Curvature Scale Research Articles

Interplays Between Mantle Flow and Slab Pull at Subduction Zones in 3D

AbstractThe understanding of the interactions between subduction‐induced mantle flow and background mantle flow (being global or regional) remains incomplete despite its potential impact on subduction dynamics and associated deformation. Here we present the results of three‐dimensional laboratory models of subduction zones at the scale of the upper mantle in which we systematically vary the plate's width and trench perpendicular background mantle flow. In particular, we test different mantle flow magnitudes and directions of flow, and evaluate their impact on the slab geometry in the vertical plane, trench shape evolution, and the superficial horizontal mantle deformation. While the chosen viscosity ratio between the convective mantle and the subducting plate in our models (∼100) is favorable to the deformation of the slab through mantle displacement, we show that the geometry of the slab in the vertical plane is only marginally affected by the imposed background flow. Instead, the background flow has a larger impact on the horizontal kinematics and deformation of the trench. It reduces along‐trench variations of trench kinematics, which in turn decreases trench curvature, and it largely disturbs the pattern of mantle deformation at slab edges, inhibiting the development of toroidal cells. We also show that the thickness of the convective layer (here, the upper mantle) controls the toroidal component of the mantle flow and the length scale of trench curvature for large subduction zones.

From a locality-principle for new physics to image features of regular spinning black holes with disks

Current observations present unprecedented opportunities to probe the true nature of black holes, which must harbor new physics beyond General Relativity to provide singularity-free descriptions. To test paradigms for this new physics, it is necessary to bridge the gap all the way from theoretical developments of new-physics models to phenomenological developments such as simulated images of black holes embedded in astrophysical disk environments.In this paper, we construct several steps along this bridge. We construct a novel family of regular black-hole spacetimes based on a locality principle which ties new physics to local curvature scales. We then characterize these spacetimes in terms of a complete set of curvature invariants and analyze the ergosphere and both the outer event as well as distinct Killing horizon. Our comprehensive study of the shadow shape at various spins and inclinations reveals characteristic image features linked to the locality principle. We also explore the photon rings as an additional probe of the new-physics effects. A simple analytical disk model enables us to generate simulated images of the regular spinning black hole and test whether the characteristic image-features are visible in the intensity map.

Characterising the most rapidly rotating AdS5-Kerr black holes

Classical censorship permits AdS5-Kerr black holes with arbitrarily large angular momenta per unit mass, which does not seem reasonable from a holographic point of view. However, it has been shown that, when these black holes are embedded in string theory, their angular momentum per unit mass is in fact bounded by , where L is the asymptotic curvature scale. One might suppose that the most rapidly rotating AdS5-Kerr black holes, with angular momentum per unit mass close to this bound, might be unstable, for example, to a superradiant instability. We show that this is not always true: there is a small domain in the AdS5-Kerr parameter space corresponding to black holes which are stable against superradiance and yet nearly saturate the stringy bound.

Mass and horizon Dirac observables in effective models of quantum black-to-white hole transition

In the past years, black holes and the fate of their singularity have been heavily studied within loop quantum gravity. Effective spacetime descriptions incorporating quantum geometry corrections are provided by the so-called polymer models. Despite the technical differences, the main common feature shared by these models is that the classical singularity is resolved by a black-to-white hole transition. In a recent paper (Bodendorfer et al 2019 Class. Quantum Grav. 36 195015), we discussed the existence of two Dirac observables in the effective quantum theory respectively corresponding to the black and white hole mass. Physical requirements about the onset of quantum effects then fix the relation between these observables after the bounce, which in turn corresponds to a restriction on the admissible initial conditions for the model. In the present paper, we discuss in detail the role of such observables in black hole polymer models. First, we revisit previous models and analyse the existence of the Dirac observables there. Observables for the horizons or the masses are explicitly constructed. In the classical theory, only one Dirac observable has physical relevance. In the quantum theory, we find a relation between the existence of two physically relevant observables and the scaling behaviour of the polymerisation scales under fiducial cell rescaling. We present then a new model based on polymerisation of new variables which allows to overcome previous restrictions on initial conditions. Quantum effects cause a bound of a unique Kretschmann curvature scale, independently of the relation between the two masses.

SCN: A Novel Shape Classification Algorithm Based on Convolutional Neural Network

Shape classification and matching is an important branch of computer vision. It is widely used in image retrieval and target tracking. Shape context method, curvature scale space (CSS) operator and its improvement have been the main algorithms of shape matching and classification. The shape classification network (SCN) algorithm is proposed inspired by LeNet5 basic network structure. Then, the network structure of SCN is introduced and analyzed in detail, and the specific parameters of the network structure are explained. In the experimental part, SCN is used to perform classification tasks on three shape datasets, and the advantages and limitations of our algorithm are analyzed in detail according to the experimental results. SCN performs better than many traditional shape classification algorithms. Accordingly, a practical example is given to show that SCN can save computing resources.

Self-gravitating Equilibria of Non-minimally Coupled Dark Matter Halos

Abstract We investigate self-gravitating equilibria of halos constituted by dark matter (DM) non-minimally coupled to gravity. In particular, we consider a theoretically motivated non-minimal coupling that may arise when the averaging/coherence length L associated with the fluid description of the DM collective behavior is comparable to the local curvature scale. In the Newtonian limit, such a non-minimal coupling amounts to a modification of the Poisson equation by a term L 2∇2 ρ proportional to the Laplacian of the DM density ρ itself. We further adopt a general power-law equation of state p ∝ ρ Γ r α relating the DM dynamical pressure p to density ρ and radius r, as expected for phase-space density stratification during the gravitational assembly of halos in a cosmological context. We confirm previous findings that, in the absence of non-minimal coupling, the resulting density ρ(r) features a steep central cusp and an overall shape mirroring the outcomes of N-body simulations in the standard ΛCDM cosmology, as described by the classic Navarro–Frenk–White or Einasto profiles. Most importantly, we find that the non-minimal coupling causes the density distribution to develop an inner core and a shape that closely follows the Burkert profile out to several core scale radii. In fact, we highlight that the resulting mass distributions can fit, with an accuracy comparable to Burkert’s one, the coadded rotation curves of dwarf, DM-dominated galaxies. Finally, we show that non-minimally coupled DM halos are consistent with the observed scaling relation between the core radius r 0 and core density ρ 0, in terms of a universal core surface density ρ 0 × r 0 among different galaxies.

Research on Contour Feature Extraction Algorithms for Arc-shaped Groove of Safety Seat Base

The spatial position of the seat base is complicated. The contour structure of arc groove is complex and its contour feature extraction is difficult. Aiming at the above problems, this paper presents an improved corner detection algorithm based on Curvature Scale Space (CSS), which uses adaptive local curvature and dynamic angle threshold to accurately extract corner points of arc groove contour. The correct corner positioning error of the algorithm proposed in this paper is only 0.99 pixel. The experimental results show that this method can effectively implement contour feature extraction.

Partial UV completion of P(X) from a curved field space

The k-essence theory is a prototypical class of scalar-field models that already gives rich phenomenology and has been a target of extensive studies in cosmology. General forms of shift-symmetric k-essence are known to suffer from formation of caustics in a planar-symmetric configuration, with the only exceptions of canonical and DBI-/cuscuton-type kinetic terms. With this in mind, we seek for multi-field caustic-free completions of a general class of shift-symmetric k-essence models in this paper. The field space in UV theories is naturally curved, and we introduce the scale of the curvature as the parameter that controls the mass of the heavy field(s) that would be integrated out in the process of EFT reduction. By numerical methods, we demonstrate that the introduction of a heavy field indeed resolves the caustic problem by invoking its motion near the would-be caustic formation. We further study the cosmological application of the model. By expanding the equations with respect to the curvature scale of the field space, we prove that the EFT reduction is successfully done by taking the limit of infinite curvature, both for the background and perturbation, with gravity included. The next leading-order computation is consistently conducted and shows that the EFT reduction breaks down in the limit of vanishing sound speed of the perturbation.

Multi-critical topological transition at quantum criticality

The investigation and characterization of topological quantum phase transition between gapless phases is one of the recent interest of research in topological states of matter. We consider transverse field Ising model with three spin interaction in one dimension and observe a topological transition between gapless phases on one of the critical lines of this model. We study the distinct nature of these gapless phases and show that they belong to different universality classes. The topological invariant number (winding number) characterize different topological phases for the different regime of parameter space. We observe the evidence of two multi-critical points, one is topologically trivial and the other one is topologically active. Topological quantum phase transition between the gapless phases on the critical line occurs through the non-trivial multi-critical point in the Lifshitz universality class. We calculate and analyze the behavior of Wannier state correlation function close to the multi-critical point and confirm the topological transition between gapless phases. We show the breakdown of Lorentz invariance at this multi-critical point through the energy dispersion analysis. We also show that the scaling theories and curvature function renormalization group can also be effectively used to understand the topological quantum phase transitions between gapless phases. The model Hamiltonian which we study is more applicable for the system with gapless excitations, where the conventional concept of topological quantum phase transition fails.

Curvature scale space-based signatures for electrical load classification in NILM

Non-intrusive load monitoring (NILM) systems have gained extensive interest due to their potential role regarding power savings for residential customers. These systems, which are mostly based on stages of detection and classification of transients on aggregated signals, rely heavily on load signatures. In the literature, the image-based voltage–current (V–I) trajectory representation is claimed as the most effective individual steady-state signature for appliance classification. However, this representation inherits some drawbacks from its generation process. This work then proposes two steady-state appliance signatures derived from the curvature scale space of V–I trajectories. These signatures aim to improve the image representations of V–I trajectories by encompassing structural elements related to the general shape of such trajectories as well as some characteristics neglected during their generation. A group of load signatures formed from the proposed signatures was evaluated on direct load classification and load disaggregation scenarios for publicly available datasets. The achieved results surpassed the sole employment of a reference image-based V–I signature for all the test scenarios executed. Also, some of the evaluated signatures outperformed all known proposals that are exclusively based on steady-state signatures for load classification on a given benchmarking dataset.

Vortices and waves in light dark matter

In a galactic halo like the Milky Way, bosonic dark matter particles lighter than about 100 eV have a de Broglie wavelength larger than the average inter-particle separation and are therefore well described as a set of classical waves. This applies to, for instance, the QCD axion as well as to lighter axion-like particles such as fuzzy dark matter. We show that the interference of waves inside a halo inevitably leads to vortices, locations where chance destructive interference takes the density to zero. The phase of the wavefunction has non-trivial winding around these points. This can be interpreted as a non-zero velocity circulation, so that vortices are sites where the fluid velocity has a non-vanishing curl. Using analytic arguments and numerical simulations, we study the properties of vortices and show they have a number of universal features: (1) In three spatial dimensions, the generic defects take the form of vortex rings. (2) On average there is about one vortex ring per de Broglie volume and (3) generically only single winding (± 1) vortices are found in a realistic halo. (4) The density near a vortex scales as r2 while the velocity goes as 1/r, where r is the distance to vortex. (5) A vortex segment moves at a velocity inversely proportional to its curvature scale so that smaller vortex rings move faster, allowing momentary motion exceeding escape velocity. We discuss observational/experimental signatures from vortices and, more broadly, wave interference. In the ultra-light regime, gravitational lensing by interference substructures leads to flux anomalies of 5–10 % in strongly lensed systems. For QCD axions, vortices lead to a diminished signal in some detection experiments but not in others. We advocate the measurement of correlation functions by axion detection experiments as a way to probe and capitalize on the expected interference substructures.

Effect of Acupuncture Combined with Tuina on Cervical Curvature and Serum Inflammatory Cytokine Levels in Patients with Cervical Spondylosis

To study the effects of acupuncture and tuina by stages on cervical curvature, serum interleukin-4, interleukin-8 and tumor necrosis factor-alpha in patients with cervical spondylosis. A total of 94 patients with cervical spondylosis admitted from June 2020 to June 2021 were divided into the control group and the study group through random number table with 47 cases in each group. Patients in the control group were treated with tuina and patients in the study group were treated with acupuncture and tuina by stages. One course of treatment was 21 d and both groups were treated for 2 courses. The clinical effects of the patients in the two groups after treatment were compared, the cervical spine curvature and visual analogue scale scores of patients in the two groups before and after treatment were compared and the serum levels of interleukin-4, interleukin-8 and tumor necrosis factor-alpha before and after treatment were compared. The total clinical effective rate of patients in the study group was 91.48 % (43/47), which was higher than 68.09 % (32/47) of patients in the control group. After treatment, the C value of cervical spine physiological curvature of patients in the two groups was higher than that before treatment and the visual analog scale scores, serum interleukin-4, interleukin-8, tumor necrosis factor-alpha levels decreased. The improvement of patients in the study group was better than that in the control group (all p<0.05). Acupuncture and tuina to treat patients with cervical spondylosis by stages can better improve the curvature of the patient’s cervical spines, reduce pain, inhibit inflammation in the body and improve the therapeutic effect.

Automatic segmentation algorithm for breast cell image based on multi-scale CNN and CSS corner detection

As the shapes of breast cell are diverse and there is adherent between cells, fast and accurate segmentation for breast cell remains a challenging task. In this paper, an automatic segmentation algorithm for breast cell image is proposed, which focuses on the segmentation of adherent cells. First of all, breast cell image enhancement is carried out by the staining regularization. Then, the cells and background are separated by Multi-scale Convolutional Neural Network (CNN) to obtain the initial segmentation results. Finally, the Curvature Scale Space (CSS) corner detection is used to segment adherent cells. Experimental results show that the proposed algorithm can achieve 93.01% accuracy, 93.93% sensitivity and 95.69% specificity. Compared with other segmentation algorithms of breast cell, the proposed algorithm can not only solve the difficulty of segmenting adherent cells, but also improve the segmentation accuracy of adherent cells.

Fluvial Sinuous Ridges of the Morrison Formation, USA: Meandering, Scarp Retreat, and Implications for Mars

AbstractSinuous ridges have been interpreted as evidence for ancient rivers on Mars, but relating ridge geometry to paleo‐hydraulics remains uncertain. Three analog ridge systems from the Morrison Formation, Utah, are composed of sandstone caprocks, up to 50 m wide and 8 m thick, atop mudstone flanks. Ridge caprocks have narrowed significantly compared to sandstone bodies preserved in outcrop, consistent with a new ridge‐erosion model that can be used to estimate original sandstone‐body extent. Ridge networks represent caprocks intersecting at distinct stratigraphic levels, rather than a preserved channel network. Caprocks are interpreted as amalgamated channel belts, rather than inverted channels, with dune and bar cross stratification that was used to reconstruct paleo‐channel dimensions. Curvilinear features on ridge tops are outcropping lateral accretion sets (LAS) from point bars and indicate meandering. We found that caprock thickness scales with paleo‐channel depth and LAS curvature scales with paleo‐channel width. Application of these relations to a ridge in Aeolis Dorsa, Mars, yielded consistent water discharge estimates (310–1,800 m3/s). In contrast, using ridge width or ridge radius of curvature as paleo‐channel proxies overestimated discharge by a factor of 30–500. In addition, the ridge‐erosion model suggests that scarp retreat may be less efficient on Mars, resulting in taller and wider ridges, with more intact caprocks. Altogether, our results support the hypothesis that ridges are exhumed channel belts and floodplain deposits implying long‐lived fluvial activity recorded within a depositional basin.

A free Lie algebra approach to curvature corrections to flat space-time

We investigate a systematic approach to include curvature corrections to the isometry algebra of flat space-time order-by-order in the curvature scale. The Poincaré algebra is extended to a free Lie algebra, with generalised boosts and translations that no longer commute. The additional generators satisfy a level-ordering and encode the curvature corrections at that order. This eventually results in an infinite-dimensional algebra that we refer to as Poincaré∞, and we show that it contains among others an (A)dS quotient. We discuss a non-linear realisation of this infinite-dimensional algebra, and construct a particle action based on it. The latter yields a geodesic equation that includes (A)dS curvature corrections at every order.

Local-gravity test of unified models of inflation and dark energy in f(R) gravity

We consider $f(R)$ gravity theories which unify $R^n$ inflation and dark energy models. First, from the final Planck data of the cosmic microwave background, we obtain a condition, $1.977 < n < 2.003$. Next, under this constraint, we investigate local-gravity tests for three models. We find that the $R^n$ term can dominate over the dark energy term even at the Earth's curvature scale, contrary to intuition; however, the $R^n$ term does not relax or tighten the constraints on the three models.

A Contour Angle Orientation for Power Equipment Infrared and Visible Image Registration

Automatic registration for infrared, and visible images of power equipment has become a challenging work in intelligent diagnosis system of the power grid. Existing registration methods usually fail in accurately aligning power equipment infrared, and visible images because of resolutions, spectrums, and viewpoints differences. To solve this problem, we propose a novel main orientation of feature points named contour angle orientation (CAO), and describe an automatic infrared, and visible image registration method named CAO-Coarse to Fine (CAO-C2F). CAO is based on the contour feature of images, and invariant to images viewpoints, and scales differences. C2F is a feature matching method to obtain correct matches. Our proposed CAO-C2F method includes four steps. First, feature points in contours are extracted by the curvature scale space (CSS) corner detector based on local, and global curvature. Second, the CAO of each feature point is computed as the main orientation. Third, modified scale-invariant feature transform (SIFT) descriptors on the main orientations are extracted, and matched by bilateral matching. Finally, accurate matches are obtained by applying the C2F method. Registration experiments on a self-established images dataset show our proposed CAO-C2F method accurately aligns images, and outperforms other state-of-arts in terms of precision, recall, and root-mean-square error.

Seismic Response of a Mountain Ridge Prone to Landsliding

ABSTRACTDuring an earthquake, site effects can play an important role in triggering landslides. To document the seismic response of steep hillslopes, we deployed broadband seismometers across a mountain ridge in Taiwan, in an area with a high earthquake-induced landslide hazard. The ridge has a simple, representative shape, and landslides have previously occurred there. Our seismometer array has recorded continuously during more than 1 yr, with both ambient-noise and regional moderate earthquakes as sources. Processing horizontal and vertical signal components, we show that the ridge has a complex response, which we attribute to the combined effects of the subsurface geology and the topographic geometry. Amplification and directionality of ground motion are observed both high and low on the ridge, giving rise to localized, elevated, earthquake-induced landslide hazard. Our database contains earthquakes with mostly similar locations, making it difficult to determine the effect of earthquake back azimuth on the ridge response. A part of the ridge response, possibly due to topographic effects, seems to be explained by a model derived from a frequency scale curvature proxy at low frequency. If correct, this would be a promising first step toward improving local ground-motion estimation in mountain areas. However, the definition of appropriate scaling parameters of site effects based on geophysical measurements, for use in regional and global landslide hazard equations applicable to mountain areas with substantial regolith thickness, remains a significant challenge.

Three-dimensional upper bound limit analysis of underground cavities using nonlinear Baker failure criterion

A generalized nonlinear Baker failure criterion is employed with the upper bound limit analysis to study the surrounding rock stability of underground cavities. A three-dimensional (3D) failure mode is established by extending the two-dimensional (2D) failure mode, which offers an upper bound expression of the surrounding rock pressure. This method is validated with a series of examples before the influence of four parameters of scale parameter, curvature parameter, shift parameter and lateral pressure coefficient, on the surrounding rock pressure is analyzed. According to these results, failure ranges of the underground cavities are determined. The following conclusions are reached: (1) the proposed approach is more accurate to predict surrounding rock pressure than the Mohr−Coulomb failure criterion; (2) the surrounding rock with large scale parameter, curvature parameter, shift parameter, and lateral pressure coefficient can lead to a more stable underground cavity; (3) the failure range in 3D mode can be predicted according to the upper bound solutions.

FAST interstellar scintillation observation of PSR B1929+10 and PSR B1842+14

In this paper, we present the Five-hundred-meter Aperture Spherical radio Telescope (FAST) observations of PSRs B1929+10 and B1842+14. Through analysis of the pulsars’ scintillation pattern, we detected the known scintillation arc from PSR B1929+10 and two previously undetected scintillation arcs from B1842+14. We find that the B1929+10 arc’s curvature scales with observing frequency as η− ∝ ν−2.1±0.1 and η+ ∝ ν−1.8±0.2, consistent with Arecibo results and the theoretical expectations of η ∝ ν−2. From the arc curvature, we infer the scattering screen to be located at 0.20±0.02 kpc from the Earth, close to what was measured by RadioAstron at 324 MHz. From B1842+14, we find two scintillation arcs for the first time. The arcs’ curvatures imply that they are caused by two scattering screens located at a distance of 0.3±0.2 kpc and 1.6±0.6 kpc from the Earth, respectively. The screen distance uncertainties mainly come from the uncertainty in pulsar’s dispersion measure (DM)-derived distance. We present these FAST scintillation observations and discuss the future prospect of FAST pulsar scintillation study.