Planar Oscillator Research Articles

DKP spin-one particles confined in a two-dimensional ring

We study the confinement of relativistic spin-one particles in two spatial dimensions by a quantum ring for systems described by the Duffin–Kemmer–Petiau (DKP) equation. The ring-like geometry is realized by introducing a pseudo-scalar funnel-shape potential into the DKP equation, leading to a generalization of the planar DKP oscillator. Having used a ten-dimensional representation of the DKP matrices, the DKP equation is then mapped into two uncoupled subproblems, the first is associated with states of zero spin-projection (natural parity states) and the second is associated with states having a spin-projection number equal to ±1 (unnatural parity states). For both subproblems the exact wave functions of the system are analytically derived and expressed through the generalized Laguerre polynomials. The corresponding energy eigenvalues are explicitly obtained for natural parity states, while in the unnatural parity case an exact energy equation from which they can be determined is derived.

The Effect of Curved Geometry on Exiting Flow of Fluidic Oscillators

Abstract Traditionally fluidic oscillators are designed to be planar. However, there are applications that may desire the exiting fluid to move in the third dimension. This could allow these oscillators to be more effective in applications such as fuel sprays, cooling flow, or flow control devices with its increase in effective spray area. This investigation designed a series of oscillators that curved the whole body and/or the exit nozzle to understand how to maximize out of plane motion. These configurations were compared to a baseline planar oscillator with no curved characteristics. Velocities were measured downstream of these oscillators within a data collection grid using a hot wire probe to determine the 3D shape of the exiting jet. Results show that configurations with only one of the two curved physical characteristics (i.e., only a curved body or a curved nozzle) produced the most curvature. Having both of the curved physical characteristics caused the nozzle width to decrease causing the axial spacing to decrease. Additionally, these curved exiting flows were only seen at mass flow rates below 40 standard liters per minute (SLPM). Higher mass flow rates caused the exiting flow to flatten, returning the flow to the baseline result of in-plane oscillations. This led to a decrease in jet spread.

Dominant higher-order vortex gyromodes in circular magnetic nanodots.

The transition to the third dimension enables the creation of spintronic nanodevices with significantly enhanced functionality compared to traditional 2D magnetic applications. In this study, we extend common two-dimensional magnetic vortex configurations, which are known for their efficient dynamical response to external stimuli without a bias magnetic field, into the third dimension. This extension results in a substantial increase in vortex frequency, reaching up to 5 GHz, compared to the typical sub-GHz range observed in planar vortex oscillators. A systematic study reveals a complex pattern of vortex excitation modes, explaining the decrease in the lowest gyrotropic mode frequency, the inversion of vortex mode intensities, and the nontrivial spatial distribution of vortex dynamical magnetization noted in previous research. These phenomena enable the optimization of both oscillation frequency and frequency reproducibility, minimizing the impact of uncontrolled size variations in those magnetic nanodevices.

Data-driven model identification using forcing-induced limit cycles

This paper presents a data-driven model identification strategy that characterizes the behavior of a general dynamical system relative to a set of limit cycles that emerge in response to periodic forcing. Using time series data to infer the phase–amplitude dynamics associated with the underlying forced limit cycles, a low-order model can be obtained that accurately captures the dynamical behavior in response to arbitrary external inputs. The proposed strategy can be readily implemented in situations where full state measurements are unavailable and does not require any prior knowledge of the underlying model equations. This technique is applied to a model of coupled planar oscillators and to a model that considers the spike rate in a population of coupled conductance-based neurons where it outperforms two other commonly used data-driven model identification techniques.

High power single-frequency 1112 nm laser by an insertable Nd:YAG/YAG bonded monolithic planar ring oscillator.

A high power single-frequency operation at 1112 nm with novel insertable monolithic planar ring oscillator based on a Nd:YAG/YAG bonded crystal is proposed. In a proof-of-principle experiment, a finely designed coating on the output surface is carried out to ensure single-wavelength oscillation at 1112 nm, together with a half-wave plate and a Tb3Ga5O12 crystal inserted in the open space of the bonded block to realize the unidirectional operation with power scalability. Consequently, the single-frequency laser delivers an output power of 3.9W at 1112.3 nm with a slope efficiency of 58.6% and an optical-to-optical efficiency of 17.7%. The power fluctuation is measured to be within ± 0.26% over 20 min, and the laser linewidth is estimated to be 4.15 MHz (Δλ = 0.017 pm).

Traveling spiral wave chimeras in coupled oscillator systems: emergence, dynamics, and transitions

Systems of coupled nonlinear oscillators often exhibit states of partial synchrony in which some of the oscillators oscillate coherently while the rest remain incoherent. If such a state emerges spontaneously, in other words, if it cannot be associated with any heterogeneity in the system, it is generally referred to as a chimera state. In planar oscillator arrays, these chimera states can take the form of rotating spiral waves surrounding an incoherent core, resembling those observed in oscillatory or excitable media, and may display complex dynamical behavior. To understand this behavior we study stationary and moving chimera states in planar phase oscillator arrays using a combination of direct numerical simulations and numerical continuation of solutions of the corresponding continuum limit, focusing on the existence and properties of traveling spiral wave chimeras as a function of the system parameters. The oscillators are coupled nonlocally and their frequencies are drawn from a Lorentzian distribution. Two cases are discussed in detail, that of a top-hat coupling function and a two-parameter truncated Fourier approximation to this function in Cartesian coordinates. The latter allows semi-analytical progress, including determination of stability properties, leading to a classification of possible behaviors of both static and moving chimera states. The transition from stationary to moving chimeras is shown to be accompanied by the appearance of complex filamentary structures within the incoherent spiral wave core representing secondary coherence regions associated with temporal resonances. As the parameters are varied the number of such filaments may grow, a process reflected in a series of folds in the corresponding bifurcation diagram showing the drift speed s as a function of the phase-lag parameter α.

평면형 발진기 적용을 통한 국방 무기체계 품질 향상 방안 연구

평면형 발진기 적용을 통한 국방 무기체계 품질 향상 방안 연구

A modified Jerusalem microstrip filter and its complementary for low phase noise X-band oscillator

AbstractThis article shows the design of two different low phase noise (LPN) planar X-band frequency oscillators using two various microstrip filters (MFs). These two MFs act as a frequency stabilization part in the loop of the microwave oscillator. The first one, the modified Jerusalem MF (MJ-MF), is based on the Jerusalem scheme. The second one, the complementary modified Jerusalem MF (CMJ-MF), is complementary of the MJ-MF. Finally, by employing the branchline coupler, the LPN MF oscillator is achieved. The MJ-MF (narrowband filter) LPN X-band oscillator operates at 8.17 GHz and denotes a phase noise (PN) of −161 dBc/Hz at 1-MHz frequency offset. The CMJ-MF (wideband filter) LPN X-band oscillator operates at 8.14 GHz and mentions a PN of −157 dBc/Hz at 1-MHz frequency offset.

Solving the thoracic inverse problem in the fruit fly

In many insect species, the thoracic exoskeletal structure plays a crucial role in enabling flight. In the dipteran indirect flight mechanism, thoracic cuticle acts as a transmission link between the flight muscles and the wings, and is thought to act as an elastic modulator: improving flight motor efficiency thorough linear or nonlinear resonance. But peering closely into the drivetrain of tiny insects is experimentally difficult, and the nature of this elastic modulation is unclear. Here, we present a new inverse-problem methodology to surmount this difficulty. In a data synthesis process, we integrate literature-reported rigid-wing aerodynamic and musculoskeletal data into a planar oscillator model for the fruit fly Drosophila melanogaster, and use this integrated data to identify several surprising properties of the fly’s thorax. We find that fruit flies likely have an energetic need for motor resonance: absolute power savings due to motor elasticity range from 0%–30% across literature-reported datasets, averaging 16%. However, in all cases, the intrinsic high effective stiffness of the active asynchronous flight muscles accounts for all elastic energy storage required by the wingbeat. The D. melanogaster flight motor should be considered as a system in which the wings are resonant with the elastic effects of the motor’s asynchronous musculature, and not with the elastic effects of the thoracic exoskeleton. We discover also that D. melanogaster wingbeat kinematics show subtle adaptions that ensure that wingbeat load requirements match muscular forcing. Together, these newly-identified properties suggest a novel conceptual model of the fruit fly’s flight motor: a structure that is resonant due to muscular elasticity, and is thereby intensely concerned with ensuring that the primary flight muscles are operating efficiently. Our inverse-problem methodology sheds new light on the complex behaviour of these tiny flight motors, and provides avenues for further studies in a range of other insect species.

Experimental and theoretical investigation of superharmonic resonances in a planar oscillator under angular base excitation

Experimental and theoretical investigation of superharmonic resonances in a planar oscillator under angular base excitation

Chimeras with uniformly distributed heterogeneity: Two coupled populations

Chimeras occur in networks of two coupled populations of oscillators when the oscillators in one population synchronize while those in the other are asynchronous. We consider chimeras of this form in networks of planar oscillators for which one parameter associated with the dynamics of an oscillator is randomly chosen from a uniform distribution. A generalization of the previous approach [Laing, Phys. Rev. E 100, 042211 (2019)2470-004510.1103/PhysRevE.100.042211], which dealt with identical oscillators, is used to investigate the existence and stability of chimeras for these heterogeneous networks in the limit of an infinite number of oscillators. In all cases, making the oscillators more heterogeneous destroys the stable chimera in a saddle-node bifurcation. The results help us understand the robustness of chimeras in networks of general oscillators to heterogeneity.

Flow physics of planar bistable fluidic oscillator with backflow limbs.

Fluidic oscillators (FOs) are used in a variety of applications, including process control and process intensification. Despite the simple design and operation of FOs, the fluid dynamics of FOs exhibit rich complexities. The inherently unstable flow, jet oscillations, and resulting vortices influence mixing and other transport processes. In this work, we computationally investigated the fluid dynamics of a new design of a planar FO with backflow limbs. The design comprised of two symmetric backflow limbs leading to bistable flow. The unsteady flow dynamics, internal recirculation, jet oscillations, secondary flow vortices were computationally studied over a range of inlet Reynolds numbers (2400-12,000). The nature and frequency of the jet oscillations were quantified. The computed jet oscillation frequency was compared with the experimentally measured (using imaging techniques) jet oscillation frequency. The flow model was then used to quantitatively understand mixing, heat transfer, and residence time distribution. The approach and the results presented in this work will provide a basis for designing FO's with desired flow and transport characteristics for various engineering applications.

Amplitude Death, Bifurcations, and Basins of Attraction of a Planar Self-Sustained Oscillator with Delayed Feedback

Amplitude Death, Bifurcations, and Basins of Attraction of a Planar Self-Sustained Oscillator with Delayed Feedback

PLANAR INTEGRABLE NONLINEAR OSCILLATORS HAVING A STABLE LIMIT CYCLE

<abstract> In this short paper, by improving some conclusions given by [<xref ref-type="bibr" rid="b2">2</xref>], we show that planar integrable nonlinear oscillators can have a stable limit cycle. We also obtain these xact parametric representations of these limit cycles. </abstract>

Supersymmetric structures of Dirac oscillators in commutative and noncommutative spaces* *Project supported by the National Natural Science Foundation of China (Grant No. 11465006).

The supersymmetric properties of a charged planar Dirac oscillator coupling to a uniform perpendicular magnetic field are studied. We find that there is an N = 2 supersymmetric structure in both commutative and noncommutative cases. We construct the generators of the supersymmetric algebras explicitly and show that the generators of the supersymmetric algebras can be mapped onto ones which only contain the left or right-handed chiral phonons by unitary transformations.

Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators.

The mechanisms underlying the emergence of seizures are one of the most important unresolved issues in epilepsy research. In this paper, we study how perturbations, exogenous or endogenous, may promote or delay seizure emergence. To this aim, due to the increasingly adopted view of epileptic dynamics in terms of slow-fast systems, we perform a theoretical analysis of the phase response of a generic relaxation oscillator. As relaxation oscillators are effectively bistable systems at the fast time scale, it is intuitive that perturbations of the non-seizing state with a suitable direction and amplitude may cause an immediate transition to seizure. By contrast, and perhaps less intuitively, smaller amplitude perturbations have been found to delay the spontaneous seizure initiation. By studying the isochrons of relaxation oscillators, we show that this is a generic phenomenon, with the size of such delay depending on the slow flow component. Therefore, depending on perturbation amplitudes, frequency and timing, a train of perturbations causes an occurrence increase, decrease or complete suppression of seizures. This dependence lends itself to analysis and mechanistic understanding through methods outlined in this paper. We illustrate this methodology by computing the isochrons, phase response curves and the response to perturbations in several epileptic models possessing different slow vector fields. While our theoretical results are applicable to any planar relaxation oscillator, in the motivating context of epilepsy they elucidate mechanisms of triggering and abating seizures, thus suggesting stimulation strategies with effects ranging from mere delaying to full suppression of seizures.

Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model

Abstract In this article multiple and generic bifurcations of planar discrete-time Hindmarsh-Rose oscillator are investigated in detail by bifurcation theory and numerical continuation techniques. Three kinds of one-parameter bifurcation and five kinds of two-parameter bifurcation are studied. Different kinds of critical cases of each bifurcation are computed by inner product method and their corresponding scenario are presented, such as possible transitions between different one-parameter bifurcation points derived from two-parameter bifurcation point. Especially, the bifurcations of higher iterations and the bifurcation distributions of two-parameter bifurcation point are observed.

A study of amplitude‐to‐phase noise conversion in planar oscillators

SummaryThis paper explores the many interesting implications for oscillator design, with optimized phase‐noise performance, deriving from a newly proposed model based on the concept of oscillator conjugacy. For the case of 2‐D (planar) oscillators, the model prominently predicts that only circuits producing a perfectly symmetric steady‐state can have zero amplitude‐to‐phase (AM‐PM) noise conversion, a so‐called zero‐state. Simulations on standard industry oscillator circuits verify all model predictions and, however, also show that these circuit classes cannot attain zero‐states except in special limit‐cases which are not practically relevant. Guided by the newly acquired design rules, we describe the synthesis of a novel 2‐D reduced‐order LC oscillator circuit which achieves several zero‐states while operating at realistic output power levels. The potential future application of this developed theoretical framework for implementation of numerical algorithms aimed at optimizing oscillator phase‐noise performance is briefly discussed.

Symmetry algebra of the planar anisotropic quantum harmonic oscillator with rational ratio of frequencies

The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are studied and the energy eigenvalues are de- termined using algebraic methods of general applicability to quantum superintegrable systems.

Solution of the κ-Deformed Dirac Equation with Vector and Scalar Interactions in the Context of Spin and Pseudospin Symmetries

The deformed Dirac equation invariant under the κ-Poincaré-Hopf quantum algebra in the context of minimal and scalar couplings under spin and pseudospin symmetry limits is considered. The κ-deformed Pauli-Dirac Hamiltonian allows us to study effects of quantum deformation in a class of physical systems, such as a Zeeman-like effect, Aharonov-Bohm effect, and an anomalous-like contribution to the electron magnetic moment, between others. In our analysis, we consider the motion of an electron in a uniform magnetic field and interacting with (i) a planar harmonic oscillator and (ii) a linear potential. We verify that the particular choice of a linear potential induces a Coulomb-type term in the equation of motion. Expressions for the energy eigenvalues and wave functions are determined taking into account both symmetry limits. We verify that the energies and wave functions of the particle are modified by the deformation parameter as well as by the element of spin.