Hole Boundary Research Articles

Topological Order, Quantum Codes, and Quantum Computation on Fractal Geometries

We investigate topological order on fractal geometries embedded in $n$ dimensions. In particular, we diagnose the existence of the topological order through the lens of quantum information and geometry, i.e., via its equivalence to a quantum error-correcting code with a macroscopic code distance or the presence of macroscopic systoles in systolic geometry. We first prove a no-go theorem that $\mathbb{Z}_N$ topological order cannot survive on any fractal embedded in 2D. For fractal lattice models embedded in 3D or higher spatial dimensions, $\mathbb{Z}_N$ topological order survives if the boundaries of the interior holes condense only loop or membrane excitations. Moreover, for a class of models containing only loop or membrane excitations, and are hence self-correcting on an $n$-dimensional manifold, we prove that topological order survives on a large class of fractal geometries independent of the type of hole boundaries. We further construct fault-tolerant logical gates using their connection to global and higher-form topological symmetries. In particular, we have discovered a logical CCZ gate corresponding to a global symmetry in a class of fractal codes embedded in 3D with Hausdorff dimension asymptotically approaching $D_H=2+\epsilon$ for arbitrarily small $\epsilon$, which hence only requires a space-overhead $\Omega(d^{2+\epsilon})$ with $d$ being the code distance. This in turn leads to the surprising discovery of certain exotic gapped boundaries that only condense the combination of loop excitations and gapped domain walls. We further obtain logical $\text{C}^{p}\text{Z}$ gates with $p\le n-1$ on fractal codes embedded in $n$D. In particular, for the logical $\text{C}^{n-1}\text{Z}$ in the $n^\text{th}$ level of Clifford hierarchy, we can reduce the space overhead to $\Omega(d^{n-1+\epsilon})$. Mathematically, our findings correspond to macroscopic relative systoles in fractals.

Improving Multiday Solar Wind Speed Forecasts

AbstractWe analyze the residual errors for the Wang‐Sheeley‐Arge (WSA) solar wind speed forecasts as a function of the photospheric magnetic field expansion factor (fp) and the minimum separation angle (d) in the photosphere between the footpoints of open field lines and the nearest coronal hole boundary. We find the map of residual speed errors are systematic when examined as a function of fp and d. We use these residual error maps to apply corrections to the model speeds. We test this correction approach using 3‐day lead time speed forecasts for an entire year of observations and model results. Our methods can readily be applied to develop corrections for the remaining WSA forecast lead times which range from 1 to 7 days in 1‐day increments. Since the solar wind density, temperature, and the interplanetary magnetic field strength all correlate well with the solar wind speed, the improved accuracy of solar wind speed forecasts enables the production of multiday forecasts of the solar wind density, temperature, pressure, and interplanetary field strength, and geophysical indices. These additional parameters would expand the usefulness of Air Force Data Assimilative Photospheric Flux Transport‐WSA forecasts for space weather clients.

New Insights into the First Two PSP Solar Encounters Enabled by Modeling Analysis with ADAPT-WSA

Parker Solar Probe's (PSP's) unique orbital path allows us to observe the solar wind closer to the Sun than ever before. Essential to advancing our knowledge of solar wind and energetic particle formation is identifying the sources of PSP observations. We report on results for the first two PSP solar encounters derived using the Wang–Sheeley–Arge (WSA) model driven by Air Force Data Assimilative Photospheric Flux Transport (ADAPT) model maps. We derive the coronal magnetic field and the 1 R ⊙ source regions of the PSP-observed solar wind. We validate our results with the solar wind speed and magnetic polarity observed at PSP. When modeling results are very reliable, we derive time series of model-derived spacecraft separation from the heliospheric current sheet, magnetic expansion factor, coronal hole boundary distance, and photospheric field strength along the field lines estimated to be connected to the spacecraft. We present new results for Encounter 1, which show time evolution of the far-side mid-latitude coronal hole that PSP corotates with. We discuss how this evolution coincides with solar wind speed, density, and temperature observed at the spacecraft. During Encounter 2, a new active region emerges on the solar far side, making it difficult to model. We show that ADAPT-WSA output agrees well with PSP observations once this active region rotates onto the near side, allowing us to reliably estimate the solar wind sources retrospectively for most of the encounter. We close with ways in which coronal modeling enables scientific interpretation of these encounters that would otherwise not have been possible.

Solar Chromospheric Network as a Source for Solar Wind Switchbacks

Recent studies suggest that the magnetic switchbacks (SBs) detected by the Parker Solar Probe carry information on the scales of solar supergranulation (large scale) and granulation (medium scale). We test this claim using high-resolution Hα images obtained with the visible spectropolarimeters of the Goode Solar Telescope in Big Bear Solar Observatory. As possible solar sources, we count all the spicule-like features standing along the chromospheric networks near the coronal hole boundary visible in the Hα blue-wing but absent in the red-wing images and measure the geometric parameters of dense sections of individual flux tubes. Intervals between adjacent spicules located along the chromospheric networks are found in the range of 0.4–1.5 Mm (0.°03–0.°12) tending to be smaller than the medium scale of SBs. Interdistances between all pairs of the flux tubes are also counted and they appear in a single peak distribution around 0.7 Mm (0.°06) unlike the waiting-time distribution of SBs in a scale-free single power-law form. The length-to-diameter ratio of the dense section of flux tubes is as high as 6–40, similar to the aspect ratio of SBs. The number of spicules along a network can be as high as 40–100, consistent with numerous SBs within a patch. With these numbers, it is argued that the medium scale of SBs can be understood as an equilibrium distance resulting from a random walk within each diverging magnetic field funnel connected to the chromospheric networks.

Optimizing trapped field in superconductors with perforations

The use of artificial holes can improve the performance of high-temperature bulk superconductors. We report the results of Monte Carlo simulations of the trapped magnetic flux in superconducting samples with different configurations of perforated holes. Vortex trapping and emission at the hole boundary were modeled to account for flux pinning on the holes. It was found that the trapped flux can reach its maximum value, which does not depend on the number of holes. The dependence of the trapped flux on the diameter and number of holes is explored and described by the suggested relations that account for pinning on the holes and the effective hole area. Recommendations are provided to attain the maximum trapped flux for a fixed number or diameter of holes.

Existence of the Closed Magnetic Field Lines Crossing the Coronal Hole Boundaries

Coronal holes (CHs) are regions with unbalanced magnetic flux and have been associated with open magnetic field (OMF) structures. However, it has been reported that some CHs do not intersect with OMF regions. To investigate the inconsistency, we apply a potential-field (PF) model to construct the magnetic fields of the CHs. As a comparison, we also use a thermodynamic magnetohydrodynamic (MHD) model to synthesize coronal images and identify CHs from the synthetic images. The results from both the potential-field CHs and synthetic MHD CHs reveal that there is a significant percentage of closed field lines extending beyond the CH boundaries and more than 50% (17%) of PF (MHD) CHs do not contain OMF lines. The boundary-crossing field lines are more likely to be found in the lower latitudes during active times. While they tend to be located slightly closer than the non-boundary-crossing ones to the CH boundaries, nearly 40% (20%) of them in PF (MHD) CHs are not located in the boundary regions. The CHs without open field lines are often smaller and less unipolar than those with open field lines. The MHD model indicates higher temperature variations along the boundary-crossing field lines than the non-boundary-crossing ones. The main difference between the results of the two models is that the dominant field lines in the PF and MHD CHs are closed and open field lines, respectively.

The Dynamic Structure of Coronal Hole Boundaries

The boundaries of solar coronal holes are difficult to uniquely define observationally but are sites of interest in part because the slow solar wind appears to originate there. The aim of this article is to explore the dynamics of interchange magnetic reconnection at different types of coronal hole boundaries—namely streamers and pseudostreamers—and their implications for the coronal structure. We describe synthetic observables derived from three-dimensional magnetohydrodynamic simulations of the atmosphere of the Sun in which coronal hole boundaries are disturbed by flows that mimic the solar supergranulation. Our analysis shows that interchange reconnection takes place much more readily at the pseudostreamer boundary of the coronal hole. As a result, the portion of the coronal hole boundary formed by the pseudostreamer remains much smoother, in contrast to the highly distorted helmet-streamer portion of the coronal hole boundary. Our results yield important new insights on coronal hole boundary regions, which are critical in coupling the corona to the heliosphere as the formation regions of the slow solar wind.

An Intelligent Identification and Repair Method for Annular Holes in 3D Printing.

With the popularization of 3D printing in the consumer goods field, there is a specific type of hole named annular hole in the narrow features, surface bumps, or folded parts of products. The traditional triangular mesh repair method is not effective for such holes. The structural characteristics of the annular hole are analyzed in this research, and the definition and identification method for annular holes is presented through the shape and position relationship of two closed hole lines. To improve the repair efficiency and the applicability of the algorithm, the traditional hole repair method and process are ameliorated. A repair strategy of hole boundary stitching and filling, triangulation optimization, implicit surface construction based on Radial Basis Function, and surface integral deformation is adopted to achieve a smooth joint of the repaired hole surface with the original triangular mesh surface. The method can ensure surface smoothness and accuracy. Finally, two experiments are carried out to verify the repair quality and efficiency of our method. Compared with Geomagic software, the proposed method can automatically identify and repair annular holes with fewer defects and similar efficiency. Compared with a traditional hole repair method, the evaluation results demonstrate that the proposed method is much faster, and the repair quality is higher without the influences of human operations. It is shown that our method can be applied to annular hole repair of 3D printing models without the participation of technicians.

Electron‐Scale Current Sheet as the Boundary of a Linear Magnetic Hole in the Terrestrial Current Sheet Observed by the Magnetospheric Multiscale Mission

AbstractIon‐scale and electron‐scale magnetic holes widely exist in many space plasma regions, and have been extensively studied. However, characteristics of the charged particles and current densities inside the linear magnetic holes (LMHs) with a size between typical ion and electron scales are unclear. Here, we report a LMH with a cross section size of ∼2.4 ion gyroradii in the terrestrial current sheet using the high‐resolution data of the Magnetospheric Multiscale Mission. We find that the electron velocity and temperature have significant variations at the sharp boundaries of this LMH, while the ion parameters have no significant change. The decrease of the magnetic field pressure is mainly balanced by the electron thermal pressure. A strong electron flow accompanied by an enhancement of the electric field is formed by electron drift motions on the outermost boundary with a thickness of 0.12–0.24 ion gyroradius. This electric field might originate from variations of the ion and electron gyrations when crossing the sharp boundary. The electron flow forms a thin current sheet on the outermost side of the LMH instead of being distributed over the entire cross section. Most of the trapped electrons are wrapped by this thin current sheet. These results could improve our understanding of the properties of LMHs with a size between typical ion and electron scales.

Tiny hole inspection of aircraft engine nacelle in 3D point cloud via robust statistical fitting

In the aircraft manufacturing industry, drilling hole inspection is a vital task for the noise reduction ability and the aircraft structure stability. Due to the complexity of the inner surface of the engine nacelle, inspecting drilling holes of a small size and a large number is fairly challenging. In this paper, we propose a framework for automatic hole inspection on composite flat parts. The raw data of traditional 3D laser scanning usually contain considerable noise and outliers, which has a great influence on tiny hole inspection. First, to perform measurement efficiently and to get raw data of good quality, we design a measurement platform to perform automatic measurement on a preset path. Instead of applying common boundary detection methods, we design a method to detect boundary points by evaluating the boundary possibility of each point, which is more likely to detect the points on a real hole boundary than noise. Based on the characteristics of laser scanning data, we then combine an effective algebraic circle fitting method with an iterative fitting strategy and develop a robust circle fitting method. The improved circle fitting method is capable of estimating a circle closest to the ground truth. Experiments demonstrate that our fitting method performs better than other common fitting methods for comparison under both synthetic and real scanning data.

Methodology for Determining the Compliance Matrix and Analyzing the Skew Anisotropic Plate with an Arbitrarily Shaped Hole

The previous analytical methods mainly focused on the analysis of orthotropic, transversely isotropic, or even isotropic materials, and little analyses have been conducted on nonorthogonal and extreme anisotropic material properties. In this study, the infinite skew anisotropic plate with an arbitrary-shaped hole are considered. Initially, two local Cartesian coordinate systems are established along the skew orientations in the plate, and the equations for the elastic constants of the material are established according to the transformation formulae under rotation of the coordinate axes. On this basis, the elastic compliance matrix for the skew anisotropic material can be obtained in combination with the engineering constants (Young’s modulus, Poisson’s ratio, and shear modulus). Subsequently, the complex variable method is utilized to derive the analytical solutions for stress along the hole boundary. The elliptical, hexagonal, and square holes perforated in skew anisotropic plates are used as examples, respectively, and the stress distributions along the hole boundary are analyzed for different external loadings. Finally, the theoretical method presented in this paper is verified by means of the Finite Element Analysis of ANSYS software.

A CAE-oriented mesh hole-filling algorithm focusing on geometry and quality

PurposeIntegrality of surface mesh is requisite for computational engineering. Nonwatertight meshes with holes can bring inconvenience to applications. Unlike simple modeling or visualization, the downstream industrial application scenarios put forward higher requirements for hole-filling, although many related algorithms have been developed. This study aims at the hole-filling issue in industrial application scenarios.Design/methodology/approachThis algorithm overcomes some inherent weakness of general methods and generates a high-level resulting mesh. Initially, the primitive hole boundary is filled with a more appropriate triangulation which introduces fewer geometric errors. And in order for better performances on shape approximation of the background mesh, the algorithm also refines the initial triangulation with topology optimization. When obtaining the background mesh defining the geometry and size field, spheres on it are packed to determine the vertex configuration and then the resulting high-level mesh is generated.FindingsThrough emphasizing geometry recovery and mesh quality, the proposed algorithm works well in hole-filling in industrial application scenarios. Many experimental results demonstrate the reliability and the performance of the algorithm. And the processed meshes are capable of being used for industrial simulation computations directly.Originality/valueThis paper makes input meshes more adaptable for solving programs through local modifications on meshes and perfects the preprocessing technology of finite element analysis (FEA).

Local piezoelectric properties of perforated ferroelectric barium–strontium titanate films

Objectives. Focused ion beam etching remains one of the most common methods for fabricating 2D photonic crystals and structures based on functional materials. This technique is quite well developed for semiconductors. But at the same time, the change in the properties of ferroelectric materials under the action of a focused ion beam, including parameters of distribution and switching of the polarization state under the action of an electric field, remains poorly studied. The purpose of this work is to determine the local piezoelectric parameters in perforated ferroelectric films of barium strontium titanate (Ba0.8Sr0.2TiO3) with ordered vertical air channels fabricated by focused ion beam etching.Methods. Experimental studies were conducted using piezoresponse force microscopy under applied electric field in planar geometry.Results. It is shown that the perforation of a ferroelectric film leads not only to the formation of significant inhomogeneities in the piezoelectric response distribution in the structure, but also to the noticeable increase in the magnitude of both the vertical and lateral components of the piezoresponse near the perforation holes. The calculation results showed that the greatest enhancement is observed for the lateral component of the piezoresponse: from 5 pm/V for a nonperforated film to 65 pm/V in the perforated area.Conclusions. The most probable mechanism for such a change in properties is the influence of a disturbed layer that occurs at the boundary and the inner surface of vertical air channels. The properties of this layer are due to two factors: amorphization of the structure as a result of the focused ion beam etching and the appearance of pinned domain states near the hole, leading to the formation of the complex piezoresponse distribution both at the hole boundary and in the gap between the perforations. The information obtained is important for understanding the peculiarities of the formation of local piezoelectric and ferroelectric responses in photonic crystals fabricated by focused ion beam etching, as well as for finding ways to control their state when an external electric field is applied.

Possible Evidence for Shear-driven Kelvin–Helmholtz Instability along the Boundary of Fast and Slow Solar Wind in the Corona

This paper reports the first possible evidence for the development of the Kelvin–Helmholtz (KH) instability at the border of coronal holes separating the associated fast wind from the slower wind originating from adjacent streamer regions. Based on a statistical data set of spectroscopic measurements of the UV corona acquired with the UltraViolet Coronagraph Spectrometer on board the SOlar and Heliospheric Observatory during the minimum activity of solar cycle 22, high temperature–velocity correlations are found along the fast/slow solar wind interface region and interpreted as manifestations of KH vortices formed by the roll-up of the shear flow, whose dissipation could lead to higher heating and, because of that, higher velocities. These observational results are supported by solving coupled solar wind and turbulence transport equations including a KH-driven source of turbulence along the tangential velocity discontinuity between faster and slower coronal flows: numerical analysis indicates that the correlation between the solar wind speed and temperature is large in the presence of the shear source of turbulence. These findings suggest that the KH instability may play an important role both in the plasma dynamics and in the energy deposition at the boundaries of coronal holes and equatorial streamers.

3D Face Geometry Optimization Using Artificial Intelligence and Computer Graphics

Human face plays an indispensable role in emotional expression and information exchange, which attracts large number of researchers to study face recognition. Nowadays, with the rapid development of computer graphics, artificial intelligence, and other technologies, the ability of the human vision system to recognize facial expressions and facial organs is enhanced. More and more experts think about how to make the computer vision system have this capability. By combining artificial intelligence and computer graphics, this paper studies how to optimize the 3D face network model and extract geometric features for 3D face recognition. We propose a 3D face network model based on Poisson equation to realize face hole recognition and boundary preprocessing. Besides, we also establish the 3D face surface equation and equal face value extraction and enhance the face feature based on facial semantic information. We study the hole repair of 3D face model based on Poisson equation integrating semantic information and achieve the purpose of optimizing the 3D face model. After the optimization, the method is compared with mesh repair and Poisson repair, which demonstrates that our Poisson-based 3D face hole repairing model obtains the best results among compared methods.

Scattering of SH waves by a circular cavity in an inhomogeneous medium: shear modulus and density are a functional form

Aiming at wave problems in continuous inhomogeneous media, this work studies the scattering of SH waves by a circular cavity in an infinite inhomogeneous medium and provides an analytical solution. The shear modulus and density of this inhomogeneous medium are given by a function. Through the construction of the elastic wave displacement field using an auxiliary function and a modulus function, the inhomogeneous governing equation is solved by assuming that both the elastic shear modulus and the medium density vary in the form of an exponential function to obtain the standard form of the Helmholtz equation. Using scattering by a cylindrical cavity as an example, the distribution of the dynamic stress concentration factor (DSCF) on the boundary of the circular hole is calculated and discussed, and the influence of each parameter on the distribution of the DSCF on the boundary of the circular hole is obtained. The results show that the DSCF at the boundary of a circular hole in an inhomogeneous medium is affected by the nonuniform parameters. When the medium density and modulus increase at a fast rate, the dynamic stress concentration coefficient changes significantly, the number of wave peaks increases, and the maximum value increases rapidly.

Total reflection of a flare-driven quasi-periodic extreme ultraviolet wave train at a coronal hole boundary

Context. A flare-driven quasi-periodic extreme ultraviolet wave train totally reflected at a coronal hole boundary was well imaged on both temporal and spatial scales by AIA/SDO. Aims. We aim to investigate the driving mechanisms of the quasi-periodic wave train and demonstrate the total reflection effect at the coronal hole boundary. Methods. The speeds of the incident and reflected wave trains are studied. The periodic correlation of the wave trains with the related flare is probed. We compare the measured incidence angle and the estimated critical angle. Results. We find that the periods of the incident and reflected wave trains are both about 100 s. The excitation of the quasi-periodic wave train was possibly due to the intermittent energy release in the associated flare since its period is similar to that of the quasi-periodic pulsations in the associated flare. Our observational results show that the reflection of the wave train at the boundary of the coronal hole was a total reflection because the measured incidence and critical angles satisfy the theory of total reflection: the incidence angle is smaller than the critical angle.

Analysis of the Distribution, Rotation and Scale Characteristics of Solar Wind Switchbacks: Comparison between the First and Second Encounters of Parker Solar Probe

The S-shaped magnetic structure in the solar wind formed by the twisting of magnetic field lines is called a switchback, whose main characteristics are the reversal of the magnetic field and the significant increase in the solar wind radial velocity. We identify 242 switchbacks during the first two encounters of Parker Solar Probe. Statistics methods are applied to analyze the distribution and the rotation angle and direction of the magnetic field rotation of the switchbacks. The diameter of switchbacks is estimated with a minimum variance analysis (MVA) method based on the assumption of a cylindrical magnetic tube. We also make a comparison between switchbacks from inside and the boundary of coronal holes. The main conclusions are as follows: (1) the rotation angles of switchbacks observed during the first encounter seem larger than those of the switchbacks observed during the second encounter in general; (2) the tangential component of the velocity inside the switchbacks tends to be more positive (westward) than in the ambient solar wind; (3) switchbacks are more likely to rotate clockwise than counterclockwise, and the number of switchbacks with clockwise rotation is 1.48 and 2.65 times those with counterclockwise rotation during the first and second encounters, respectively; (4) the diameter of switchbacks is about 105 km on average and across five orders of magnitude (103–107 km).

Alternative characterization of a black hole boundary

After reviewing the shortcomings of existing definitions used to characterize the boundary of a black hole, we present a new method for its characterization. This definition could potentially be applied to locate the boundary of general black hole solutions of the Einstein field equations. Using our definition in general spherically symmetric spacetimes, we argue that an observer falling into a black hole encounters an infinite energy density, pressure, and flux at the black hole boundary. This result is interpreted as a firewall that prevents the growth of classical black holes. However, the possibility of black hole growth via quantum mechanical tunneling cannot be ruled out.

A High-resolution Study of Magnetic Field Evolution and Spicular Activity around the Boundary of a Coronal Hole

Abstract In this study, we analyze high-spatial-resolution (0.″24) magnetograms and high-spatial-resolution (0.″10) Hα off-band (± 0.8 Å) images taken by the 1.6 m Goode Solar Telescope to investigate the magnetic properties associated with small-scale ejections in a coronal hole boundary region from a statistical perspective. With one and a half hours of optical observations under excellent seeing, we focus on the magnetic structure and evolution by tracking the magnetic features with the Southwest Automatic Magnetic Identification Suite (SWAMIS). The magnetic field at the studied coronal hole boundary is dominated by negative polarity with flux cancellations at the edges of the negative unipolar cluster. In a total of 1250 SWAMIS-detected magnetic cancellation events, ∼39% are located inside the coronal hole with an average flux cancellation rate of 2.0 × 1018 Mx Mm−2 hr−1, and ∼49% are located outside the coronal hole with an average flux cancellation rate of 8.8 × 1017 Mx Mm−2 hr−1. We estimated that the magnetic energy released due to flux cancellation inside the coronal hole is six times more than that outside the coronal hole. Flux cancellation accounts for ∼9.5% of the total disappearance of magnetic flux. Other forms of its disappearance are mainly due to fragmentation of unipolar clusters or merging with elements of the same polarity. We also observed a number of significant small-scale ejections associated with magnetic cancellations at the coronal hole boundary that have corresponding EUV brightenings.