frequencies plays a defining role in determining the long-time state of the system. For ω_{0}=0, the system reaches a synchronized stationary state at long times, characterized by a time-independent nonzero value of the synchronization order parameter that quantifies macroscopic order in the system. Moreover, we find that resetting even an infinitesimal fraction of the total number of oscillators, in the extreme limit of infinite resetting rate, has the drastic effect of synchronizing the entire system, even in parameter regimes in which the bare evolution does not support global synchrony. By contrast, for ω_{0}≠0, the dynamics allows at long times either a synchronized stationary state or an oscillatory synchronized state, with the latter characterized by an oscillatory behavior as a function of time of the order parameter, with a nonzero time-independent time average. Our results thus imply that the nonreset subsystem always gets synchronized at long times through the act of resetting of the reset subsystem. Our results, analytical using the Ott-Antonsen ansatz as well as those based on numerical simulations, are obtained for two representative oscillator frequency distributions, namely, a Lorentzian and a Gaussian. Given that it is easier to reset a fraction of the system constituents than the entire system, we discuss how subsystem resetting may be employed as an efficient mechanism to control attainment of global synchrony in the Kuramoto system.

Sensor-Less Control of Mirror Manipulator Using Shape Memory Polyimide Composite Actuator: Experimental Work.

Integrated thin film-based shape memory polyimide composites (SMPICs) are potentially attractive for efficient and compact design, thereby offering cost-effective applications. The objective of this article is to design and evaluate a mirror manipulator using an SMPIC as an actuator and a sensor with control. A sensor-less control strategy using the SMPIC (a self-sensing actuator) with a proportional derivative combined variable structure controller (PD-VSC) is proposed for position control of the mirror in both the vertical and angular directions. The mirror manipulator is able to move the mirror in the vertical and angular directions by 3.39 mm and 10.5 deg, respectively. A desired fast response is obtained as the performance under control. In addition, some benefits from the proposed control realization include good tracking, stable switching, no overshoot, no steady state oscillations, and robust disturbance rejection. These superior properties are experimentally validated to reflect practical feasibility.

Targeting Ribosome Biogenesis as a Novel Therapeutic Approach to Overcome EMT-related Chemoresistance in Breast Cancer.

This study uncovers the crucial involvement of ribosome biogenesis (RiBi) in the regulation of epithelial and mesenchymal state oscillations in breast cancer cells, which plays a major role in the development of chemoresistant metastasis. By proposing a novel therapeutic strategy targeting the RiBi pathway, the study offers significant potential to enhance treatment efficacy and outcomes for patients with advanced breast cancer. This approach could help overcome the limitations of current chemotherapy options and address the complex challenges posed by EMT-mediated chemoresistance.

Self-phoretic oscillatory motion in a harmonic trap.

We consider the motion of a harmonically trapped overdamped particle, which is submitted to a self-phoretic force, that is proportional to the gradient of a diffusive field for which the particle itself is the source. In agreement with existing results for free particles or particles in a bounded domain, we find that the system exhibits a transition between an immobile phase, where the particle stays at the center of the trap, and an oscillatory state. We perform an exact analysis giving access to the bifurcation threshold, as well as the frequency of oscillations and their amplitude near the threshold. Our analysis also characterizes the shape of two-dimensional oscillations that take place along a circle or a straight line. Our results are confirmed by numerical simulations.

Numerical investigation on the energy extraction characteristics of parallel multi foils arranged in columns

Abstract The oscillating foil is a focus device in the clean energy utilization field. The presence of an oscillating foil structure within the flow field significantly impacts the energy extraction capabilities of the system. In this paper, three types of parallel multi-foil structures arranged in columns are proposed. The energy extraction characteristics of diverse multi-foil structures under various oscillation conditions are analyzed numerically. The flow field structure and the impact of parallel multi foils on the aerodynamic characteristics are investigated. Results demonstrate that the multi-foil structure with a phase difference of 180° achieves the highest level of energy extraction performance, and the maximal mean power coefficient achieves 0.894, which is 11.03% higher than that of the structure with a smaller phase difference. The size of the trailing edge vortex under the structure with a phase difference of 180° is significantly larger, leading to an obvious fluctuation in the aerodynamic lift.

Time-dependent heating problem of the solar corona in fractal dimensions: A plausible solution

The coronal heating problem is considered one of the most puzzling problems in solar physics. It is based on the question of why the corona temperature reaches a temperature of over 2×106K whereas the temperature of the surface of the sun has about 103-104K. Since the corona is far away from the source of heat, it is realistic that the outer surface should be cooler. Solar physicists and astrophysicists have tried for several decades to solve this puzzle by supplying heat to the corona, despite several advances in MHD theory, computational and numerical simulations. Although these candidates’ sources of energy hold a number of drawbacks, the problem is still open. A motivating approach has been proposed by Walsh which consists of supplying a time-dependent sinusoidal heating function to the heat to preserve the loop at coronal temperature. Yet, the loop temperature at ∼2×106K is preserved and cools only if a critical frequency is exceeded. In this study, it was found that the MHD formulation of the Walsh approach in fractal dimensions may offer a potential solution to the problem. In particular, oscillations of the temperature in the space-fractal dimension close to unity relax quicker than those with smaller values. For time-fractal dimensions much smaller than unity, the temperature enters a state of steady state oscillations after a long time. Our analyses also reveal irregularities in the propagation of temperature over a long period of time. For low frequency and space-fractal dimensions close to unity and low time-fractal dimensions, the temperature enters a cycle of an oscillating phase by rising and falling gradually. It is probable that the loop will stay hot after a series of cycles, and extended periods of no heating are not possible for small frequencies. Additional features related to the propagation of the magnetic field in low-Reynolds numbers are discussed.

Phase autoencoder for limit-cycle oscillators.

We present a phase autoencoder that encodes the asymptotic phase of a limit-cycle oscillator, a fundamental quantity characterizing its synchronization dynamics. This autoencoder is trained in such a way that its latent variables directly represent the asymptotic phase of the oscillator. The trained autoencoder can perform two functions without relying on the mathematical model of the oscillator: first, it can evaluate the asymptotic phase and the phase sensitivity function of the oscillator; second, it can reconstruct the oscillator state on the limit cycle in the original space from the phase value as an input. Using several examples of limit-cycle oscillators, we demonstrate that the asymptotic phase and the phase sensitivity function can be estimated only from time-series data by the trained autoencoder. We also present a simple method for globally synchronizing two oscillators as an application of the trained autoencoder.