Global Geometry Research Articles

A Hale-like Cycle in the Solar Twin 18 Scorpii

Abstract Characterizing the cyclic magnetic activity of stars that are close approximations of our Sun offers our best hope for understanding our Sun’s current and past magnetism, the space weather around solar-type stars, and more generally, the dynamos of other cool stars. The nearest current approximation to the Sun is the solar twin 18 Scorpii, a naked-eye Sun-like star of spectral type G2 Va. However, while 18 Scorpii’s physical parameters closely match those of the Sun, its activity cycle is about 7 yr, and shorter than the solar cycle. We report the measurement of a periodicity of 15 yr that corresponds to a longer activity cycle for 18 Scorpii based on observations extending to the last three decades. The global magnetic geometry of 18 Scorpii changes with this 15 yr cycle and appears to be equivalent to the solar 22 yr magnetic polarity cycle. These results suggest that 18 Scorpii is also a magnetic proxy for a younger Sun, adding an important new datum for testing dynamo theory and magnetic evolution of low-mass stars. The results perturb our understanding of the relationship between cycle and rotation, constrain the Sun’s magnetism and the Sun–Earth connection over the past billion years, and suggest that solar Schwabe and Hale cycle periods have increased over that time span.

Load-Balanced Collaborative Offloading for LEO Satellite Networks

Low earth orbit (LEO) satellite networks have become one of the hot research areas as an essential part of satellite communication networks. The dynamic topology and unbalanced traffic demand may lead to inter-satellite link congestion, thus, improving network load balancing performance is one of the key issues to be addressed in LEO satellite networks. We propose a load-balanced collaborative offloading (LBCO) strategy to achieve a balanced traffic distribution in LEO satellite networks. LBCO strategy consists of two algorithms, namely, channel-aware gradient fair association (CAGFA) algorithm and inter-satellite links collaborative offloading (ISLCO) algorithm. The CAGFA algorithm aims to maximize the aggregate weighted utility, and the ISLCO algorithm aims to achieve the traffic offloading and download observation data from the LEO satellite network. Specifically, we first determine the actual downloading satellite set and neighboring satellite set by constructing an earth station (ES) time-share graph and a space-time topology graph. Then, the LBCO strategy uses the CAGFA algorithm to obtain the optimal satellite terminal association indicator and the load of downloading satellites. Finally, the ISLCO algorithm is proposed to achieve proportional offloading of traffic among the neighboring satellites and download massive observation data. Simulations show that the proposed CAGFA algorithm improves the weighted utility by 3.3% and the convergence by 47.6% compared with the benchmark stochastic gradient descent-based association (SGDA) algorithm. We also validate the performance of the LBCO strategy by data download throughput, which performs better than other benchmark algorithms under three different load scenarios.

Iron Kα echoes from the circumnuclear disk orbiting Sɡr A⋆

Context. Molecular clouds in the Galactic center (GC) reprocess radiation from past outbursts of nearby high-energy sources, generating a bright Fe Kα fluorescence at 6.4 keV. The closest clouds to the GC are only ≃1.5 pc from Sgr A⋆, forming a torus-like structure known as the circumnuclear disk (CND). The study of fluorescence emission can lead to a characterization of the illuminating source(s), the reflecting clouds, and the global geometry of such a system lying in the GC. Aims. The primary purpose of our study is to analyze possible fluorescence signals arising in the CND. This signal would allow us to constrain the CND’s physical properties and the source-reflector system’s geometry. Methods. By exploiting the last ≃20 yr of XMM-Newton observations of the GC, we studied the variability of the Fe Kα line in the region around Sgr A⋆. We identified regions with a flux excess and computed the spectrum therein. We then derived the hydrogen column density of the CND after relating the intensity of the 6.4 keV line to the total energy emitted by known transient sources in the region. Results. Starting from data collected in 2019, we find significant line excesses in a region compatible with the eastern portion of the CND. The echo radiation can be linked to the 2013 outburst of the magnetar SGR J1745-2900. We derive a mean effective hydrogen column density of the CND in the eastern region of ≃1023 cm−2. Conclusions. The scenario depicted is physically plausible, given the luminosity, the position of the illuminating source, and the expected density of the CND. Further observations could link the variability of the echo signal to the light curve of the illuminating source. In this way, it would be possible to characterize the cloud response to the radiation front, achieving a more accurate estimate of the cloud parameters.

Visual Process Monitoring by Data-Dependent Kernel Discriminant Analysis with t-Distributed Similarities.

Visual process monitoring would provide more directly appreciable and more easily comprehensible information about the process operating status as well as clear depictions of the occurrence path of faults; however, as a more challenging task, it has been sporadically discussed in the research literature on conventional process monitoring. In this paper, the Data-Dependent Kernel Discriminant Analysis (D2K-DA) model is proposed. A special data-dependent kernel function is constructed and learned from the measured data, so that the low-dimensional visualizations are guaranteed, combined with intraclass compactness, interclass separability, local geometry preservation, and global geometry preservation. The new optimization is innovatively designed by exploiting both discriminative information and t-distributed geometric similarities. On the construction of novel indexes for visualization, experiments of visual monitoring tasks on simulated and real-life industrial processes illustrate the merits of the proposed method.

Effects of the Relative Dynamics of Ionospheric Irregularities and GPS Satellites on Receiver Tracking Loop Performance

AbstractTransionospheric satellite signals are exposed to perturbation, caused by irregularities generated in the ionosphere. However, the characteristics of the satellite motion can have an additional impact on signal perturbation, in addition to the effects of irregularity structures, that drift from west to east during geomagnetic quiet conditions. This paper reports the effect of Global Positioning System satellite geometry, on tracking loop performance of ground‐based receivers, during occurrence of ionospheric scintillations. Observations are made from station Calcutta (22.58°N, 88.38°E geographic; magnetic dip 34.54°), located near the northern crest of Equatorial Ionization Anomaly, during three different solar activity periods (March 2014, March 2015, and March 2022). Efforts have been made to study the correlation of east‐west component of satellite velocity at Ionospheric Pierce Point (IPP) with duration of loss‐of‐lock and rate of signal fading (<−10 dB), from ground scintillation pattern observations. Results of this study show 75%–78% correlation between duration of loss‐of‐lock and eastward component of satellite velocity, for all three period of observation. Subsequently, shorter duration of loss‐of‐lock has been observed corresponding to satellite velocity being westward. Signal fading rate is found to decrease with increasing satellite velocity, having median value of the fading rate cumulative distribution percentage, corresponding to satellite velocity of 16.69, 31.76, and 19.14 m/s respectively during March 2014, March 2015, and March 2022. Results of this study also indicate direction and component of satellite velocity at IPP to be a dominant cause of signal outage, even during periods of weak to moderate scintillations.

Thermodynamics of FLRW apparent horizon in the presence of UV/IR mixing

Generalized uncertainty principle (GUP) and Extended uncertainty principle (EUP) are well-known phenomenological gates to the issue of the so-called Gravitational Quantum Mechanics. Two fundamental impacts of the GUP and EUP are the concepts of minimal measurable length and minimal measurable momentum. The minimal measurable length as the possible smallest uncertainty in position measurement can remove the spacetime singularities arising from the general theory of relativity in UV regime. On the other hand, the minimal measurable momentum as the possible smallest uncertainty in momentum measurement puts an IR cutoff on the late-time (low energy) dynamics of the universe. This minimal momentum essentially arises due to the curvature of the background spacetime manifold. A combination of GUP and EUP gives a UV–IR complete uncertainty principle which is called usually as EGUP in literature. Motivated by these facts, we aim to study the impact of the EGUP with minimal measurable length and minimal measurable momentum on Friedmann equations. We first find the EGUP-modified entropy expression in Friedmann–Lemaître–Robertson–Walker (FLRW) universe. Then, we obtain the EGUP-corrected Friedmann equations by employing the unified first law of thermodynamics. We explore the deceleration parameter in the EGUP setup. We then check whether the generalized second law of thermodynamics is fulfilled and then study some related issues. As a result, we find some constraints on the EGUP parameters.

Thermodynamics of the three-dimensional black hole with torsion

The stationary black hole solution of a Chern-Simons model based on the semi-simple extension of the Poincaré gauge group is studied. The solution resembles the metric properties of the BTZ geometry but contains, in addition, non-vanishing torsion. The global structure of spacetime is characterized by three conserved charges: two associated with the mass and angular momentum and one extra constant triggered by spacetime torsion. Consequently, we show that the entropy deviates from the standard Bekenstein-Hawking value and discuss the implications of torsional charges in the context of black hole thermodynamics.

Theory of gravitational lensing on a curved cosmic string

It is discussed in detail the complete mathematical model of gravitational lensing on a single cosmic string (CS) of general shape and position with respect to the line of sight. CS are one-dimensional extended objects assuredly predicted by modern cosmology. The presence of CS changes the global geometry of the Universe, could clarify the properties of the early Universe, including inflation models, and could serve as a unique proof of higher-dimensional theories. Despite the fact that CS have not yet been reliable detected, there are several strong independent indications of the existence of the CS, based of CMB analysis and search of gravitational lens chains with special properties (The recent new indication of the existence of the CSs is the nHz gravitational waves in the NANOGrav and other PTA Collaborations data.) However, early considered models of straight CS presented only a small fraction of the general CS-configurations to be observed. Now we propose model which could significantly increase the possibilities of CS observational search. It is considered more realistic models have necessarily include the inclinations and bends of the CS. Besides, the recent analysis of observational data on the search for gravitational-lens candidates, shows a large number of pairs that could be explained by the complex geometry of the CS.

Exploring β-symmetry in heterotic theory at order α′ with boundary term

This paper investigates the β-symmetry of the heterotic string theory at order α′ in the context of open spacetime manifolds. Our analysis reveals that the parity-odd component of the effective action at this order remains invariant under β-transformations. Furthermore, we demonstrate that the corresponding β-transformations leave the Gibbons-Hawking boundary term invariant.

The microwave spectrum of the sesamol (1,3-benzodioxol-5-ol) monomer and an analysis of its internal motion

The microwave spectrum of the sesamol (CH2O2C6H3OH) monomer has been collected using CP-FTMW spectroscopy in the 5.5–18.75 GHz region of the electromagnetic spectrum. Density functional theory calculations of the monomer have been performed. B3LYP|cc-pVTZ predicts the global minimum geometry to be s-trans-sesamol where the hydroxyl group is oriented 180° away from the dioxole ring. A second, local minimum, geometry for s-cis-sesamol was calculated to have the hydroxyl group oriented 0° towards the dioxole ring, and the zero-point energy difference between the two geometries is predicted to be 1.4 kJ/mol. Both unique conformers have been identified in the experimental spectrum. In accordance with the predicted dipole moments, only b-type transitions have been observed for s-trans-sesamol, while a- and b-type transitions have been assigned to s-cis-sesamol. The relative intensities in the observed spectrum indicate that the molecular beam contains a higher population of the s-trans-sesamol monomer. Satellite transitions were observed for both sesamol conformers. Treating the parent and satellite transitions as coupled vibrational states, the energy differences and Coriolis coupling constants were determined for each conformer. The magnitude of the coupling constants, the energy difference between the states, and a comparison to a similar state observed in 1,3-benzodioxole indicate that the excited states correspond with CH2 puckering of the dioxiole ring. The second moments of inertia and their contributions from the ring puckering have been analyzed for a series of functionalized molecules including piperonal, 1,3-benzodioxole and sesamol.

Extracting spatial knowledge from track and field broadcasts for monocular 3D human pose estimation

Collecting large datasets for investigations into human locomotion is an expensive and labor-intensive process. Methods for 3D human pose estimation in the wild are becoming increasingly accurate and could soon be sufficient to assist with the collection of datasets for analysis into running kinematics from TV broadcast data. In the domain of biomechanical research, small differences in 3D angles play an important role. More precisely, the error margins of the data collection process need to be smaller than the expected variation between athletes. In this work, we propose a method to infer the global geometry of track and field stadium recordings using lane demarcations. By projecting estimated 3D skeletons back into the image using this global geometry, we show that current state-of-the-art 3D human pose estimation methods are not (yet) accurate enough to be used in kinematics research.

Space–time flow computation with boundary layer and contact representation: a 10-year history

In computation of flow problems with moving solid surfaces, moving-mesh methods such as the space–time (ST) variational multiscale method enable mesh-resolution control near the solid surfaces and thus high-resolution boundary-layer representation. There was, however, a perception that in computations where the solid surfaces come into contact, high-resolution boundary-layer representation and actual-contact representation without leaving a mesh protection opening between the solid surfaces were mutually exclusive objectives in a practical sense. The introduction of the ST topology change (ST-TC) method in 2013 changed the perception. The two objectives were no longer mutually exclusive. The ST-TC makes moving-mesh computation possible even without leaving a mesh protection opening. The contact is represented as an actual contact and the boundary layer is represented with high resolution. Elements collapse or are reborn as needed, and that is attainable in the ST framework while retaining the computational efficiency at a practical level. The ST-TC now has a 10-year history of achieving the two objectives that were long seen as mutually exclusive. With the ST-TC and other ST computational methods introduced before and after, it has been possible to address many of the challenges encountered in conducting flow analysis with boundary layer and contact representation, in the presence of additional intricacies such as geometric complexity, isogeometric discretization, and rotation or deformation of the solid surfaces. The flow analyses conducted with these ST methods include car and tire aerodynamics with road contact and tire deformation and ventricle-valve-aorta flow. To help widen awareness of these methods and what they can do, we provide an overview of the methods, including those formulated in the context of isogeometric analysis, and the computations performed over the 10-year history of the ST-TC.

Boson star with parity-odd symmetry in wormhole spacetime

In this paper, we revisit the model of bosonic matter in the form of a free complex scalar field with a nontrivial wormhole spacetime topology supported by a free phantom field. We obtain a new type of boson star with wormhole solutions, in which the complex scalar field possess full parity-odd symmetry with respect to the two asymptotically flat spacetime regions. When the size of the throat is small, the behavior of boson stars with wormhole approaches that of boson stars. When the size of the throat is intermediate, the typical spiraling dependence of the mass and the particle number on the frequency of the boson stars is replaced by a loop structure. However, as the size becomes relatively large, the loop structure will also disappear. In particular, The complex scalar field could form two boson stars with opposite phase differences with respect to the two spacetime regions in the limit of vanishing throat size. We analyze the properties of this new type of boson stars with wormhole and further show that the wormhole spacetime geometry.

Automated crack segmentation on 3D asphalt surfaces with richer attention and hybrid pyramid structures

ABSTRACT Automated pavement crack detection is crucial to supporting fine pavement maintenance and ensuring safety for road facilities. Due to the complex pavement condition and crack features, it is still a critical challenge in intelligent pavement surveys. This paper proposed a novel pixel-level pavement crack segmentation network, PCSNet, to provide a solution to this challenge. The network has richer attention and hybrid pyramid structures, which implement full-process crack feature fusion and enhancement. The richer attention module consists of cascaded self-attention and attention gate modules. It captures the crack spatial dependence information and prunes the feature response. The hybrid pyramid structures consist of a multistage convolutional pyramid module and a pyramid pooling module. It integrates contextual information at multiple receptive field scales to enhance the potential crack feature representation. The proposed structure enriches the crack details and optimises the scene parsing on the global geometry of the cracks. A sizeable 3D pavement crack dataset is built for training and testing. The proposed network exhibited the best performance, achieving F1-score, mean intersection of union, and mean pixel accuracy of 81.21%, 77.13%, and 87.17%, respectively. The network can reconstruct the complete crack geometry, preserve the crack edges well, and optimises the detection of shallow and complex cracks. The method exhibits superior and robust performance, facilitating accurate pavement technical condition assessment and maintenance decisions.

A note on gluing via fiber products in the (classical) BV-BFV formalism

In classical field theory, gluing spacetime manifolds along boundary corresponds to taking a fiber product of the corresponding spaces of fields (as differential graded Fréchet manifolds) up to homotopy. We construct this homotopy explicitly in several examples in the setting of BV-BFV formalism (Batalin–Vilkovisky formalism with cutting–gluing).

Koenigs Theorem and Superintegrable Liouville Metrics

In a first part, we give a new proof of Koenigs theorem and, in a second part, we determine the local form of all the superintegrable Riemannian Liouville metrics as well as their global geometries.

Symmetries of κ-Minkowski space-time: a possibility of exotic momentum space geometry?

The quest for a quantum gravity phenomenology has inspired a quantum notion of space-time, which motivates us to study the fate of the relativistic symmetries of a particular model of quantum space-time, as well as its intimate connection with the plausible emergent curved “physical momentum space”. We here focus on the problem of Poincare symmetry of κ-Minkowski type non-commutative (quantum) space-time, where the Poincare algebra, on its own, remains undeformed, but in order to preserve the structure of the space-time non-commutative (NC) algebra, the actions of the algebra generators on the operator-valued space-time manifold must be enveloping algebra valued that lives in entire phase space i.e. the cotangent bundle on the space-time manifold (at classical level). Further, we constructed a model for a spin-less relativistic massive particle enjoying the deformed Poincare symmetry, using the first order form of geometric Lagrangian, that satisfies a new deformed dispersion relation and explored a feasible regime of a future Quantum Gravity theory in which the momentum space becomes curved. In this scenario there is only a mass scale (Planck mass mp), but no length scale. Finally, we relate the deformed mass shell to the geodesic distance in this curved momentum space, where the mass of the particle gets renormalized as a result of noncommutativity. We show, that under some circumstances, the Planck mass provides an upper bound for the observed renormalized mass.

Topologically nontrivial black holes of Lovelock gravity sourced by logarithmic electrodynamics

I investigate the topologically nontrivial black holes of Lovelock gravity sourced by logarithmic electrodynamics. To calculate the solution describing these black holes, additional constraints are also imposed on the base manifold of the higher dimensional spacetime. Relying on the selection of geometric mass, electric charge, and the nonlinearity parameter, this solution can be portrayed as a black hole with a single horizon, two horizons, or naked singularity. I also look into how the thermodynamical and conserved quantities of this solution are affected by the logarithmic electromagnetic field. Additionally, it is demonstrated that these quantities correspond to the first law of thermodynamics. At last, the local and global thermodynamic stabilities of the accomplished black hole are studied as well.

A Role for the Fauxrizon in the Semiclassical Limit of a Fuzzball

AbstractRecent work on the status of astrophysical modeling in the wake of quantum gravity indicates that a “fauxrizon” (a portmanteau of faux horizon), such as is relevant to understanding astrophysical black holes according to the fuzzball proposal within string theory, might ultimately solve the familiar black hole evaporation paradox. I clarify, with general upshots for the foundations of quantum gravity research, some of what this suggestion would amount to: identification of intertheoretic constraints on global spacetime structure in (observer-relative) semiclassical models of fuzzballs.

Higher-order curvature operators in causal set quantum gravity

We construct higher-order curvature invariants in causal set quantum gravity. The motivation for this work is twofold: First, to characterize causal sets, discrete operators that encode geometric information on the emergent spacetime manifold, e.g., its curvature invariants, are indispensable. Second, to make contact with the asymptotic-safety approach to quantum gravity in Lorentzian signature and find a second-order phase transition in the phase diagram for causal sets, going beyond the discrete analog of the Einstein–Hilbert action may be critical. Therefore, we generalize the discrete d’Alembertian, which encodes the Ricci scalar, to higher orders. We prove that curvature invariants of the form R^{2} -2 Box R (and similar invariants at higher powers of derivatives) arise in the continuum limit.