Mode Index Research Articles

Seasonal forecasting of East African short rains

The variability of East African short rains (October–December) has profound socioeconomic and environmental impacts on the region, making accurate seasonal rainfall predictions essential. We evaluated the predictability of East African short rains using model ensembles from the multi-system seasonal retrospective forecasts from the Copernicus Climate Change Service (C3S). We assess the prediction skill for 1- to 5-month lead times using forecasts initialized in September for each year from 1993 to 2016. Although most models exhibit significant mean rainfall biases, they generally show skill in predicting OND (October–December) precipitation anomalies across much of East Africa. However, skill is low or absent in some northern and western parts of the focus area. Along the East African coasts near Somalia and over parts of the western Indian Ocean, models demonstrate skill throughout the late winter (up to December–February), likely due to the persistence of sea surface temperature anomalies in the western Indian Ocean. Years when models consistently outperform persistence forecasts typically align with the mature phases of El Niño Southern Oscillation (ENSO) and/or Indian Ocean Dipole (IOD). This latter mode, when tracked using the Dipole Mode Index, is generally able to predict the sign of the rainfall anomaly in all models. Despite East Africa’s proximity to the west pole of the IOD, the correlation between short rains and IOD maximizes when both east and west are considered. This finding confirms previous studies based on observational datasets, which indicate that broader-scale IOD variability associated with changes in the Walker Circulation, rather than local SST fluctuations, is the primary driver behind East African rainfall.

Selective Passive Tuning of Cavity Resonance by Mode Index Engineering of the Partial Length of a Cavity

Selective Passive Tuning of Cavity Resonance by Mode Index Engineering of the Partial Length of a Cavity

A physics-aware neural network for effective refractive index prediction of photonic waveguides

Neural network (NN)—based surrogates have been effectively used for modeling dynamic systems, including photonic devices. However, black-box data-driven modeling approaches significantly suffer from performance reduction in high-dimensional spaces.As a remedy, we propose a novel physics-aware NN architecture for the effective index prediction of photonic strip waveguides. The model learns a translation between the strip waveguide and an equivalent infinite slab waveguide by employing physical loss terms in the loss function. The proposed method exhibits significantly lower error, with more than 50% reduction, compared to a black-box NN and a variational method. Because of its physical basis, the proposed NN can predict field distributions in rectangular waveguides and the effective indices of higher-order modes.

Predicting early cessation of exclusive breastfeeding using machine learning techniques.

Identification of mother-infant pairs predisposed to early cessation of exclusive breastfeeding is important for delivering targeted support. Machine learning techniques enable development of transparent prediction models that enhance clinical applicability. We aimed to develop and validate two models to predict cessation of exclusive breastfeeding within one month among infants born after 35 weeks gestation using machine learning techniques. Utilizing a nationwide dataset from Statistics Denmark, including infants born between the 1st of January 2014 and the 31st of December 2015, we employed random forest machine learning to develop two predictive models. The first model included 11 well-established factors associated with cessation of exclusive breastfeeding within one month. The second model was expanded to include 21 additional factors associated with complications during pregnancy and delivery that potentially impede breastfeeding. Feature importance was applied to elucidate the factors driving model predictions. The dataset comprised 110,206 infants and 106,835 mothers. The first model predicted cessation of exclusive breastfeeding within one month with an area under the receiver operating curve of 62.0% (95% confidence interval 61.3% - 62.7%) and an accuracy of 60.4% (95% confidence interval 59.8% - 61.0%). The second model predicted cessation of exclusive breastfeeding within one month with an area under the receiver operating curve of 62.2% (95% confidence interval 61.5% - 62.9%) and an accuracy of 60.0% (95% confidence interval 59.3% - 60.6%). In both models, birthplace, maternal education, delivery mode, and maternal body mass index were the most important factors influencing the overall model performance. The two models could not accurately predict cessation of exclusive breastfeeding within one month among infants born after 35 weeks gestation. Contrary to our expectations, including additional factors in the model did not increase model performance.

The Semidiurnal Tidal Response of the Low Latitude Ionosphere to Northern Hemisphere Polar Vortex Strength (2020–2023) From COSMIC‐2 Global Ionospheric Specification

AbstractThis paper investigates the day‐to‐day global tidal variability in the ionosphere/thermosphere system due to fluctuations in the strength of the northern hemisphere stratospheric polar vortex. Using COSMIC‐2 (Constellation Observing System for Meteorology, Ionosphere, and Climate‐2) Global Ionospheric Specification data, ionospheric tides are derived, with the Northern Annular Mode (NAM) index indicating polar vortex variability. The semidiurnal migrating solar tide shows the largest response, with relative electron density in the F‐region significantly higher ( 60%) under a weak vortex and lower ( 20%) under a strong vortex, correlated at −0.58 with the NAM index. The study compares solar/geomagnetic forcing and vortex impacts using SD‐WACCM‐X (Specified Dynamics Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension) model runs. Findings suggest tidal modulation of the E‐region dynamo as the coupling mechanism. Our study can potentially improve ionospheric space weather predictability because the NAM index can be known a few days in advance.

Sources of low-frequency δ18O variability in coastal ice cores from Dronning Maud Land (Antarctica)

The low-frequency variability of the δ18O recorded in ice cores (FK17 and TIR18) recently drilled at two different locations in Dronning Maud Land (Antarctica), is investigated using multi-taper spectral method and singular spectrum analysis. Multiple dominant peaks emerge in these records with periods between 3 and 20 years. The two sites show distinct spectral signatures, despite their relative proximity in space (about 100 km apart), suggesting that different processes are involved in generating the variability at these two sites. In order to clarify which processes are acting on δ18O at these two locations, the impact of several climate indices as well as sea ice area is investigated using a causal method, known as the Liang-Kleeman rate of information transfer. The analysis of the origin of this low-frequency variability from external sources reveals that the El Niño-Southern Oscillation (ENSO), the Pacific Decadal Oscillation (PDO), the Southern Annular Mode (SAM), the Dipole Mode Index (DMI) and the sea ice area display important causal influences on δ18O at FK17. For TIR18, the main influences are from ENSO, PDO, DMI, the sea ice area, and the Atlantic Multidecadal Oscillation (AMO), revealing the complexity of the interactions in Dronning Maud Land. The two locations share several drivers, but also show local specificities potentially linked to ocean proximity and differences in air mass trajectories.

Analyzing Drought Propagation and Its Influential Factors in the Upper Nan Watershed, Thailand

Understanding drought propagation is essential for effective water resource management. This study employs an innovative approach to examine the transition from meteorological drought (MD) to hydrological drought (HD) in the Upper Nan Watershed (UNW), Thailand, using the standardized precipitation evapotranspiration index (SPEI) and standardized streamflow index (SSI). Cross-wavelet transform (XWT) and Pearson’s correlation analyses reveal a significant positive correlation between MD and HD, with the drought propagation time (DPT) ranging from 2 to 5 months, notably shorter during the dry season. The eastern UNW (Zone I) has the longest DPT, while the western UNW (Zone III) has the shortest. This study is distinguished by its integration of global teleconnection factors, such as El Niño-Southern Oscillation (ENSO), the Dipole Mode Index (DMI), and Pacific Decadal Oscillation (PDO), alongside local factors like climate, slope, and watershed morphometry. This dual focus provides a comprehensive analysis of drought dynamics, enhancing the understanding of drought propagation and its complexities. The integration of global and local influences provides insights applicable across diverse water resource management contexts. It highlights the critical role of forests in regulating water flow and extending the DPT, emphasizing the need for forest conservation and land use regulation in the headwaters. Despite challenges associated with highland meteorological data, findings offer improvements to existing drought monitoring and early warning systems, underscoring the importance of combining global and local factors in effective drought management strategies.

Role of QBO and MJO in Sudden Stratospheric Warmings: A Case Study

The impact of the quasi-biennial oscillation (QBO) and Madden–Julian oscillation (MJO) on the dynamics of major sudden stratospheric warmings (SSWs) observed in the winters of 2018, 2019, and 2021 is investigated. Using data from the MERRA-2 reanalysis, we analyze the daily mean variability of critical atmospheric parameters at the 10 hPa level, including zonal mean polar cap temperature, zonal mean zonal wind, and the amplitudes of planetary waves 1 and 2. The results reveal dramatic increases in polar cap temperature and significant wind reversals during the SSW events, particularly in 2018. The analysis of planetary wave (PW) amplitudes demonstrates intensified wave activity coinciding with the onset of SSWs, underscoring the pivotal role of PWs in these stratospheric disruptions. Further examination of outgoing long-wave radiation (OLR) anomalies highlights the influence of QBO phases on tropical convection patterns. During westerly QBO (w-QBO) phases, enhanced convective activity is observed in the western Pacific, whereas the easterly QBO (e-QBO) phase shifts convection patterns to the maritime continent and central Pacific. This modulation by QBO phases influences the MJO’s role during SSWs, affecting tropical and extra-tropical weather patterns. The day-altitude variability of upward heat flux reveals distinct spatiotemporal patterns, with pronounced warming in the polar regions and mixed heat flux patterns in low latitudes. The differences observed between the SSWs of 2017–2018 and 2018–2019 are likely related to the varying QBO phases, emphasizing the complexity of heat flux dynamics during these events. The northern annular mode (NAM) index analysis shows varied responses to SSWs, with stronger negative anomalies observed during the e-QBO phase compared to the w-QBO phases. This variability highlights the significant role of the QBO in shaping the stratospheric and tropospheric responses to SSWs, impacting surface weather patterns and the persistence of stratospheric anomalies. Overall, the study demonstrates the intricate interactions between stratospheric dynamics, QBO, and MJO during major SSW events, providing insights into the broader implications of these atmospheric phenomena on global weather patterns.

Plastic Behaviour Buffers Climate Variability in the Wandering Albatross.

Climate change has marked effects on global weather patterns and oceanic systems, impacting animal behaviour and fitness in potentially profound ways. Despite this, we lack detailed information about species' responses to climatic variation. Using an 11-year tracking dataset of over 300 individual birds, we explore the consequences of variation in the southern annular mode (SAM) and southern oscillation index (SOI) for individual behaviour and fitness in wandering albatrosses Diomedea exulans breeding in the Southern Indian Ocean. Our results reveal distinct responses between males and females to climatic variation that align with the impacts of each climatic index on the distinct foraging ranges of each sex. In positive SAM phases, linked to poorer foraging conditions in female ranges and better conditions in male ranges, females exhibited behaviour consistent with reduced foraging success: that is, fewer prey capture attempts and more movement between feeding patches. Males, on the other hand, showed no behavioural change. During positive SOI phases, associated with good foraging conditions in both male and female foraging ranges, both sexes showed evidence of more successful foraging, with birds engaging in more search behaviour, and taking shorter trips with fewer prey capture attempts, together indicating increased food intake per unit time. We found limited evidence for a role of individual variation, as measured through differences in personality, suggesting that plastic responses to climate are sufficiently important so as to obscure inter-individual variation. Supporting this was the finding that individual breeding success was unaffected by climatic variation, suggesting that plastic foraging behaviour allows albatrosses to mitigate climate impacts and maintain reproductive output.

Modeling and optimization of photonic integrated Silicon-LiNbO3 hybrid interferometer for E-S-C-L wavelength band

Abstract The Silicon on Insulator (SOI) is a potential technology for thin-film optical waveguide, enabling the design of optical interconnects, including modulators and interferometers. The manuscript presents the broadband modulator for phase and intensity modulation. The nanoscale optimized interferometric modulator utilizes Silicon (Si) and Electro-optic material Lithium Niobate (LiNbO3) as the guiding material to work in terahertz regime, without any bends in the structure. Optimization of the structure is validated by the evaluation of the confinement factor at the operational wavelength of 1550 nm using Finite Element Method (FEM) based simulation. To excite the SOI interferometric modulator, an external RF signal with a maximum amplitude of 5 V is used. The hybrid structure of Si and LiNbO3-based modulators shows the electro-optic phenomenon caused by nonlinearities, namely the Pockels effect and Kerr effect, which in turn changes the effective mode index, providing π phase shift along with −0.92 dB/cm absorption loss, 117 μm electrode length at V π Volts and 265 nm 3dB optical bandwidth covering the E-S-C-L optical bands. The device footprint calculated is 667 μm2, whereas the active region footprint is ∼46.8 μm2.

Ocean-atmosphere interrelation of Bjerknes feedback loop associated with Indian Ocean Dipole retrieved from altimeter radar and microwave radiometer of satellite altimetry

ABSTRACT In the past few decades, satellite altimetry has surpassed tremendous achievements in examining the mesoscale of ocean dynamics. Recently, new potential of the satellite in observing the variability of climate phenomena through atmospheric medium has been unlocked. As it has been ascertained that satellite altimetry is not only outstanding in monitoring ocean dynamics but also in observing atmospheric variability, we intuitively propose a hypothesis that satellite altimetry is reliable in monitoring Bjerknes feedback: a feedback loop that involves interactions between atmosphere and oceans. Thus, the aim of this study is to determine the capability of satellite altimetry in observing Bjerknes feedback through Precipitable Water Vapour (PWV) and Sea Level Anomaly (SLA) during the anomalous climate mode of Indian Ocean Dipole (IOD). The results signify convincing arguments as both PWV and SLA indexes are highly correlated with Dipole Mode Index (DMI), particularly in the western region of the Indian Ocean, which have correlations of 0.67 and 0.62, respectively. The correlations of PWV and SLA indexes are also significantly high: 0.73 and 0.69 in western and eastern regions, respectively. The Principal Component Analysis (PCA) results are also convincing as the spatial pattern of primary (PC1) and secondary (PC2) components of both PWV and SLA are associated with positive and negative IOD, respectively. The temporal patterns of PC1 for PWV and SLA have relatively high correlation with positive IOD. The substantially high temporal correlation (0.81) between PWV and SLA PC1 has reinforced the confidence in the capability of satellite altimetry in observing the Bjerknes feedback.

Impact Mechanisms of Different Ecological Forest Restoration Modes on Soil Microbial Diversity and Community Structure in Loess Hilly Areas

The Loess Plateau, with a fragile ecological environment, is one of the most serious water- and soil-eroded regions in the world, which has been improved by large-scale projects involving returning farmland to forest and grassland. This work is mainly aimed at exploring a more reasonable and efficient ecological forest restoration mode and revealing synergistic restoration mechanisms. This study sampled typical Loess Plateau areas and designed the restoration modes for pure forests of Armeniaca sibirica L. (AR), Amygdalus davidiana (Carrière) de Vos ex Henry. (AM), Medicago sativa L. (MS), and mixed forests of apricot–peach–alfalfa (AR&AM&MS), using abandoned land (AL) as a control treatment. The effects of these modes on the physical and chemical properties and enzyme activities of various soils were investigated in detail. Moreover, the soil microbial diversity and community structure, functional gene diversity, and differences in the restoration modes were deeply analyzed by meta-genomic sequencing technology, and the inherent driving correlation and mechanisms among these indicators were discussed. The results showed that the soil water content and porosity of the AR, AM, and AR&AM&MS treatments increased significantly, while the bulk density decreased significantly, compared with AL. Moreover, the total carbon, total nitrogen, nitrate nitrogen, total phosphorus, available phosphorus, total potassium, and available potassium contents of the AR&AM&MS restoration mode increased significantly. Compared to CK, there was no significant change in the catalase content of pure forest and mixed forest; however, the contents of urease, phosphatase, sucrase, B-glycanase, and N-acetylglucosaminidase in the restoration mode of the mixed forest all increased significantly. The species diversity index of the restoration modes is similar, and the dominant bacteria in soil microorganisms include Proteobacteria, Acidobacteria, Actinobacteria, Bacteroidetes, and Gemmatimonadetes. The mixed forest restoration mode had the highest microbial abundance. The functional gene diversity of the different restoration modes was also similar, including kegg genes, eggNOG genes, and carbohydrate enzymes. The functional genes of the mixed forest restoration mode were the most abundant, and their restoration mechanism was related to the coupling effect of soil–forest grass. After evaluation, the restoration mode of mixed forest was superior to that of pure forest or pure grass. This is attributed to the fact that the mode can improve soil structure, retain soil moisture, enhance soil enzyme activity, optimize soil microbial community structure, and improve microbial diversity and functional gene activity. This provides key data for the restoration of fragile ecological areas, and the promotion of sustainable management of forests and grass in hilly areas of the Loess Plateau.

Silicon‐Nitride‐Integrated Hybrid Optical Fibers: A New Platform for Functional Photonics

AbstractHybrid optical fibers that integrate exotic materials within more traditional silica glass architectures open a route for the development of highly functional all‐fiber photonic systems. Here, a compact hybrid optical fiber platform is reported formed by depositing a silicon nitride (SiNx ‐ nitride‐rich) nanolayer onto the surface of fused‐silica microfibers via plasma‐enhanced chemical vapor deposition. The SiNx thickness can be precisely tuned over a range of tens of nanometers, while maintaining an ultra‐smooth deposition surface, allowing for tunable coupling between the modes guided predominantly in the nanolayer and the fiber core. The effective indices of the hybrid modes display an anti‐crossing behavior under resonant conditions, resulting in a rich dispersion landscape that can be tailored via adjusting the SiNx thickness. By fabricating a SiNx‐silica hybrid microfiber with precise dispersion engineering and a low insertion loss, a flat supercontinuum spectrum spanning >1.5 octaves (−20 dB level) has been generated. The results demonstrate that SiNx‐silica hybrid microfibers can offer a unique combination of broadband transmission and wide tunablity of the mode properties, while still retaining the benefits of robust integration with conventional silica glass fiber networks, providing a rich playground for hybrid fiber‐based photonic systems.

Ultra-compact broadband polarizing beam splitter a using tilted nano-grating-based bridge waveguide

An ultra-compact broadband silicon polarizing beam splitter is demonstrated with the assistance of a tilted nano-grating-based bridge waveguide. By tilting the grating elements to gain polarization control over the anisotropy of the equivalent medium, a new design freedom to engineer the effective mode index and circumvent small variable duty cycles can be adopted to benefit the device fabrication. The transverse magnetic (TM) light can be resonantly coupled to the cross port, while the transverse-electric (TE) light can almost completely output from the through port. The length of the coupling region is only 13.6 µm, which can realize an extinction ratio of 30.57 dB for TM light or 31.15 dB for TE light at a 1550-nm wavelength theoretically. The fabricated device can achieve an extinction ratio of 29.35 dB for TM or 22.6 dB for TE light with a low excess loss, and an extinction ratio of more than 20 dB can be realized in the wavelength range from 1525 to 1610 nm for both polarizations. The presented device also shows a good fabrication tolerance, which would facilitate its practical applications in commercial photonic integrated circuits.

Closed-form eigensolutions and exact complex mode superposition method for non-proportionally rate-independent damped systems

PurposeThe main objectives of this paper are to develop a novel perturbation method (PM) to solve the complex-orthogonal eigenvalue problem and further propose an exact complex mode superposition method (CMSM) for the non-proportionally rate-independent damped systems.Design/methodology/approachA novel PM is developed to solve the eigenvalue problem. The PM reduced the N-order generalized complex eigenvalue problem into a set of n algebraic equations by the perturbation theory. The convergence and accuracy of the PM are demonstrated by several numerical examples. Further, an exact CMSM is presented. The influences of the imaginary part response of the modal coordinate and the off-diagonal elements of the damping matrix as well as the modal truncation on the solution by CMSM are discussed to illustrate the effectiveness of the developed CMSM.FindingsThe eigenvalues obtained by PM would converge to the exact ones with the increase of the modal numbers. For seismic response, the influence of the imaginary part solutions of the modal coordinate would increase with the increase of the coupling factor. The contribution of higher modes to acceleration response is greater than that to the displacement. The cumulative mode contribution coefficient of acceleration is developed to estimate the numbers of the complex modes for the acceleration seismic response by the CMSM.Originality/value1. An eigenvalue perturbation method for a rate-independent damped system is proposed. 2. PM is carried out by the real mode and accomplishes the reduction of the matrix. 3. CMSM is established for rate-independent damped systems. 4. CMSM considers the effect of imaginary part solutions of the modal coordinate. 5. Modal truncation index is developed to estimate the complex mode number for CMSM.

Modulation of hybrid plasmon phonon polaritons mode in circular cylindrical three-layer graphene waveguide

In this present research article, we have investigated analytically the characteristics of the fundamental mode of hybrid surface plasmon phonon polariton (HSPPhPs) mode in a circular cylindrical three-layer graphene (CTLG) waveguide structure. The dispersion equation of HSPPhPs is derived by using Maxwell’s equations and continuity conditions of tangential components of electric and magnetic fields in cylindrical geometry. The dispersion curve has been illustrated and thoroughly examined in relation to the effects of temperature and chemical potential (μc) of graphene, as well as variations in the thickness of silicon dioxide (SiO2) and hexagonal boron nitride (hBN) layers, and found that in the presence of hBN, the effective mode index exhibits hyperbolic behavior with wave number. Up to the first Reststrahlen band (∼830.57 cm⁻¹), it varies slightly with graphene temperature; increasing graphene's (μc) lowers the index, while a thicker hBN layer reduces it, whereas the index increases with SiO₂ layer thickness. Also, we looked at how the CTLG waveguide structure is affected by the electric field distribution, phase speed, and propagation length.

Reconfiguration of functional brain network organization and dynamics with changing cognitive demands in children with attention-deficit/hyperactivity disorder

BackgroundThe pathophysiology of attention-deficit/hyperactivity disorder (ADHD) is characterized by atypical brain network organization and dynamics. Although functional brain networks adaptively reconfigure across cognitive contexts, previous studies have largely focused on network dysfunction during the resting-state. This preliminary study examined how functional brain network organization and dynamics flexibly reconfigure across rest and two cognitive control tasks with different cognitive demands in 30 children with ADHD and 36 typically developing (TD) children (8-12 years). MethodsWe leveraged graph theoretical analyses to interrogate the segregation (modularity, within-module degree) and integration (global efficiency, node dissociation index) of fronto-parietal, cingulo-opercular/salience, default mode, somatomotor, and visual networks. We also conducted edge timeseries analyses to quantify connectivity dynamics within and between these networks. ResultsAcross resting and task-based states, children with ADHD demonstrated significantly lower whole-graph modularity and greater node dissociation index between default mode and visual networks. Further, a significant task-by-diagnosis interaction was observed for fronto-parietal network within-module degree, which decreased from rest to task in children with ADHD but increased in TD children. Finally, children with ADHD displayed significantly more dynamic connectivity within and across cingulo-opercular/salience, default mode, and somatomotor networks, especially during task performance. Exploratory analyses revealed associations between network dynamics, cognitive performance, and ADHD symptoms. ConclusionsBy integrating static and dynamic network analyses across changing cognitive demands, this study provides novel insight into how context-specific, context-general, and timescale-dependent network connectivity is altered in children with ADHD. Our findings highlight the involvement and clinical relevance of both association and sensory/motor systems in ADHD.

A New ENSO Statistical Prediction Model considering Extratropical Effects and Its Application to the Prediction of the 2015/16 El Niño Event

Abstract Understanding the evolution mechanisms and providing accurate predictions for ENSO continue to be a challenge for the research community. In recent years, some studies pointed out that the extratropical Pacific atmosphere and ocean variations may affect the evolution of ENSO, which is different from the classical theoretical framework of ENSO. In this study, by combining tropical atmosphere and ocean predictors with extratropical precursors, an ENSO statistical prediction model was constructed. It was found that including extratropical predictors can significantly enhance the prediction skills of the model. The Victoria mode index (VMI) can significantly improve the prediction skills in the 10–12-month lead model and can effectively help the model cross the spring predictability barrier (SPB). When predicting 6–8 months in advance, the South Pacific Oscillation index (SPOI) can improve the prediction skills, but the degree of the improvement is relatively small. The model was also applied to conduct prediction experiments on the 2015/16 El Niño event. It was found that the model can successfully predict the event nearly 1 year in advance, mainly due to the inclusion of the VMI. Due to the interdecadal variation in the relationship between predictors and ENSO, when constructing the 6-month lead model, using data since 2000 and replacing the 6-month lead VMI with a 10-month lead, one can effectively improve the model’s prediction skills, especially in predicting the intensity of 2015/16 El Niño events, which has shown significant improvement.

Electrically tunable graded photonic crystal lens based on graphene plasmons.

Controlling the nonlinear relationship between surface plasmon polariton (SPP) mode index and chemical potential of graphene can be used in the field of active transformation optics. Here, we propose an electrically tunable 2D Graded Photonic Crystal (GPC) lens based on graphene SPP platform. Our platform comprises a graphene monolayer integrated into a back-gated structure with nano-patterned gate insulators. When the chemical potential of the graphene surface is designed to operate in the nonlinear region, the designed GPC lens can be continuously transformed between a Maxwell's fish-eye lens and a Luneburg lens by tuning the gate voltage. The range of the lens background chemical potential for allowing this transformation is systematically studied. To compensate for the significant errors inherent in the conventional effective medium theory (EMT) during the homogenization of photonic crystals (PCs), we propose a generalized effective medium theory (GEMT). The validity and accuracy of this approach are verified through comparisons with true values (based on rigorous eigenvalue solutions) and EMT values. Due to its advantages of on-site controls and easy fabrication characteristics, the proposed graphene GPC provides a new way for practical on-chip light manipulation.

Quadratic Frequency Dispersion in the Oscillations of Intermediate-mass Stars

Asteroseismology, the study of stellar vibration, has met with great success, shedding light on stellar interior structure, rotation, and magnetism. Prominently known as δ Scutis, the intermediate-mass main-sequence oscillators that often exhibit rapid rotation and possess complex internal stratification are important targets of asteroseismic study. δ Scuti pulsations are driven by the κ (opacity) mechanism, resulting in a set of acoustic modes that can be challenging to interpret. Here, we apply machine learning to identify new patterns in the pulsation frequencies of δ Scuti stars, discovering resonances spaced according to quadratic functions of integer mode indices. This unusual connection between mode frequencies and indices suggests that rotational influence may play an important role in determining the frequencies of these acoustic oscillations.