Boundary Loop Research Articles

Causal diamonds in ( 2+1 )-dimensional quantum gravity

We develop the reduced phase space quantization of causal diamonds in pure ($2+1$)-dimensional gravity with a nonpositive cosmological constant. The system is defined as the domain of dependence of a topological disc with fixed boundary metric. By solving the initial value constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of ${\text{Diff}}^{+}({S}^{1})/\mathrm{PSL}(2,\mathbb{R})$. To quantize this phase space we apply Isham's group-theoretic quantization scheme, with respect to a ${\mathrm{BMS}}_{3}$ group, and find that the quantum theory can be realized by wave functions on some coadjoint orbit of the Virasoro group, with labels in irreducible unitary representations of the corresponding little group. We find that the twist of the diamond boundary loop is quantized in integer or half-integer multiples of the ratio of the Planck length to the boundary length.

Structure and electronic properties of closed-ring defects in epitaxial graphene

A number of past studies have focused on point and line defects in graphene epitaxially grown on SiC substrates. However, few studies have investigated closed-ring defects formed within grain boundary loops. The present study addresses this issue by applying low-temperature scanning tunneling microscopy/spectroscopy to investigate the atomic structures of closed-ring defects in graphene epitaxially grown on 4H-SiC, and to evaluate their effects on the electron state density. The results indicate that the orientations of the graphene lattice inside and outside of grain boundary loop structures are rotated uniformly by an angle of 30° relative to each other, suggesting that closed-ring defects are highly ordered and are mainly composed of clusters of pentagon-heptagon carbon rings and highly ordered pentagon-heptagon chains. In addition, the spectroscopy results reveal for the first time that the density of electron states inside a closed-ring defect is strongly localized and position-dependent. Moreover, these closed-ring defects can eliminate intervalley scattering while maintaining intravalley scattering. These findings are not only helpful for contributing to a deeper understanding of the effects of closed-ring defects in graphene, but also present a potentially useful valley-filtering mechanism for charge carries that can be applied to the practical development of all-electric valley-based devices.

Circular Wilson loops in defect mathcal{N} = 4 SYM: phase transitions, double-scaling limits and OPE expansions

We consider circular Wilson loops in a defect version of mathcal{N} = 4 super-Yang- Mills theory which is dual to the D3-D5 brane system with k units of flux. When the loops are parallel to the defect, we can construct both BPS and non-BPS operators, depending on the orientation of the scalar couplings in the R-symmetry directions. At strong ’t Hooft coupling we observe, in the non supersymmetric case, a Gross-Ooguri-like phase transition in the dual gravitational theory: the familiar disk solution dominates, as expected, when the operator is far from the defect while a cylindrical string worldsheet, connecting the boundary loop with the probe D5-brane, is favourite below a certain distance (or equivalently for large radii of the circles). In the BPS case, instead, the cylindrical solution does not exist for any choice of the physical parameters, suggesting that the exchange of light supergravity modes always saturate the expectation value at strong coupling. We study the double-scaling limit for large k and large ’t Hooft coupling, finding full consistency in the non-BPS case between the string solution and the one-loop perturbative result. Finally we discuss, in the BPS case, the failure of the double-scaling limit and the OPE expansion of the Wilson loop, finding consistency with the known results for the one-point functions of scalar composite operators.

Efficient Coverage Hole Detection Algorithm Based on the Simplified Rips Complex in Wireless Sensor Networks

The appearance of coverage holes in the network leads to transmission links being disconnected, thereby resulting in decreasing the accuracy of data. Timely detection of the coverage holes can effectively improve the quality of network service. Compared with other coverage hole detection algorithms, the algorithms based on the Rips complex have advantages of high detection accuracy without node location information, but with high complexity. This paper proposes an efficient coverage hole detection algorithm based on the simplified Rips complex to solve the problem of high complexity. First, Turan’s theorem is combined with the concept of the degree and clustering coefficient in a complex network to classify the nodes; furthermore, redundant node determination rules are designed to sleep redundant nodes. Second, according to the concept of the complete graph, redundant edge deletion rules are designed to delete redundant edges. On the basis of the above two steps, the Rips complex is simplified efficiently. Finally, from the perspective of the loop, boundary loop filtering and reduction rules are designed to achieve coverage hole detection in wireless sensor networks. Compared with the HBA and tree-based coverage hole detection algorithm, simulation results show that the proposed hole detection algorithm has lower complexity and higher accuracy and the detection accuracy of the hole area is up to 99.03%.

Competing factors in grain boundary loop shrinkage: Two-dimensional hard sphere colloidal crystals.

A grain boundary (GB) loop in a two-dimensional solid is the boundary of a domain or grain whose lattice orientation is mismatched with its uniform surroundings. Understanding the factors that influence the rate at which the interior of a GB loop relaxes to the orientation of its surroundings is an important step toward control and predictability of grain coarsening in general. Recent computational and experimental studies looking at the rate of GB loop shrinkage in two-dimensional colloidal hard sphere solids have uncovered contradictory trends: in experiments, GB loops with low misorientation angles shrank the fastest, while in simulations, they persisted the longest. In this study, the computational system's behavior is brought into qualitative agreement with the experimental results through increasing the lateral packing pressure, decreasing the domain size, and mimicking the experimental protocol used to form the GB loop. Small GB loops with the same misorientation, but displaying either a hexagonal or starlike grain shape depending on the orientation of their six dislocations, are shown to differ in their rates of shrinkage by two orders of magnitude. The evidence suggests that both the barrier to generating new dislocations as well as the pattern of dislocations formed by different GB loop preparation methods will determine which trend is observed.

Shrinkage mechanisms of grain boundary loops in two-dimensional colloidal crystals

We discuss the various mechanisms involved in the spontaneous shrinkage of circular grain boundaries in two-dimensional colloidal crystals. We provide experimental evidence that these grain boundary loops shrink owing to three intermittent mechanisms proposed for atomic materials, namely purely curvature-driven migration, coupled grain boundary migration, and grain boundary sliding. Throughout shrinkage, the product of the radius and misorientation of the grain boundary loop remains higher than a fundamental limit resulting from the specific dislocation structure of grain boundary loops, except for the very last stage where the loop character is lost. Despite its complexity, this process can be effectively described by a single kinetic coefficient, allowing for a simplified description of grain boundary loop kinetics.Graphical abstract

Dislocation-controlled formation and kinetics of grain boundary loops in two-dimensional crystals

The formation and kinetics of grain boundaries are closely related to the topological constraints imposed on their complex dislocation structure. Loop-shaped grain boundaries are unique structures to establish such a link because their overall topological "charge" is zero due to their null net Burgers vector. Here, we observe that a local rotational deformation of a 2D colloidal crystal with an optical vortex results in a grain boundary loop only if the product of its radius and misorientation exceeds a critical value. Above this value, the deformation is plastic and the grain boundary loop spontaneously shrinks at a rate that solely depends on this product, while otherwise, the deformation is elastically restored. We show that this elastic-to-plastic crossover is a direct consequence of the unique dislocation structure of grain boundary loops. At the critical value, the loop is structurally equivalent to the so-called "flower defect" and the shrinkage rate diverges. Our results thus reveal a general limit on the formation of grain boundary loops in 2D crystals and elucidate the central role of defects in both the onset of plasticity and the kinetics of grain boundaries.

Propagation-based marching cubes algorithm using open boundary loop

The marching cubes (MC) algorithm is employed to generated triangular meshes for visualizing medical images, sculpture scans and mathematical surfaces. It sequentially traverses cuberille data composed of sampled points of a scalar volumetric data. This paper proposes a propagation-based MC algorithm that uses the open boundary loop concept. The open boundary loop is used to determine adjacent cells for the next iteration of the MC algorithm. After inserting each triangle, the open boundary loop is reevaluated. Simultaneously, it is ensured that all triangles are coherently oriented and there are no holes on the isosurface. Several tests are conducted to determine the performance of the algorithm in comparison with the original MC algorithm. Results from these tests indicate that, for large-scale problems, the proposed algorithm performs better than the original.

Finite-size corrections for universal boundary entropy in bond percolation

We compute the boundary entropy for bond percolation on the square lattice in the presence of a boundary loop weight, and prove explicit and exact expressions on a strip and on a cylinder of size LL. For the cylinder we provide a rigorous asymptotic analysis which allows for the computation of finite-size corrections to arbitrary order. For the strip we provide exact expressions that have been verified using high-precision numerical analysis. Our rigorous and exact results corroborate an argument based on conformal field theory, in particular concerning universal logarithmic corrections for the case of the strip due to the presence of corners in the geometry. We furthermore observe a crossover at a special value of the boundary loop weight.

An Automatic Method for Complete Triangular Mesh Conversion into Quadrilateral Mesh for Multiple Domain Geometry

This research developed an automatic two-dimensional finite element meshing system to resolve practical engineering problems in the fields of geology, hydrology, and water resources. This system first used the Delaunay triangulation method to create reasonable-density triangular mesh and then converted it into quadrilateral mesh by combining proper pairs of adjacent triangles. A series of combination patterns aiming at three cases were established. The effect of the number of boundary edges on the subsequent meshing procedures were studied and summarized. For the geometry with multiple domains an adjustment method is proposed to completely eliminate the residual triangles during quadrilateral meshing through adjusting the number of boundary edges in each loop to be even. A special boundary loop identification method is proposed for priority treatment. Corresponding treatment methods aimed at three different situations are established for common boundary loops. For a certain boundary loop with an odd number of boundary edges, the appropriate edge for new point insertion is determined by the position properties and relative density errors. Practical applications confirm that the method proposed in this paper could successfully implement the full conversion from the triangular mesh to the quadrilateral mesh.

Interactive mesh cloning driven by boundary loop

In order to copy arbitrary irregular mesh between two models continuously, this paper presents an interactive mesh cloning approach based on pyramid spherical coordinates driven by boundary loop. T...

Design and Reuse of Freeform Features on Mesh Surface

To solve the difficulty of reusing complex freeform features on mesh surface,a detail-preserving method is proposed. By means of differential geometry information contained in Laplacian coordinates,such as curvature,normal and so on,put forward a new method to parameterize the boundary loop of features,which is based on differential coordinates. The method of parameterization based on differential coordinates can preserve the length,curvature and the shape of features' boundary curve,which can reduce the deformation of the boundary curve mapped onto the target mesh. The target mesh is parameterized by Geodesic Polar Coordinates method. The boundary curve of features is mapped onto target mesh by the principle of common parameter coordinates. Thus the boundary constraint conditions including position constraint conditions and normal constrain conditions,which are used as the constrain conditions of mesh deformation; can get from the mapped boundary loop. Finally,the feature is deformed to match the target mesh using Laplacian deformation which combines with linear rotation-invariant coordinates. The algorithm avoids parameterizing the reuse features directly,which makes it easy to work with the complex features,and unrelated with the number of feature genus. The results show that the proposed method is robust,effective and can be used to clone the complex features.

Effects of a grain boundary loop on the thermal conductivity of graphene: A molecular dynamics study

Thermal transport in graphene with one type of grain boundary loop was investigated using non-equilibrium molecular dynamics simulation method. The results showed that thermal conductivity is very sensitive to defect concentration. It rapidly decreases in the presence of a defect. This is attributed the phonon defects scattering which shorten the phonon mean free paths leading to the reduction in thermal conductivity. Furthermore, temperature dependency of thermal conductivity of pristine and defected graphene was determined. The results indicated that thermal conductivity of defect-free graphene varies significantly with temperature, while thermal conductivity of graphene with defect remains nearly invariant with the temperature of the system. This implies the possibility of phonon-defect scattering domination over Umklapp phonon–phonon scattering in graphene with defect.

More about one-loop effective action of open superstring in AdS5 × S5

We reconsider the calculation of the one-loop effective action for an open Green-Schwarz superstring in the $AdS_5\times S^5$ background for a circular boundary loop. By an explicit computation of the ratio of relevant determinants, describing semi-classical fluctuations about the minimal surface in AdS and flat spaces, we show that it does not depend upon the AdS regularizing parameter $\epsilon$. The only dependence upon $\epsilon$ resides in the reparametrization path integral of the exponential of the classical boundary action. We analyze how the result depends on the choice of the boundary condition imposed on fluctuating fields and show that, despite the fact that the contribution of individual angular modes changes, the product over the modes remains unchanged.

Role of grain boundary and dislocation loop in H blistering in W: A density functional theory assessment

We report a first-principles density functional theory study on the role of grain boundary and dislocation loop in H blistering in W. At low temperature, the Σ3(111) tilt grain boundary can trap up to six H atoms per (1×1) unit in (111) plane before significant sliding occurs. This amount of H weakens greatly the cohesion across the boundary. At room temperature, when only three H can be trapped, this effect can be still significant. A dislocation loop in (100) plane can trap four H per (1×1) unit even at room temperature, whose detrimental effect is strong enough to break the crystal. Our numerical results demonstrate unambiguously the grain boundaries and dislocation loops can serve as precursors of H blistering. In addition, we find no H2 molecules can be formed in either environment before fracture of W bonds starts, well explaining the H blistering in the absence of voids during non-damaging irradiation.

Development and validation of a tokamak skin effect transformer model

A lumped parameter, state space model for a tokamak transformer including the slow flux penetration in the plasma (skin effect transformer model) is presented. The model does not require detailed or explicit information about plasma profiles or geometry. Instead, this information is lumped in system variables, parameters and inputs. The model has an exact mathematical structure built from energy and flux conservation theorems, predicting the evolution and non-linear interaction of plasma current and internal inductance as functions of the primary coil currents, plasma resistance, non-inductive current drive and the loop voltage at a specific location inside the plasma (equilibrium loop voltage). Loop voltage profile in the plasma is substituted by a three-point discretization, and ordinary differential equations are used to predict the equilibrium loop voltage as a function of the boundary and resistive loop voltages. This provides a model for equilibrium loop voltage evolution, which is reminiscent of the skin effect. The order and parameters of this differential equation are determined empirically using system identification techniques. Fast plasma current modulation experiments with random binary signals have been conducted in the TCV tokamak to generate the required data for the analysis. Plasma current was modulated under ohmic conditions between 200 and 300 kA with 30 ms rise time, several times faster than its time constant L/R ≈ 200 ms. A second-order linear differential equation for equilibrium loop voltage is sufficient to describe the plasma current and internal inductance modulation with 70% and 38% fit parameters, respectively. The model explains the most salient features of the plasma current transients, such as the inverse correlation between plasma current ramp rates and internal inductance changes, without requiring detailed or explicit information about resistivity profiles. This proves that a lumped parameter modelling approach can be used to predict the time evolution of bulk plasma properties such as plasma inductance or current with reasonable accuracy; at least under ohmic conditions without external heating and current drive sources.

Grain boundary loops in graphene

Topological defects can affect the physical properties of graphene in unexpected ways. Harnessing their influence may lead to enhanced control of both material strength and electrical properties. Here we present a new class of topological defects in graphene composed of a rotating sequence of dislocations that close on themselves, forming grain boundary loops that either conserve the number of atoms in the hexagonal lattice or accommodate vacancy/interstitial reconstruction, while leaving no unsatisfied bonds. One grain boundary loop is observed as a "flower" pattern in scanning tunneling microscopy (STM) studies of epitaxial graphene grown on SiC(0001). We show that the flower defect has the lowest energy per dislocation core of any known topological defect in graphene, providing a natural explanation for its growth via the coalescence of mobile dislocations.

An approach to B-rep model simplification based on region suppression

This paper presents a simplification method for boundary representation (B-rep) models using region suppression. This method suppresses every complex unwanted region of a B-rep model so as to efficiently generate a simplified version of the original model that preserves its original rough shape. In this method, the new surfaces that are used to cover each suppressed region are constructed based on the boundary loop decomposition of the suppressed region rather than through the time-consuming face extension and intersection operations widely applied in previous studies. An evaluation of experimental results is presented to demonstrate the efficiency and robustness of the method.

Notes on supersymmetric Wilson loops on a two-sphere

We study a recently discovered family of 1/8-BPS supersymmetric Wilson loops in $ \mathcal{N} = 4 $ super Yang-Mills theory and their string theory duals. The operators are defined for arbitrary contours on a two-sphere in space-time, and they were conjectured to be captured perturbatively by 2d bosonic Yang-Mills theory. In the AdS dual, they are described by pseudo-holomorphic string surfaces living on a certain submanifold of AdS 5 × S 5. We show that the regularized area of these string surfaces is invariant under area preserving diffeomorphisms of the boundary loop, in agreement with the conjecture. Further, we find a connection between the pseudo-holomorphicity equations and an auxiliary σ-model on S 3, which may help to construct new 1/8-BPS string solutions. We also show that the conjectured relation to 2d Yang-Mills implies that a connected correlator of two Wilson loops is computed by a Hermitian Gaussian two-matrix model. On the AdS dual side, we argue that the connected correlator is described by two disconnected disks interacting through the exchange of supergravity modes, and we show that this agrees with the strong coupling planar limit of the two-matrix model.

Renormalized Area and Properly Embedded Minimal Surfaces in Hyperbolic 3-Manifolds

We study the renormalized area functional \({\mathcal{A}}\) in the AdS/CFT correspondence, specifically for properly embedded minimal surfaces in convex cocompact hyperbolic 3-manifolds (and somewhat more broadly, Poincare-Einstein spaces). Our main results include an explicit formula for the renormalized area of such a minimal surface Y as an integral of local geometric quantities, as well as formulae for the first and second variations of \({\mathcal{A}}\) which are given by integrals of global quantities over the asymptotic boundary loop γ of Y. All of these formulae are also obtained for a broader class of nonminimal surfaces. The proper setting for the study of this functional (when the ambient space is hyperbolic) requires an understanding of the moduli space of all properly embedded minimal surfaces with smoothly embedded asymptotic boundary. We show that this moduli space is a smooth Banach manifold and develop a \({\mathbb{Z}}\) -valued degree theory for the natural map taking a minimal surface to its boundary curve. We characterize the nondegenerate critical points of \({\mathcal{A}}\) for minimal surfaces in \({\mathbb{H}^3}\) , and finally, discuss the relationship of \({\mathcal{A}}\) to the Willmore functional.