Asymptotic Frequency Research Articles

Asteroseismic measurement of core and envelope rotation rates for 2006 red giant branch stars

Context. Tens of thousands of red giant stars in the Kepler data exhibit solar-like oscillations. The mixed-mode characteristics of their oscillations enable us to study the internal physics from the core to the surface, such as differential rotation. However, envelope rotation rates have only been measured for about a dozen red giant branch (RGB) stars so far. This limited the theoretical interpretation of angular momentum transport in post-main sequence phases. Aims. We report the measurements of g-mode properties and differential rotation in the largest sample of Kepler RGB stars. Methods. We applied a new approach to calculate the asymptotic frequencies of mixed modes, which accounts for so-called near-degeneracy effects (NDEs) and leads to improved measurements of envelope rotation rates. By fitting these asymptotic expressions to the observations, we obtained measurements of the properties of g modes (period spacing, ΔΠ1, coupling factor, q, g-mode offset term, εg, small separation, δν01) and the internal rotation (mean core, Ωcore, and envelope, Ωenv, rotation rates). Results. Among 2495 stars with clear mixed-mode patterns, we found that 800 show doublets and 1206 show triplets, while the remaining stars do not show any rotational splittings. We measured core rotation rates for 2006 red giants, doubling the size of pre-existing catalogues. This led us to discover an over-density of stars that are narrowly distributed around a well-defined ridge in the plane, showing core rotation rate versus evolution along the RGB. These stars could experience a different angular momentum transport compared to other red giants. With this work, we also increased the sample of stars with measured envelope rotation rates by two orders of magnitude. We found a decreasing trend between envelope rotation rates and evolution, implying that the envelopes slow down with expansion, as expected. We found 243 stars whose envelope rotation rates are significantly larger than zero. For these stars, the core-to-envelope rotation ratios are around Ωcore/Ωenv ∼ 20 and show a large spread with evolution. Several stars show extremely mild differential rotations, with core-to-surface ratios between 1 and 2. These stars also have very slow core rotation rates, suggesting that they go through a peculiar rotational evolution. We also discovered more stars located below the ΔΠ1–Δν degeneracy sequence, which presents an opportunity to study the history of plausible stellar mergers.

Dispersion curve engineering for automated topology design of a unit cell in spoof surface plasmon polaritons

In this paper, an automatic design method is proposed for unit cell in spoof surface plasmon polaritons (SSPP) with an almost arbitrary dispersion curve. In this method, the pixel configuration is considered for the unit cell and, by using the binary particle swarm optimization method, the proper topology of the unit cell is explored so as to reach the target dispersion curve. Unlike the traditional method of controlling the dispersion curve, which is performed based on changing the geometric parameters of the predetermined unit cell, in this method, there is no need to know the shape of the unit cell, and the dispersion curve of the modes of SSPP unit cell can be controlled independently with more freedom. Two unit cell samples are designed in order to show the efficiency of the procedure. In the first sample, the dispersion curve is designed to have the lowest asymptotic frequency; in the second sample, the dispersion curve of the second mode is controlled independently from the first mode and is changed arbitrarily. SSPP transmission lines which are related to the unit cells of the two samples are designed, and it is demonstrated that measurement and simulation results are greatly in line with each other.

Design of low‐pass filter with improved equalization based on lossy grounded spoof surface plasmon polaritons

AbstractA new method for designing multifunctional low‐pass filter with controllable equalizing capability is presented in this letter. By constructing the novel unit cell, namely, loading surface mount resistor on the grounded spoof surface plasmon polaritons (SSPPs), the filter not only achieves filtering and equalizing functions at the same time, but also improves the equalizing response in the low‐band effectively. To illustrate the principle, the extraction method of equivalent circuit of the lossy unit cell is introduced, and the equalization and filtering properties characterized by attenuation constant and asymptotic frequency are explored. To verify the concept, a prototype operating from 0.5 to 3.4 GHz with 10 dB equalizing value is implemented, fabricated, and measured. Good agreement is achieved between simulation and measurement. The result shows that the filter is provided with a smooth equalizing curve at the low frequency of the passband compared with the ungrounded SSPPs.

Miniaturized electronically controlled notched band filter based on spoof surface plasmon polaritons

In this paper, a novel miniaturized electronical controlled notch band filter based on spoof surface plasmon polaritons (SSPPs) with inverted “山”-shaped unit is designed and experimentally demonstrated. The notch band filter is mainly composed of four parts: microstrip transmission line, transition structure, inverted “山”-shaped SSPPs, and split ring resonator (SRR) structure, and a varactor diode is embedded in the slit notch of the SRR structure to realize electronic control. Comparing with the traditional SSPP unit with the same lateral size, the dispersion curve of the proposed inverted “山”-shaped unit shows better slow wave characteristics, and the asymptotic frequency is reduced to 55%. The frequency of the notch band can be dynamically controlled by adjusting the external bias voltage at both ends of the varactor diode. As the external bias voltage increases from 0.5 V to 30 V, the notch band frequency can be changed from 2.1 GHz to 2.3 GHz and achieve easily electronic regulation. The simulation results show that the notched band filter achieves low insertion loss (<i>S</i><sub>21</sub> < –1 dB) and great return loss (<i>S</i><sub>11</sub> > –10 dB) in the pass band, which has the advantage of miniaturization with the size only 0.78<i>λ</i><sub>g</sub> × 0.35<i>λ</i><sub>g</sub>. It is worth noting that when the equivalent capacitance of the slit notch is changed, the transmission coefficient of the notched band is always less than –15 dB, showing superior band-stop performance. At the same time, by comparing and analyzing the electric field distribution of notch band filter, the transmission mechanism of microwave signal is further verified. In order to verify the its effectiveness, the traditional printed circuit board technology is used to fabricate notch band filter. The measurement results are in good agreement with the simulation ones, verifying the feasibility of the design. The electronically controlled notch band filter has higher integration and can effectively suppress the interference frequency band.

Ultra-Compact Low-Pass Spoof Surface Plasmon Polariton Filter Based on Interdigital Structure.

An ultra-compact low-pass spoof surface plasmon polariton (SSPP) filter based on an interdigital structure (IS) is designed. Simulated dispersion curves show that adding the interdigital structure in an SSPP unit effectively reduces its asymptotic frequency compared with traditional and T-shaped SSPP geometries, and the unit dimensions can be conversely reduced. Based on that, three IS-based SSPP units are, respectively, designed with different maximum intrinsic frequencies and similar asymptotic frequencies to constitute the matching and waveguide sections of the proposed filter, and the unit number in the waveguide section is adjusted to improve the out-of-band suppression. Simulation results illustrate the efficient transmission in the 0~5.66 GHz passband, excellent out-of-band suppression (over 24 dB) in the 5.95~12 GHz stopband and ultra-shape roll-off at 5.74 GHz of the proposed filter. Measurement results on a fabricated prototype validate the design, with a measured cut-off frequency of 5.53 GHz and an ultra-compact geometry of 0.5 × 0.16 λ02.

The Asymptotic Frequency of Stochastic Oscillators

We study stochastic perturbations of ODEs with stable limit cycles — referred to as stochastic oscillators — and investigate the response of the asymptotic (in time) frequency of oscillations to changing noise amplitude. Unlike previous studies, we do not restrict our attention to the small-noise limit, and we account for the fact that large deviation events may push the system out of its oscillatory regime. To do so, we consider stochastic oscillators conditioned on their remaining in an oscillatory regime for all time. This leads us to use the theory of quasi-ergodic measures, and to define quasi-asymptotic frequencies as conditional, long-time average frequencies. We show that quasi-asymptotic frequencies exist under minimal assumptions, though they may or may not be observable in practice. Our discussion recovers and expands upon previous results on stochastic oscillators in the literature. In particular, existing results imply that the asymptotic frequency of a stochastic oscillator depends quadratically on the noise amplitude. We describe scenarios where this prediction holds, though we also show that it is not true in general — potentially, even for small noise.

PSO-Algorithm-Assisted Design of Compact SSPP Transmission Line

This letter proposes a compact spoof surface plasmon polariton (SSPP) transmission line (TL) structure. The particle swarm optimization (PSO) algorithm is utilized to numerically optimize the traditional rectangular groove SSPP structure. The SSPP unit cell is pixelated into 23 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 9 pixels with a resolution of 0.2 mm, and the asymptotic frequency is reduced to 5.4 GHz through optimization. The developed SSPP TL exhibits a compact structure, and its electrical dimension is only about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.842\lambda _{g} \times 0.28\lambda _{g}$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda _{g}$ </tex-math></inline-formula> is the wavelength of the cutoff frequency. A prototype of the developed SSPP TL is fabricated and tested, and the experimental result agrees well with the simulated one. The proposed optimization approach is applicable to both single- and dual-conductor SSPP structures. The results are of great significance to the miniaturization of components and circuits based on SSPP.

Robust Distributed Secondary Control for AC Microgrids With Time-Varying Delay

Non-smooth, nonuniform, and even unbounded communication time delays, which are called irregular time delays, are unavoidable in many practical systems. Currently, there is no available approach that can solve the secondary voltage and frequency restoration control problem for an ac microgrid (MG) in the presence of such unknown irregular time delays. In this brief, we propose a resilient secondary control scheme to solve the problem. To ensure system stability and achieve asymptotic voltage and frequency restoration, sufficient conditions are established in the form of algebraic gains using a multidimensional small gain approach. Simulation and experimental case studies validate that the proposed control scheme can effectively solve this problem in a tested ac MG.

Asteroseismology of hot subdwarf B stars observed with TESS: discovery of two new gravity mode pulsating stars

TIC 033834484 and TIC 309658435 are long-period pulsating subdwarf B stars, which were observed extensively (675 and 621 days, respectively) by the Transiting Exoplanet Survey Satellite (TESS). The high-precision photometric light curve reveals the presence of more than 40 pulsation modes including both stars. All the oscillation frequencies that we found are associated with gravity (g)-mode pulsations, with frequencies spanning from ∼80 µHz (2 500 s) to ∼400 µHz (12 000 s). We utilize the asteroseismic tools including asymptotic period spacings and rotational frequency multiplets in order to identify the pulsational modes. We found dipole (l = 1) mode sequences for both targets and calculate the mean period spacing of dipole modes (ΔPl=1), which allows us to identify the modes. Frequency multiplets provide a rotation period of ∼64 d for TIC 033834484. From follow-up ground-based spectroscopy, we find that TIC 033834484 has an effective temperature of 24 210 K (140), a surface gravity of log g/cms-2 = 5.28 (03) and TIC 309658435 has an effective temperature of 25 910 K (150), a surface gravity of log g/cms-2 = 5.48 (03).

Singularities of regular black holes and the monodromy method for asymptotic quasinormal modes* *C.L. acknowledges support from the National Natural Science Foundation of China (12175108)

We use the monodromy method to investigate the asymptotic quasinormal modes of regular black holes based on the explicit Stokes portraits. We find that, for regular black holes with spherical symmetry and a single shape function, the analytical forms of the asymptotic frequency spectrum are not universal and do not depend on the multipole number but on the presence of complex singularities and the trajectory of asymptotic solutions along the Stokes lines.

Millimeter-Wave E-Plane Waveguide Bandpass Filters Based on Spoof Surface Plasmon Polaritons

A class of millimeter-wave E-plane waveguide bandpass filters (BPFs) based on spoof surface plasmon polaritons (SSPPs) have been presented in this article. Three kinds of SSPPs, with different patterns coated on the dielectric substrate, are inserted into the E-plane of WR-10 standard rectangular waveguide for the design of BPFs. To clarify the filtering characteristics of the proposed BPFs, the dispersive properties of different SSPP unit cells are investigated and discussed. The electromagnetic simulation results demonstrate that the bandwidths and center frequencies of the proposed E-plane waveguide BPFs can be flexibly adjusted by controlling the asymptotic frequencies of SSPP unit cells. For verifying the design feasibility, these three E-plane waveguide BPFs are fabricated and measured. Good agreement between measurements and simulations indicates that the proposed idea will be a good candidate for the BPF design with low insertion loss and flexible adjustment of center frequency and bandwidth.

A Unified Passivity-Based Framework for Control of Modular Islanded AC Microgrids

Voltage and frequency control in an islanded ac microgrid (ImG) amounts to stabilizing an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> unknown ImG equilibrium induced by loads and changes in topology. This article puts forth a unified control framework, which, while guaranteeing such stability, allows for modular ImGs interconnecting multiple subsystems, that is, dynamic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$RLC$ </tex-math></inline-formula> lines, nonlinear constant impedance, current, power (ZIP) and exponential (EXP) loads, and inverter-based distributed generation units (DGUs) controlled with different types of primary controllers. The underlying idea of the framework is based on the equilibrium-independent passivity (EIP) of the ImG subsystems, which enables stability certificates of ImG equilibria without explicit knowledge of these equilibria. In order to render DGUs EIP, we propose a decentralized controller synthesis algorithm based on port-Hamiltonian systems (PHSs). We also show that EIP, being the key to stability, provides a general framework, which can embrace other solutions available in the literature. Furthermore, we provide a novel argument based on LaSalle’s theorem for proving asymptotic voltage and frequency stability. Finally, we analyze the impact of actuator saturation on the stability results by exploiting the inherent EIP properties of the PHS DGU model. Theoretical findings are backed up by realistic simulations based on the medium-voltage CIGRE benchmark network.

Compact and high-performance lowpass filter based on surface plasmonic polaritons waveguide

A terahertz spoof surface plasmonic polaritons waveguide with metallic rectangular spiral is proposed in the paper. By analyzing dispersion relation and electric field distribution, it is found that the proposed waveguide has a lower asymptotic frequency, a tighter localized field with 11.7 times enhancement, and a more compact size compared with the T-grooves waveguide. Based on a rectangular spiral waveguide structure, a compact and very sharp roll-off lowpass filter is investigated and experimentally verified by scaling down frequency to the microwave region. The fabricated lowpass filter has a high roll-off rate of 566 dB GHz−1, ultrahigh figure-of-merit of 43039, and compact size. Therefore, it may be applicable for various compact integrated devices and circuits in THz and microwave frequency ranges.

Asymptotic bit frequency in Fibonacci words

Abstract It is known that binary words containing no k consecutive 1s are enumerated by k-step Fibonacci numbers. In this note we discuss the expected value of a random bit in a random word of length n having this property.

A Compact Filter Based on Spoof Surface Plasmon Polariton Waveguide for Wide Stopband Suppression

An spoof surface plasmon polaritons (SSPPs) bandpass filter (BPF) supported by trident-shaped complementary grooves is proposed in this letter. Compared with the traditional rectangular-groove SSPP unit cell, the vertical size of the proposed SSPP unit cell is reduced by 40% under the condition of the same asymptotic frequency. Then, a matching feeding structure is introduced by designing microstrip-to-slotline transition (MST) and thus a low cut-off frequency can be obtained. The low cut-off frequency of the passband is determined by the MST structure and the high cut-off frequency of the passband is determined by the SSPP structure. Consequently, a BPF with controllable frequency band and wide stopband suppression is formed by the MST structure and the proposed SSPP structure. Finally, the designed BPF was fabricated and measured. Both numerical and experimental results suggest good filtering performance of the proposed BPF in the frequency band from 2.1 to 8 GHz.

A Windmill-Shaped SSPP Waveguide for High-Efficiency Microwave and Terahertz Propagation

We propose a novel type of spoof surface plasmon polariton (SSPP) waveguide based on windmill-shaped units for high-efficiency microwave and terahertz propagation. The dependence of terahertz dispersion characteristics on geometrical parameters of the proposed waveguide is detailed and investigated. Compared with the conventional comb-shaped and T-shaped SSPP waveguide units, the proposed windmill-shaped unit shows a lower asymptotic frequency and stronger field-confinement characteristics for the supported fundamental SSPP mode. To demonstrate the properties of the windmill-shaped SSPP waveguide, a tapered conversion is designed to connect the windmill-shaped SSPP waveguide and the microstrip for smooth momentum and impedance matching. The simulated results show that the whole waveguide has excellent transmission performance with S11 &lt; −10 dB and S21 &gt; −1 dB from 0 THz to 5.68 THz, as well as a large out-of-band rejection response (S21 &lt; −80 dB). Then, a scaled microwave windmill-shaped waveguide prototype is fabricated and measured. The numerical and experimental results are in good agreement, which further validates the proposed SSPP waveguide design. The proposed waveguide has excellent microwave and terahertz propagation and rejection characteristics, which may have great potential applications in various microwave and terahertz devices and circuits.

Novel high‐efficiency and ultra‐compact low‐pass filter using double‐layered spoof surface plasmon polaritons

AbstractIn this letter, a novel ultra‐compact spoof surface plasmon polaritons (SSPPs) low‐pass filter which shows a high‐efficiency transmission and an excellent out‐of‐band suppression is investigated. It consists of a pair of double‐layer SSPPs, the top layer using interdigital strip and meander‐line, and the bottom layer is metal gratings of fish‐bone shape. The vast advantages of the proposed SSPPs structure in lower asymptotic frequency mode compared with traditional SSPPs structure with the same size enables the proposed low‐pass filter to be more miniaturized. The dimensions of the miniaturized structure are 0.75λ0 × 0.1λ0 (λ0 is the wavelength corresponding to the central operating frequency). The high‐efficient mode conversion is achieved by gradient meander‐line lengths. Moreover, we also investigate the transmission performance of the proposed structure when it is conformal. To validate the design concept, the prototype of a straight and bend low‐pass filter has been manufactured and measured. The experimental results of the fabricated sample agree with the simulation results well, in which the insertion loss is less than 0.5 dB, the reflection coefficient less than −15 dB, and excellent out‐of‐band rejection of the attenuation is greater than 30 ‐dB, which proves the design validity. The proposed ultra‐compact SSPPs structure may have great potential applications in miniaturized integrated circuits in the microwave and terahertz (THz) frequencies.

Novel ELC-like and Z-shaped plasmonic waveguides to reach ultra-strong field confinements

In this paper, two novel waveguides with ELC like-shaped and Z-shaped grooves have been proposed to achieve highly efficient and strongly confined spoof surface plasmon polaritons (SSPPs) propagation. Low-dispersion bands can be realized by such structures with tight field confinement of SSPPs, resulting in size miniaturization of the proposed waveguides. Specifically, our method yields deep physical insight into the effect that the geometrically induced modifications of the supporting structure has on the dispersion properties and field confinement capabilities of SSPPs. In comparison, SSPP waveguide results presented in Aziz (2021 Results Opt. 5 100116) are given which is regarded to have stronger SSPPs field confinement as compared to previously reported different grooves shapes based SSPP waveguides. It is found that the dispersion and waveguide propagation characteristics can be directly manipulated by varying the geometrical parameters of the horizontal and slanted slits of Z-shaped and ELC-like shaped plasmonic waveguides without increasing the lateral dimension of the waveguides. Based on this waveguiding scheme, the proposed waveguides exhibit much lower asymptotic frequency of the dispersion relation and even tighter SSPPs field confinement than I-shaped plasmonic waveguide. Then, broadband transitions with a tapered metallic strip and an array of graded height ELC-like and Z-shaped units with good impedance matching and high mode conversion efficiency are designed. Fully controlled field enhancement functionality has been performed, by using such metamaterial particles in the form of grooves, decorated in SSPP waveguide. Simulated results have demonstrated that the proposed SSPP waveguides have much stronger field confinement than the highly efficient I-shaped grooves based SSPP waveguide. The proposed waveguides can be a significant contribution towards the advancement of plasmonic functional devices and integrated circuits in microwave frequencies.

Seismic signature of electron degeneracy in the core of red giants: Hints for mass transfer between close red-giant companions

The detection of mixed modes in red giants with space missions COROT and Kepler has revealed their deep internal structure. These modes allow us to characterize the pattern of pressure modes (through the measurement of their asymptotic frequency separation Δν) and the pattern of gravity modes (through the determination of their asymptotic period spacing ΔΠ1). It has been shown that red giant branch (RGB) stars regroup on a well-defined sequence in the Δν − ΔΠ1 plane. Our first goal is to theoretically explain the features of this sequence and understand how it can be used to probe the interiors of red giants. Using a grid of red giant models computed with MESA, we demonstrate that red giants join the Δν − ΔΠ1 sequence whenever electron degeneracy becomes strong in the core. We argue that this can be used to estimate the central densities of these stars, and potentially to measure the amount of core overshooting during the main sequence part of the evolution. We also investigate a puzzling subsample of red giants that are located below the RGB sequence, in contradiction with stellar evolution models. After checking the measurements of the asymptotic period spacing for these stars, we show that they are mainly intermediate-mass red giants. This is doubly peculiar because these stars should have nondegenerate cores and they are expected to be located well above the RGB sequence. We show that these peculiarities are well accounted for if these stars result from the interaction between two low-mass (M ≲ 2 M⊙) close companions during the red giant branch phase. If the secondary component has already developed a degenerate core before mass transfer begins, it becomes an intermediate-mass giant with a degenerate core. The secondary star is then located below the degenerate sequence, which is in agreement with the observations.

Design of a Differential Spoof Surface Plasmon Sensor for Dielectric Sensing and Defect Detection

A new design of a highly confined Spoof Surface Plasmon (SSP) line splitter-based differential phase sensor is presented for the THz frequency region. The position, orientation and shape of the stem cells are properly optimized to realize highly confined, compact SSP design. The designed differential splitter facilitates the relative phase difference between the transmission coefficient phase corresponding to the reference arm and the test arm. The dispersion characteristic i.e, asymptotic frequency response of stem shaped unit cell founds to be quite improved over its conventional counterpart. The incorporated splitter shaped topology provides a symmetric differential sensing environment in both THz and MW region. The proposed sensor facilitates quite high sensitivity due to its improved electric field confinement than that of the microstrip counterpart. The obtained phase difference changes with a relative change in the effective dielectric constant of the test sample at a specified frequency. The design is then scaled accordingly, and the prototype is fabricated to validate its defect detection performance in the microwave (MW) frequency region. In the present scenario, FR-4 samples (with thickness 0.8 mm, 1.6 mm) having two different defect profiles are considered for experimental validation. It is found that the developed sensor can produce substantial phase difference even for the small presence of the defect. In the present case, the measured average phase differences corresponding to the FR-4 sample having 1 mm void distributed uniformly with an interspacing of 1.25 mm, are 74.02° and 92.35° and 2.5 mm spacing between the same void gives phase difference of 31.18° and 40.26° for 0.8 mm and 1.6 mm sample thickness, respectively over the frequency range of 8–12 GHz.