Two-dimensional Polygons Research Articles

Particle-based and continuum models for confined nematics in two dimensions.

We use the particle-based stochastic multi-particle collision dynamics (N-MPCD) algorithm to simulate confined nematic liquid crystals in regular two-dimensional polygons such as squares, pentagons and hexagons. We consider a range of values of the nematicities, U, and simulation domain sizes, R, that canvass nano-sized polygons to micron-sized polygons. We use closure arguments to define mappings between the N-MPCD parameters and the parameters in the continuum deterministic Landau-de Gennes framework. The averaged N-MPCD configurations agree with those predicted by Landau-de Gennes theory, at least for large polygons. We study relaxation dynamics or the non-equilibrium dynamics of confined nematics in polygons, in the N-MPCD framework, and the kinetic traps bear strong resemblance to the unstable saddle points in the Landau-de Gennes framework. Finally, we study nematic defect dynamics inside the polygons in the N-MPCD framework and the finite-size effects slow down the defects and attract them to polygon vertices. Our work is a comprehensive comparison between particle-based stochastic N-MPCD methods and deterministic/continuum Landau-de Gennes methods, and this comparison is essential for new-age multiscale theories.

Two-dimensional polygon classification and pairwise clustering for pairing in ship parts nesting

Two-dimensional polygon classification and pairwise clustering for pairing in ship parts nesting

A pore-scale reconstruction-based approach to analyze the tobacco-containing segment in electrically heated cigarettes

A new pore-scale reconstruction method based on image processing and automated modeling was proposed in this paper to investigate the electrically heated cigarettes (EHC) porous tobacco-containing segment pyrolysis. First, the two-dimensional images of the microscope were binarized, noise filtered, and boundaries identified to form numerous two-dimensional polygons that describe the skeleton of porous media. Then, three-dimensional (3D) entities were generated through an automated modeling program. The model must be procedurally cleaned up geometrically for successful mesh generation. Second, the fluid flow, heat transfer, latent heat release, and chemical reaction heat in the actual pyrolysis process were considered in numerical simulation. The Arrhenius equation based on experimental data was used to describe the reaction process when chemical equations are challenging to determine. The simulation's pressure losses and component releases were validated with experimental data. The results show that the model reconstructed from the pore structure can accurately describe the flow, heat transfer, and component release in EHC and can completely describe the detailed information of the flow and temperature fields within the pore structure. The major components in EHC all dropped below 50% after ten smoking cycles. Glycerol in EHC near the heat generator is released rapidly to 0 at the beginning of the working process.

The Applications of Metallacycles and Metallacages

Metallacycles and metallacages constitute a class of coordination compounds composed of metal ions and organic ligands. Because of their precise stoichiometry, the flexibility and viability of design, metallacycles and metallacages have attracted considerable attention as supramolecular assemblies. Various two-dimensional polygons, three-dimensional polyhedra, and other nanoscale materials have been constructed and applied. The highly diverse structures, sizes, and shapes endow metallacycles and metallacages with unique physical and chemical properties and make them suitable for various applications such as encapsulation, separation, catalysis, and biological science. Herein, we review the recent developments in various metallacycles and metallacages in different fields. The text highlights biomedical applications involving molecular recognition and binding, antibacterial activity, and especially cancer diagnosis and treatment, including imaging, chemotherapy, PDT, and PTT.

Beautiful on the inside: Aesthetic preferences and the skeletal complexity of shapes.

A plain, blank canvas does not look very beautiful; to make it aesthetically appealing requires adding structure and complexity. But how much structure is best? In other words, what is the relationship between beauty and complexity? It has long been hypothesized that complexity and beauty meet at a "sweet spot," such that the most beautiful images are neither too simple nor too complex. Here, we take a novel experimental approach to this question, using an information-theoretic approach to object representation based on an internal "skeletal" structure. We algorithmically generated a library of two-dimensional polygons and manipulated their complexity by gradually smoothing out their features-essentially decreasing the amount of information in the objects. We then stylized these shapes as "paintings" by rendering them with artistic strokes, and "mounted" them on framed canvases hung in a virtual room. Participants were shown pairs of these mounted shapes (which possessed similar structures but varied in skeletal complexity) and chose which shape looked best by previewing each painting on the canvas. Experiment 1 revealed a "Goldilocks" effect: participants preferred paintings that were neither too simple nor too complex, such that moderately complex shapes were chosen as the most attractive paintings. Experiment 2 isolated the role of complexity per se: when the same shapes were scrambled (such that their structural complexity was undermined, while other visual features were preserved), the Goldilocks effect was dramatically diminished. These findings suggest a quadratic relationship between aesthetics and complexity in ways that go beyond previous measures of each and demonstrate the utility of information-theoretic approaches for exploring high-level aspects of visual experience.

Using Isovists in Measuring Surveillance and Expected Guardianship in Residential Neighborhood Property Crimes

Purpose: Assessing a level of surveillability, supervision, and expected guardianship in residential neighborhoods has been a topic of interest since the early work of Jacobs’ ‘eyes on the street’, and Newman’s ‘defensible space’. This paper reports on the use of isovists (two-dimensional polygons that represent the characteristics of the visual field) in understanding incidents of ‘breaking and entering’ in Ypsilanti, Michigan. Approach: Two measures relevant to environmental criminology were assessed: accessibility and surveillability. Findings: The findings indicate associations between incidents of crime and measures of visual accessibility. However, the level of homeownership was found to interact with the predictive models, suggesting the possible effect of ‘guardianship’. The geometrical shape of the isovist may also indicate where along a particular route, a crime is more likely to be committed. Originality: The results have the potential to assist law enforcement in identifying ‘hotspots’, and city planners in understanding the implications of urban design on crime.

Testing the spatial association of different types of polygons

In spatial statistics, we want to test hypotheses about the spatial association between two spatial patterns of geometric shapes. The spatial entities representing these geometric shapes are two-dimensional polygons, but researchers have often reduced these polygons to points to use point pattern methods. In this work, we developed techniques to test hypotheses related to polygon patterns that take advantage of all the information present in them. Our method is centered on a Monte Carlo toroidal shift approach to generate the reference null distribution. However, this approach comes with a caveat: the original polygons are broken into pieces. We were able to adapt the toroidal shift to work with polygon objects, eliminating this issue. In addition, extensions of the K12 function used for point patterns were proposed. We carried out a simulation study to demonstrate our method’s efficacy and to compare different test statistics. We illustrate the method by applying it to a real large data-set with different grass species.

Optimization Algorithm Design of Laser Marking Contour Extraction and Graphics Hatching Based on Image Processing Technology

On the premise of solving the problem in a specific situation, this paper aims at the laser marking machine for the design and optimization of the outline extraction of the two-dimensional composite curve figure and the figure hatching scheme. The scanning line algorithm based on computer graphics and the polygon hatching are based on the algorithm theory. Based on the foundation, an improved polygon scan line algorithm model is established, and the contour extraction and graphic shadows of two-dimensional polygons are realized by MATLAB programming. The simulation results show that our algorithm model can meet our requirements well, and at the same time has a certain improvement effect. At the same time, compared with traditional two-dimensional polygon scanning and hatching algorithms, our algorithm model has strong analysis and processing capabilities and strong applicability. Compared with traditional two-dimensional polygon scanning and shading algorithms, model analysis can still run stably in a high refresh rate environment. We hope to further optimize the algorithm in the later stage, so that it can be better used in related engineering fields.

Geographic Information Systems (GIS) as a Tool for Positive Identification from Frontal Sinus Radiographs

Frontal sinus radiographs are frequently used to identify human remains. However, the method of visually comparing antemortem (AM) to postmortem (PM) cranial radiographs has been criticized for being a subjective approach that relies on practitioner experience, training, and judgment rather than on objective, quantifiable procedures with published error rates. The objective of this study was to explore the use of ArcMap and its spatial analysis tool, Similarity Search, as a quantifiable, reliable, and reproducible method for identifying frontal sinus matches from cranial radiographs. Using cranial radiographs of 100 individuals from the William M. Bass DonatedSkeletal Collection, the frontal sinuses were digitized to create two-dimensional polygons. Similarity Search was evaluated on its ability to identify the correct AM radiograph using three variables: the number of scallops and the area and perimeter values of the polygons. Using all three variables, Similarity Search correctly identified the true match AM polygon in 58% of the male groups and in 62% of the female groups. These results indicate that ArcMap can be used with frontal sinus radiographs. However, further analysis of the three variables revealed that scallop number did not provide sufficient information about frontal sinus shape to increase the accuracy of Similarity Search, and area and perimeter only captured the size of the frontal sinus polygons, not shape. This research is a first step in developing a user-friendly, quantifiable frontal sinus comparison method for the purpose of positive identification.

Inside Front Cover: Metallacycles, metallacages, and their aggregate/optical behavior

Metal-organic complexes (MOCs), including metallacycles and metallacages, are discrete and well-defined molecular entities using platinum, palladium, iron, zinc, and silver as the metal centers. To date, multiple two-dimensional polygons and three-dimensional polyhedra have been prepared and were used for biochemical and biomedical applications. In this review, we summarized the latest progress in this area in approximately the last five years. (Aggregate. 2021;2:e94)

Populations using public-supply groundwater in the conterminous U.S. 2010; Identifying the wells, hydrogeologic regions, and hydrogeologic mapping units

Most Americans receive their drinking water from publicly supplied sources, a large portion of it from groundwater. Mapping these populations consistently and at a high resolution is important for understanding where the resource is used and needs to be protected. The results show that 269 million people are supplied by public supply, 107 million are supplied by groundwater and 162 million are supplied by surface water. The population using public supply drinking water was mapped in two ways: the census enhanced method (CEM) evenly distributes the population across populated census blocks, and the urban land-use enhanced method (ULUEM) distributes the population only to certain urban land use designations. In addition, a two-dimensional polygon dataset was created for the conterminous U.S. that identifies 177 unique Hydrogeologic Mapping Units (HMUs) with similar hydrogeologic characteristics. The HMUs do not overlap, but they can delineate areas where stacked hydrogeologic regions (HRs) contribute drinking water from below the surface. HRs are waterbearing geologic regions identified as either a principal aquifers (PA) or secondary hydrogeologic regions (SHR). Within each HMU, the wells were used to determine the proportion of each HR that is providing groundwater to the HMU. In 63% of the HMUs, a single HR is providing water to the public supply wells located within it, while the rest of the HMUs show that the wells are tapping up to a maximum of four stacked HRs. In total, groundwater from 108 HRs provide drinking water for public supply, six of which provide more than 50% of the groundwater used for public supply drinking water. The aquifer serving the largest number of equivalent people (>17 million) is the glacial aquifer. The HR providing the greatest number of people per km2 is the Biscayne aquifer in Florida at nearly 453 people per km2.

Space decomposition based on visible objects in an indoor environment

When a person moves, the set of objects in their visual range changes. Hence, the set of objects perceived from a specific range of locations may be considered as a signature (possibly non-unique) of this region and be used for the localization of this person. In the case of fixed objects, the number of regions with a set of specific visible objects is limited. A verbal description containing references to elements of this set of visible objects could then be used to localize a person in the space. This paper proposes an approach for decomposing a space into regions that are characterized by such sets of visible objects. In our approach, at least a portion of partial surfaces of an object must be visible (beyond single points) to make part of the signature. Our method calculates two-dimensional visibility polygons for a portion of an object’s surface. Overlaying these polygons, we partition the space in regions of visibility signatures. The approach has been implemented, and we demonstrate how to represent space by qualitative locations using these visibility signatures. We further show how this representation can be used to locate a person within a space by a set of visible objects.

Accelerating laser processes with a smart two-dimensional polygon mirror scanner for ultra-fast beam deflection

Abstract In laser processing, the possible throughput is directly scaling with the available average laser power. To avoid unwanted thermal damage due to high pulse energy or heat accumulation during MHz-repetition rates, energy distribution over the workpiece is required. Polygon mirror scanners enable high deflection speeds and thus, a proper energy distribution within a short processing time. The requirements of laser micro processing with up to 10 kW average laser powers and high scan speeds up to 1000 m/s result in a 30 mm aperture two-dimensional polygon mirror scanner with a patented low-distortion mirror configuration. In combination with a field programmable gate array-based real-time logic, position-true high-accuracy laser switching is enabled for 2D, 2.5D, or 3D laser processing capable to drill holes in multi-pass ablation or engraving. A special developed real-time shifter module within the high-speed logic allows, in combination with external axis, the material processing on the fly and hence, processing of workpieces much larger than the scan field.

Tailored nematic and magnetization profiles on two-dimensional polygons.

We study dilute suspensions of magnetic nanoparticles in a nematic host, on two-dimensional polygons. These systems are described by a nematic order parameter and a spontaneous magnetization, in the absence of any external fields. We study the stable states in terms of stable critical points of an appropriately defined free energy, with a nemato-magnetic coupling energy. We numerically study the interplay between the shape of the regular polygon, the size of the polygon, and the strength of the nemato-magnetic coupling for the multistability of this prototype system. Our notable results include (1) the coexistence of stable states with domain walls and stable interior and boundary defects, (2) the suppression of multistability for positive nemato-magnetic coupling, and (3) the enhancement of multistability for negative nemato-magnetic coupling.

AI-powered landslide susceptibility assessment in Hong Kong

Landslide susceptibility assessment is essential for regional landslide risk assessment and mitigation. Most past studies involved cell-based analysis that takes landslide incidents as geo-spatial points. Nevertheless, given that a landslide is a two-dimensional polygon on maps and a three-dimensional object in the real world, an object-wise assessment is more logical. Fusing with artificial intelligence (AI) techniques, this paper proposes a novel AI-powered object-based landslide susceptibility assessment method to address this issue. First, landslide and non-landslide objects are defined based on an optimal object size determined by statistics of historical landslides. Next, landslide and non-landslide samples are constructed by integrating geoenvironmental data layers derived from multi-source data. Subsequently, AI techniques are applied to learn susceptibility prediction based on the prepared samples. To illustrate the proposed method, a comprehensive case study of Hong Kong is conducted, in which six AI algorithms are evaluated including logistic regression (area under curve, AUC = 0.949), random forest (AUC = 0.951), LogitBoost (AUC = 0.958), convolutional neural network (CNN) (AUC = 0.966), bidirectional long short-term memory architecture of recurrent neural network (BiLSTM-RNN) (AUC = 0.966), and CNN-LSTM (AUC = 0.972), among which the BiLSTM-RNN and CNN-LSTM algorithms are applied in landslide susceptibility assessment for the first time. Results confirm that the proposed object-based method outperforms the traditional cell-based method significantly. Equally importantly, the case study produced the first set of AI-based territory-wide landslide susceptibility maps for Hong Kong. These maps can be used as a fundamental tool for quantifying natural terrain landslide risk and identifying susceptible zones where landslide mitigation measures may be needed.

Curvature profiles for quantum gravity

Building on the recently introduced notion of quantum Ricci curvature and motivated by considerations in nonperturbative quantum gravity, we advocate a new, global observable for curved metric spaces, the curvature profile. It is obtained by integrating the scale-dependent, quasilocal quantum Ricci curvature, and therefore also depends on a coarse-graining scale. To understand how the distribution of local, Gaussian curvature is reflected in the curvature profile, we compute it on a class of regular, two-dimensional polygons with isolated conical singularities. We focus on the case of the tetrahedron, for which we have a good computational control of its geodesics, and compare its curvature profile to that of a smooth sphere. The two are distinct, but qualitatively similar, which confirms that the curvature profile has averaging properties which are interesting from a quantum point of view.

High Throughput Laser Drilling with High Power Lasers Using a Two-Dimensional Polygon Mirror Scanner

High Throughput Laser Drilling with High Power Lasers Using a Two-Dimensional Polygon Mirror Scanner

A Reduced Study for Nematic Equilibria on Two-Dimensional Polygons

We study reduced nematic equilibria on regular two-dimensional polygons with Dirichlet tangent boundary conditions in a reduced two-dimensional Landau--de Gennes framework, discussing their relevance in the full three-dimensional framework too. We work at a fixed temperature and study the reduced stable equilibria in terms of the edge length, $\lambda$, of the regular polygon, $E_K$, with $K$ edges. We analytically compute a novel “ring solution” in the $\lambda \to 0$ limit, with a unique point defect at the center of the polygon for $K \neq 4$. The ring solution is unique. For sufficiently large $\lambda$, we deduce the existence of at least $[K/2 ]$ classes of stable equilibria and numerically compute bifurcation diagrams for reduced equilibria on a pentagon and hexagon, as a function of $\lambda^2$, thus illustrating the effects of geometry on the structure, locations, and dimensionality of defects in this framework.

A Vertex Concavity-Convexity Detection Method for Three-Dimensional Spatial Objects Based on Geometric Algebra

Vertex concavity-convexity detection for spatial objects is a basic algorithm of computer graphics, as well as the foundation for the implementation of other graphics algorithms. In recent years, the importance of the vertex concavity-convexity detection algorithm for three-dimensional (3D) spatial objects has been increasingly highlighted, with the development of 3D modeling, artificial intelligence, and other graphics technologies. Nonetheless, the currently available vertex concavity-convexity detection algorithms mostly use two-dimensional (2D) polygons, with limited research on vertex concavity-convexity detection algorithms for 3D polyhedrons. This study investigates the correlation between the outer product and the topology of the spatial object based on the unique characteristic that the outer product operation in the geometric algebra has unified and definitive geometric implications in space, and with varied dimensionality. Moreover, a multi-dimensional unified vertex concavity-convexity detection algorithm framework for spatial objects is proposed, and this framework is capable of detecting vertex concavity-convexity for both 2D simple polygons and 3D simple polyhedrons.

Construction of Stimuli-Responsive Functional Materials via Hierarchical Self-Assembly Involving Coordination Interactions.

Supramolecular self-assembly, which creates the ordered structures as a result of spontaneous organization of building blocks driven by noncovalent interactions (NCIs), is ubiquitous in nature. Recently, it has become increasingly clear that nature often builds up complex structures by employing a hierarchical self-assembly (HSA) strategy, in which the components are brought together in a stepwise process via multiple NCIs. Inspired by the dedicated biological structures in nature, HSA has been widely explored to construct well-defined assemblies with increasing complexity. The employment of direct metal-ligand bonds to drive the formation of discrete metallosupramolecular architectures has proven to be a highly efficient strategy to prepare structurally diverse architectures like two-dimensional (2-D) polygons and three-dimensional (3-D) polyhedra with well-defined shapes, sizes, and geometries. Such well-defined organometallic assemblies provide an ideal platform for designing novel artificial supramolecular systems with the increasing complexity though HSA. The presence of a well-defined organometallic scaffold brings an additional dimension to the final nanoscale structures. Moreover, the multilevel dynamic nature of hierarchical self-assemblies brings more structural and functional possibilities of resultant supramolecular systems. This Account will focus on our recent advance on construction of stimuli-responsive functional materials through HSA involving coordination interactions. In our study, a series of functionalized metallacycles were first constructed through coordination-driven self-assembly (CDSA). Then, the secondary noncovalent interaction sites were integrated within the functionalized metallacycle system via either preassembly or postassembly approach. Different segments, such as alkyl chains, dendrimers, cholesteryl moiety, covalent macrocycles, and even polymeric fragments, which could provide hydrophobic and hydrophilic interactions, van der Waals forces, hydrogen bonding, CH-π and π-π interactions, and host-guest interactions, have been utilized to provide the secondary NCIs. Further self-assembly of functionalized metallacycles gives rise to the formation of complex higher-order structures driven by other NCIs by taking advantages of orthogonal property of coordination bonds with other NCIs. By changing the type of additional NCIs embodied in building blocks, different supramolecular architectures, such as the ordered nanostructures, supramolecular polymers and gels, fluorescent materials and sensors, have been successfully prepared with the tailored chemical and physical properties. In particular, the dynamic nature of coordination bonds as well as other NCIs endows final assemblies with stimuli-responsive functions. Collectively, our studies suggest that combining coordination and other NCIs in a well-defined and precise manner is a highly efficient strategy to achieve the complex architectures and functional materials. Therefore, it is very promising to develop the desired functional materials with high precision and fidelity by employing HSA involving coordination interactions.