Period Spacing Research Articles

Well‐posedness of degenerate fractional differential equations with finite delay in complex Banach spaces

AbstractWe study the well‐posedness of the degenerate fractional differential equations with finite delay: on Lebesgue–Bochner spaces and periodic Besov spaces , where and are closed linear operators in a complex Banach space satisfying , and are fixed, when , and the delay operator is a bounded linear operator from (resp. ) into . Using known operator‐valued Fourier multiplier theorems on and , we completely characterize the ‐well‐posedness and the ‐well‐posedness of above equations. We also give concrete examples that our abstract results may be applied.

Asteroseismic g-mode period spacings in strongly magnetic rotating stars

ABSTRACT Strong magnetic fields are expected to significantly modify the pulsation frequencies of waves propagating in the cores of red giants or in the radiative envelopes of intermediate- and high-mass main-sequence stars. We calculate the g-mode frequencies of stars with magnetic dipole fields which are aligned with their rotational axes, treating both the Lorentz and Coriolis forces non-perturbatively. We provide a compact asymptotic formula for the g-mode period spacing and universally find that strong magnetism decreases this period spacing substantially more than is predicted by perturbation theory. These results are validated with explicit numerical mode calculations for realistic stellar models. The approach we present is highly versatile: once the eigenvalues λ of a certain differential operator are pre-computed as a function of the magnetogravity and rotational frequencies (in units of the mode frequency), the non-perturbative impact of the Coriolis and Lorentz forces is understood under a broad domain of validity and is readily incorporated into asteroseismic modelling.

Inferring Coupling Strengths of Mixed-mode Oscillations in Red Giant Stars Using Deep Learning

Asteroseismology is a powerful tool that may be applied to shed light on stellar interiors and stellar evolution. Mixed modes, behaving like acoustic waves in the envelope and buoyancy modes in the core, are remarkable because they allow for probing the radiative cores and evanescent zones of red giant stars. Here, we have developed a neural network that can accurately infer the coupling strength, a parameter related to the size of the evanescent zone, of solar-like stars in ∼5 ms. In comparison with existing methods, we found that only ∼43% of inferences were in agreement with a difference less than 0.03 in a sample of ∼1700 Kepler red giants. To understand the origin of these differences, we analyzed a few of these stars using independent techniques such as the Monte Carlo Markov Chain method and echelle diagrams. Through our analysis, we discovered that these alternate techniques are supportive of the neural-net inferences. We also demonstrate that the network can be used to yield estimates of coupling strength and period spacing in stars with structural discontinuities. Our findings suggest that the rate of decline in the coupling strength in the red giant branch is greater than previously believed. These results are in closer agreement with calculations of stellar-evolution models than prior estimates, further underscoring the remarkable success of stellar evolution theory and computation. Additionally, we show that the uncertainty in measuring period spacing increases rapidly with diminishing coupling strength.

Realization and topological properties of third-order exceptional lines embedded in exceptional surfaces

As the counterpart of Hermitian nodal structures, the geometry formed by exceptional points (EPs), such as exceptional lines (ELs), entails intriguing spectral topology. We report the experimental realization of order-3 exceptional lines (EL3) that are entirely embedded in order-2 exceptional surfaces (ES2) in a three-dimensional periodic synthetic momentum space. The EL3 and the concomitant ES2, together with the topology of the underlying space, prohibit the evaluation of their topology in the eigenvalue manifold by prevailing topological characterization methods. We use a winding number associated with the resultants of the Hamiltonian. This resultant winding number can be chosen to detect only the EL3 but ignores the ES2, allowing the diagnosis of the topological currents carried by the EL3, which enables the prediction of their evolution under perturbations. We further reveal the connection between the intersection multiplicity of the resultants and the winding of the resultant field around the EPs and generalize the approach for detecting and topologically characterizing higher-order EPs. Our work exemplifies the unprecedented topology of higher-order exceptional geometries and may inspire new non-Hermitian topological applications.

Data-driven method for optimized supply temperatures in residential buildings

The energy required for space heating amounts to approximately 68% of the total energy demand of existing buildings in Europe. The heat requirement of a building, and thus its carbon emission, can be lowered by optimizing the supply and return temperature of the heating system. A lower supply temperature enables a wider variety of transition pathways towards sustainable heating with reduced carbon emissions. However, the minimum supply temperature that guarantees acceptable indoor temperatures in existing dwellings during design weather conditions is still unknown. In this study, we determine the minimum supply temperature by fitting a 2 R–2C model to hourly measurement data. The measurement data is obtained from a representative set of 220 existing gas-fired dwellings in the Netherlands. The heating system of each dwelling was equipped with a pulse flowmeter and temperature sensors on both the supply and return side. Additionally, data was collected from the thermostat in the main living room and the gas boiler. The data was supplemented with weather data from a nearby weather station. The data-driven model shows that the minimum supply temperature can be lower than 55 °C for 60% of the dwellings during design weather conditions (i.e., −10 °C in the Netherlands). Moreover, the minimum supply temperature is poorly correlated with general building properties, such as the building typology, construction period or specific annual space heating demand (kWh/(m2yr)). On the contrary, the ratio between the required and installed heat output of the radiators in the heating system is a promising parameter to predict the minimum design supply temperature of an individual dwelling that guarantees an acceptable indoor temperature during design weather conditions.

A Quasi Universal Matalon-Packter Law for a Periodically Precipitating System of Iron(II) Hydroxide Involving Volumes and Concentrations of the Invading Electrolyte.

The Matalon-Packter (MP) empirical law of periodically precipitating (Liesegang phenomenon) systems under non-equilibrium conditions describes the dependence of the periodicity (spacing coefficient) on the initial concentration of the outer electrolyte. We aim to present the MP law in a more generalized form using a realistic approach wherein mass transfer in the gel column plays a role instead of the initial concentrations. This work is an attempt to make such progress. The Liesegang bands of Fe(OH)2 were studied by varying the reservoir concentrations (c) and volumes (V) of the outer electrolyte (NH4OH). The spacing coefficient was found to be a function of the volume and concentration of the outer electrolyte. It was observed that the amount of chemical substance (cV) and the average molar diffusion flux (Fdiff) of the ions of the outer electrolyte could be a unifying quantity for expressing the MP law instead of the initial electrolyte concentration. We demonstrated that a single model is possible for a system, irrespective of the V value. Three different volumes were employed, and the calculations were performed under small, intermediate, and larger reservoir volume regimes. Interestingly, a single model was observed for the diffusion coefficients for all of the Fdiff values.

Asteroseismological analysis of the polluted ZZ Ceti star G 29 − 38 with TESS

ABSTRACT G 29 − 38 (TIC 422526868) is one of the brightest (V = 13.1) and closest (d = 17.51 pc) pulsating white dwarfs with a hydrogen-rich atmosphere (DAV/ZZ Ceti class). It was observed by the TESS spacecraft in sectors 42 and 56. The atmosphere of G 29 − 38 is polluted by heavy elements that are expected to sink out of visible layers on short time-scales. The photometric TESS data set spans ∼51 d in total, and from this, we identified 56 significant pulsation frequencies, that include rotational frequency multiplets. In addition, we identified 30 combination frequencies in each sector. The oscillation frequencies that we found are associated with g-mode pulsations, with periods spanning from ∼ 260 to ∼ 1400 s. We identified rotational frequency triplets with a mean separation δνℓ = 1 of 4.67 μHz and a quintuplet with a mean separation δνℓ = 2 of 6.67 μHz, from which we estimated a rotation period of about 1.35 ± 0.1 d. We determined a constant period spacing of 41.20 s for ℓ = 1 modes and 22.58 s for ℓ = 2 modes. We performed period-to-period fit analyses and found an asteroseismological model with M⋆/M⊙ = 0.632 ± 0.03, $T_{\rm eff}=11\, 635\pm 178$ K, and log g = 8.048 ± 0.005 (with a hydrogen envelope mass of MH ∼ 5.6 × 10−5M⋆), in good agreement with the values derived from spectroscopy. We obtained an asteroseismic distance of 17.54 pc, which is in excellent agreement with that provided by Gaia (17.51 pc).

Mixed-mode Ensemble Asteroseismology of Low-luminosity Kepler Red Giants

We present measurements of the dipole mode asymptotic period spacing (ΔΠ1), the coupling factor between the p- and g-modes (q), the g-mode phase offset (ϵ g ), and the mixed-mode frequency rotational splitting (δ ν rot) for 1074 low-luminosity red giants from the Kepler mission. Using oscillation mode frequencies extracted from each star, we apply Bayesian optimization to estimate ΔΠ1 from the power spectrum of the stretched-period spectrum and to perform the subsequent forward modeling of the mixed-mode frequencies. With our measurements, we show that the mode coupling factor q shows significant anticorrelation with both the stellar mass and metallicity, and can reveal highly metal-poor stars. We present the evolution of ϵ g up the lower giant branch up to before the luminosity bump, and find no significant trends in ϵ g or δ ν rot with the stellar mass and metallicity in our sample. Additionally, we identify six new red giants showing anomalous distortions in their g-mode pattern. Our data products, code, and results are provided in a public repository.

Mode coupling coefficients between the convective core and radiative envelope of γ Doradus and slowly pulsating B stars

Context. Signatures of coupling between an inertial mode in the convective core and a gravito-inertial mode in the envelope have been found in four-year Kepler light curves of 16 rapidly rotating γ Doradus (γ Dor) stars. This makes it possible to obtain a measurement of the rotation frequency in their convective core. Despite their similar internal structure and available data, inertial modes have not yet been reported for slowly pulsating B (SPB) stars. Aims. We aim to provide a numerical counterpart of the recently published theoretical expressions for the mode-coupling coefficients, ε and ε̃. These coefficients represent the two cases of a continuous and a discontinuous Brunt-Väisälä frequency profile at the core-envelope interface, respectively. We consider γ Dor and SPB stars to shed light on the difference between these two classes of intermediate-mass gravito-inertial mode pulsators in terms of core and envelope mode coupling. Methods. We used asteroseismic forward models of two samples consisting of 26 SPB stars and 37 γ Dor stars to infer their numerical values of ε and ε̃. For both samples, we also computed: the linear correlation coefficients between ε or ε̃ and the near-core rotation frequency, the chemical gradient, the evolutionary stage, the convective core masses and radii, and the Schönberg-Chandrasekhar limiting mass representing the maximum mass of an inert helium core at central hydrogen exhaustion that can still withstand the pressure of the overlaying envelope. Results. The asteroseismically inferred values of ε and ε̃ for the two samples are between 0.0 and 0.34. While ε is most strongly correlated with the near-core rotation frequency for γ Dor stars, the fractional radius of the convective core instead provides the tightest correlation for SPB stars. We find ε to decrease mildly as the stars evolve. For the SPB stars, ε and ε̃ have similar moderate correlations with respect to the core properties. For the γ Dor stars, ε̃ reveals systematically lower and often no correlation to the core properties; their ε is mainly determined by the near-core rotation frequency. The Schönberg-Chandrasekar limit is already surpassed by the more massive SPB stars, while none of the γ Dor stars have reached it yet. Conclusions. Our asteroseismic results for the mode coupling support the theoretical interpretation and reveal that young, fast-rotating γ Dor stars are most suitable for undergoing couplings between inertial modes in the rotating convective core and gravito-inertial modes in the radiative envelope. The phenomenon has been found in 2.4% of such pulsators with detected period spacing patterns, whereas it has not been seen in any of the SPB stars so far.

Frequency analysis of the hybrid δ Sct-γ Dor star CoRoT-102314644

Context. Observations from space missions allowed significant progress due to the absence of atmospheric noise contributions and having uninterrupted data sets. This has been extremely beneficial in asteroseismology because many oscillation frequencies, not observable from the ground, can be detected. One example of this success is the large number of hybrid δ Sct-γ Dor stars discovered. These stars have radial and non-radial p and g modes simultaneously excited, allowing us to probe both the external and near-to-core layers. Aims. We aim to analyse the light curve of the hybrid δ Sct-γ Dor star CoRoT ID 102314644 and characterise its frequency spectrum. Using the detected frequencies, we intend to perform an initial interpretation developing stellar models. Methods. The frequency analysis was obtained with a classical Fourier analysis. A detailed analysis of the individual frequencies is performed using phase diagrams and other light curve characteristics. Initial stellar modelling was performed using the Cesam2k and the GYRE code. Results. We detected 29 γ Dor type frequencies in the [0.32 − 3.66] c/d range and a series of six equidistant periods with a mean period spacing of ΔΠ = 1612 s. In the δ Sct domain, we found 38 frequencies in the [8.63 − 24.73] c/d range and a quintuplet centred on the frequency p1 = 11.39 c/d, which suggests a rotational period of 3.06 d. The frequency analysis suggests the presence of spots. Nevertheless, we could not dismiss the possibility of a binary system. The initial modelling of the frequency data allowed us to refine its astrophysical parameters. Conclusions. The observed period spacing, a p-mode quintuplet, the possible rotation period, and the analysis of the individual frequencies impose significant constraints on our understanding of differential rotation and magnetic fields operating in A–F-type stars. Nevertheless, it is fundamental to accompany photometric data with spectroscopic measurements to distinguish variations between surface activity from a companion.

Asteroseismic Modeling of 1153 Kepler Red Giant Branch Stars: Improved Stellar Parameters with Gravity-mode Period Spacings and Luminosity Constraints

This paper reports the estimated stellar parameters of 1153 Kepler red giant branch stars determined with asteroseismic modeling. We use radial-mode oscillation frequencies, gravity-mode period spacings, Gaia luminosities, and spectroscopic data to characterize these stars. Compared with previous studies, we find that the two additional observed constraints, i.e., the gravity-mode period spacing and luminosity, significantly improve the precision of fundamental stellar parameters. The typical uncertainties are 2.9% for the mass, 11% for the age, 1.0% for the radius, 0.0039 dex for the surface gravity, and 0.5% for the helium core mass, making this the best-characterized large sample of red giant stars available to date. With better characterizations for these red giants, we recalibrate the seismic scaling relations and study the surface term on the red giant branch. We confirm that the surface term depends on the surface gravity and effective temperature, but there is no significant correlation with metallicity.

Well-posedness of fractional differential equations with finite delay in complex Banach spaces

We study the well-posedness of the fractional differential equations with finite delay: Dαu(t) + BDβu(t) = Au(t) + Fut + f(t), (0 ≤ t ≤ 2π) on Lebesgue-Bochner spaces and periodic Besov spaces , where A and B are closed linear operators in a complex Banach space X satisfying D(A) ⊂ D(B), 0 ≤ β < α, α ≥ 1 and F is a bounded linear operator from Lp ([−2π, 0]; X) (resp. into X. We give necessary and sufficient conditions for the Lp -well-posedness and the -well-posedness of above equations by using known operator-valued Fourier multiplier theorems.

An improved equivalent beam model of large periodic beam-like space truss structures

Space truss structures are essential components for space-based remote sensing loads with high spatial and temporal resolutions. To achieve high-precision vibration control, an accurate and efficient dynamics model is essential. In addition to the current equivalent beam model (EBM) based on the classical continuum theory, an improved equivalent beam model (IEBM) is proposed that considers the impact of the distinction between trusses and beams on torsional and shear deformations, as well as the impact of shear deformation on flexural rigidity. According to the displacement expressions of spatial beams, torsional, shear, and bending correction coefficients are introduced to derive expressions of strain energy and kinetic energy. The energy equivalence principle is then utilized to calculate the elasticity and inertia matrices, and dynamics equations are established using the finite element method. Subsequently, an IEBM is constructed by employing the particle swarm optimization approach to determine the correction coefficients with the truss natural frequency as the optimization target. The natural vibration characteristics of the structure are estimated for various material properties. Compared with the full-scale finite element model, the EBM reaches a maximum error of 80% for a low modulus of elasticity, while the maximum error of the IEBM is less than 2% for any given parameters, indicating its superior accuracy to the EBM.

PERCEPTION OF STYLE INFLUENCES IN ARCHITECTURAL SPACE

This research presents a theoretical study, which reflects the importance, possibilities, and character of stylistics observed in some periods of time and manifested in objects and interior elements in public or private architectural spaces in Moldova. The author reflects on the role of research by observing and exploiting the stylistic interference of other cultures and nations, the creations of representatives in the field, and by forming a complex picture of the Moldovan interior space. The influence of stylistic elements on the interior space in different periods of time is elucidated, observed, and implemented in the residential or non-residential space through form and constructive materials, interior design, organization and zoning, furniture, stylistic detailing, but also through visual arts in painting and graphics, real historical portraits, landscape paintings, interiors from different localities and periods of time, demonstrating the undeniable richness of the cultural heritage of the Republic of Moldova, but also the need for research and exploitation of the national treasure.

Precise masses and ages of ~1 million RGB and RC stars observed by LAMOST

We construct a catalogue of stellar masses and ages for 696 680 red giant branch (RGB) stars, 180 436 primary red clump (RC) stars, and 120 907 secondary RC stars selected from the LAMOSTDR8. The RGBs, primary RCs, and secondary RCs are identified with the large frequency spacing (∆ν) and period spacing (∆P) estimated from the LAMOST spectra with spectral signal-to-noise ratios (S/Ns) &gt; 10 using a neural network method supervised with seismologic information from LAMOST-Kepler sample stars. The purity and completeness of both RGB and RC samples are better than 95% and 90%, respectively. The mass and age of RGBs and RCs are determined again with the neural network method by taking the LAMOST-Kepler giant stars as the training set. The typical uncertainties on stellar mass and age are 10% and 30%, respectively, for the RGB stellar sample. For RCs, the typical uncertainties on stellar mass and age are 9% and 24%, respectively. The RGB and RC stellar samples cover a large volume of the Milky Way (5 &lt; R &lt; 20 kpc and |Z| &lt; 5 kpc), which are valuable data sets for various Galactic studies.

Direct Steady-State Calculation of Electromagnetic Devices Using Field-Circuit Models

Field-circuit models are very often used to model electromagnetic devices with conductive and non-linear magnetic materials. The numerical calculations of the field in the magnetic material must be combined with an equation of an external coil placed in the magnetic circuit. This means that the partial differential equations of the electromagnetic field in non-linear conductive materials and the non-linear ordinary differential equations must be solved together. Effective algorithms for solving such problems are still being developed. The article presents an algorithm directly providing the steady state solution without the simulation of transients. The basic assumption is that the solution can be predicted as a periodic time and space function, which is represented by appropriate Fourier series. The developed algorithm uses discrete partial differential operators for time and space derivatives. It allows us to create finite difference equations directly from the field and circuit equations, which take the form of algebraic equations, generally non-linear. This is a unique approach developed by us, which till now did not exist (and is not mentioned) in the literature. That algorithm is tested on a simple case of a solenoid coil with a ferromagnetic and conductive cylindrical core, in 2D space of radius and time. The calculation results confirm the effectiveness of the proposed approach both qualitatively, with regard to physical phenomena in ferromagnetic and conductive material, and quantitatively, in comparison with the results from specialized commercial software.

Spatio-Temporal Self-Supervised Learning for Traffic Flow Prediction

Robust prediction of citywide traffic flows at different time periods plays a crucial role in intelligent transportation systems. While previous work has made great efforts to model spatio-temporal correlations, existing methods still suffer from two key limitations: i) Most models collectively predict all regions' flows without accounting for spatial heterogeneity, i.e., different regions may have skewed traffic flow distributions. ii) These models fail to capture the temporal heterogeneity induced by time-varying traffic patterns, as they typically model temporal correlations with a shared parameterized space for all time periods. To tackle these challenges, we propose a novel Spatio-Temporal Self-Supervised Learning (ST-SSL) traffic prediction framework which enhances the traffic pattern representations to be reflective of both spatial and temporal heterogeneity, with auxiliary self-supervised learning paradigms. Specifically, our ST-SSL is built over an integrated module with temporal and spatial convolutions for encoding the information across space and time. To achieve the adaptive spatio-temporal self-supervised learning, our ST-SSL first performs the adaptive augmentation over the traffic flow graph data at both attribute- and structure-levels. On top of the augmented traffic graph, two SSL auxiliary tasks are constructed to supplement the main traffic prediction task with spatial and temporal heterogeneity-aware augmentation. Experiments on four benchmark datasets demonstrate that ST-SSL consistently outperforms various state-of-the-art baselines. Since spatio-temporal heterogeneity widely exists in practical datasets, the proposed framework may also cast light on other spatial-temporal applications. Model implementation is available at https://github.com/Echo-Ji/ST-SSL.

The Phenomenon of Trust in Domestic Scientific Discourse

This article is devoted to the analysis of the phenomenon of trust in public scientific discourse. The authors consider various approaches to the research of the phenomenon of trust in economics, sociology, psychology and other branches of scientific knowledge. In-depth theoretical and methodological analysis of the understanding of the confidence phenomenon in the interpretation of different sociological directions is conducted. The author’s interpretation of the concept of trust from the point of view of the activity-phenomenological approach is given. The available approaches to the study of trust are systematized. In the empirical part of the research, in order to study how science responded to modern challenges related to trust in the network space in different chronological periods, the method of quantitative and qualitative content analysis was applied on the basis of scientific papers published in the period from 2000 to 2021. On the basis of the results, the authors were able to reproduce a list of 55 areas of knowledge and to derive thematic areas in which the phenomenon of trust is being studied.

Carbon–oxygen ultra-massive white dwarfs in general relativity

ABSTRACT We employ the La Plata stellar evolution code, lpcode, to compute the first set of constant rest-mass carbon–oxygen ultra-massive white dwarf evolutionary sequences for masses higher than 1.29 M⊙ that fully take into account the effects of general relativity on their structural and evolutionary properties. In addition, we employ the lp-pul pulsation code to compute adiabatic g-mode Newtonian pulsations on our fully relativistic equilibrium white dwarf models. We find that carbon–oxygen white dwarfs more massive than 1.382 M⊙ become gravitationally unstable with respect to general relativity effects, being this limit higher than the 1.369 M⊙ we found for oxygen–neon white dwarfs. As the stellar mass approaches the limiting mass value, the stellar radius becomes substantially smaller compared with the Newtonian models. Also, the thermo-mechanical and evolutionary properties of the most massive white dwarfs are strongly affected by general relativity effects. We also provide magnitudes for our cooling sequences in different passbands. Finally, we explore for the first time the pulsational properties of relativistic ultra-massive white dwarfs and find that the period spacings and oscillation kinetic energies are strongly affected in the case of most massive white dwarfs. We conclude that the general relativity effects should be taken into account for an accurate assessment of the structural, evolutionary, and pulsational properties of white dwarfs with masses above ∼1.30 M⊙.

Semi-analytical Expression of G-mode Period Spacing: The Case of Brunt–Väisälä Frequency with Not a Jump but a Ramp

To decipher complex patterns of gravity-mode period spacings observed for intermediate-mass main-sequence stars is an important step toward a better understanding of the structure and dynamics in the deep radiative region of the stars. In this study, we apply the JWKB approximation to derive a semi-analytical expression of the g-mode period spacing pattern, for which the gradient in the Brunt–Väisälä frequency is taken into account. The formulation includes the term P −1 B ⋆, where P and B ⋆ represent the g-mode period and degree of the structural variation, the latter of which especially is related to the steepness of the gradient of the Brunt–Väisälä frequency. Tests with one-dimensional stellar models show that the semi-analytical expression derived in this study is useful for inferring the degree of the structural variation B ⋆ with an accuracy of ∼10 % in the case of relatively massive intermediate-mass models with the mass M larger than 3 M ⊙. The newly formulated expression will possibly allow us to put further constraints on, e.g., mixing processes inside intermediate-mass main-sequence g-mode pulsators such as β Cep, SPB, and γ Dor stars that have been principal targets in asteroseismology.