Point Geometry Research Articles

Assessing spatial interpolation based on sampling size and point geometry in elevation mapping applications


 
 
 
 In order to produce a correct elevation map, it is necessary to use not only the accurate technology for data acquisition, but also to utilize an appropriate method of interpolation, which will reflect the topographic features in a reliable manner. The first key element in elevation map production is the proper geometrical distribution of measurement points. The second key component is the density of measurement points, which indicates the distance between pairs in the dataset. In this study, two different types of sampling design were taken into account, random and systematic sampling, to create the elevation map. In random sampling, 33 points were used with the distance in the range of 15–30 km. In systematic sampling, a total of 100 points were utilized located at the distance of 5 km apart. Then, two distinct methods of interpolation were applied to produce a map: deterministic (Inverse Distance Weighting) and geostatistical (Ordinary Kriging with application of the Gaussian, Exponential, and Spherical fitting separately). These methods were compared using a statistical approach to validate the predictive abilities of the chosen interpolation methods. As the results showed, the geostatistical method, namely, Ordinary Kriging with Exponential fitting, revealed better performance compared to the deterministic. It was seen that the overall performance of the interpolated map varies with the number of points in the dataset and strongly relates to the sampling design. In the case of systematic sampling, the accuracy of the map was found to be much better compared to the results of random sampling. It was also proposed to use the error maps in order to identify areas with the maximum residuals. It became apparent that in the case of random sampling, the greatest errors were mostly concentrated in the areas where distances between the measured points were fairly large. By contrast, in the case of systematic sampling, the largest residuals were found in areas with complex topological patterns, especially in the regions with a steep slope gradient. Choosing the appropriate method of interpolation with the minimum error is of great importance in geostatistical operations and topographic engineering. Thus, the current manuscript may serve as a guideline in making the right decision concerning the interpolation method in elevation mapping applications of 1:2000000–1:1000000 scales.
 
 
 

Point line geometry in the tropical plane

We study the classical result by Bruijn and Erdős regarding the bound on the number of lines determined by a n-point configuration in the plane, and in the light of the recently proven Tropical Sylvester-Gallai theorem, come up with a tropical version of the above-mentioned result. In this work, we introduce stable tropical lines, which help in answering questions pertaining to incidence geometry in the tropical plane. Projective duality in the tropical plane helps in translating the question for stable lines to stable intersections that have been previously studied in depth. Invoking duality between Newton subdivisions and line arrangements, we are able to classify stable intersections with shapes of cells in subdivisions, and this ultimately helps us in coming up with a bound. In this process, we also encounter various unique properties of linear Newton subdivisions which are dual to tropical line arrangements.

Theoretical studies of the reactions of 1-Propanol, and 2-Propanol with hydrogen atom and methyl radical

Ab initio and direct kinetics study of the 1-C3H7OH + H, 2-C3H7OH + H, 1-C3H7OH + CH3 and 2-C3H7OH + CH3 reactions was performed over the temperature range of 300–1500 K. The geometries of all stationary points were optimized at the M06-2X/cc-pVTZ level of theory and the electronic energies were refined by the CCSD(T)/CBS method. The rate coefficients were calculated by the MS-CVT/SCT theory and agreed well with the experimental data. The dominant channels in the 1-C3H7OH + R (R = H, CH3) reactions are H-abstraction from the α-CH2 groups at low-temperature; the dominant channels in the 2-C3H7OH + R (R = H, CH3) reactions are H-abstraction from the -CH groups.

Enabling Rapid and Accurate Construction of CCSD(T)-Level Potential Energy Surface of Large Molecules Using Molecular Tailoring Approach.

The construction of a potential energy surface (PES) of even a medium-sized molecule employing correlated theory, such as CCSD(T), is arduous due to the high computational cost involved. The present study reports the possibility of efficiently constructing such a PES of molecules containing up to 15 atoms and 550 basis functions by employing the fragment-based molecular tailoring approach (MTA) on off-the-shelf hardware. The MTA energies at the CCSD(T)/aug-cc-pVTZ level for several geometries of three test molecules, viz., acetylacetone, N-methylacetamide, and tropolone, are reported. These energies are in excellent agreement with their full calculation counterparts with a time advantage factor of 3-5. The energy barrier from the ground to transition state is also accurately captured. Further, we demonstrate the accuracy and efficiency of MTA for estimating the energy gradients at the CCSD(T) level. As a further application of our MTA methodology, the energies of acetylacetone at ∼430 geometries are computed at the CCSD(T)/aug-cc-pVTZ level and used for generating a Δ-machine learning (Δ-ML) PES. This leads to the H-transfer barrier of 3.02 kcal/mol, well in agreement with the benchmarked barrier of 3.19 kcal/mol. The fidelity of this Δ-ML PES is examined by geometry optimization and normal mode frequency calculations of global minima and saddle point geometries. We trust that the present work is a major development for the rapid and accurate construction of PES at the CCSD(T) level for molecules containing up to 20 atoms and 600 basis functions using off-the-shelf hardware.

Stability-Order Reversal in FSiY and FYSi (Y = N and P) Molecules after the Insertion of a Noble Gas Atom.

Recent theoretical prediction and experimental identification of fluorinated noble gas cyanides and isocyanides motivate us to explore a unique novel series of neutral noble gas-inserted heavier cyanofluoride isomers, FNgYSi and FNgSiY (Ng = Kr, Xe, and Rn; Y = N and P), theoretically using quantum chemical calculations. The concerned minima and saddle point geometries have been optimized using DFT, MP2, and CCSD(T) methods. The precursor molecule FSiY is more stable than its isomer FYSi, and the stability order is found to be reversed after the insertion of a noble gas (Ng) atom into them which is in contrast to the previously reported FCN/FNC systems where the stability order in the precursors remains intact after the insertion of a Ng atom into them. The predicted FNgYSi molecules are metastable in nature as they are kinetically stable but thermodynamically unstable with respect to the global minima products (FYSi and Ng). All the calculations for the corresponding FNgSiY molecules clearly indicate that the less stable FNgSiY behaves similarly to the FNgYSi in all respects. The energetics, force constant, and spectroscopic data strongly reinforce the possibility of occurrence of these predicted FNgYSi and FNgSiY molecules which might be experimentally realized under suitable cryogenic condition(s).

Mechanistic studies of the reactions of nitrogen dioxide with dimethyl ether and methyl ethyl ether

Ab initio and direct kinetics study of the CH3OCH3 + NO2 and CH3OC2H5 + NO2 reactions was performed over the temperature range of 300–1500 K. The geometries of all stationary points were optimized at the M06-2X/cc-pVTZ level of theory and the electronic energies were refined by the CCSD(T)/CBS method. The rate coefficients calculated by CVT theory including the small curvature tunneling (SCT) correction agreed well with the experimental data. Note that the H-abstraction from ethers to produce cis-HONO was the dominant channel at temperatures lower than 1000 K and the three channels to produce HNO2, trans-HONO and cis-HONO proceeded simultaneously.

Analysis of the interactions between joint and component properties during clinching

Clinching is a joining process that is becoming more and more important in industry due to the increasing use of multi-material designs. Despite the already widespread use of the process, there is still a need for research to understand the mechanisms and design of clinched joints. In contrast to the tool parameters, process and material disturbances have not yet been investigated to a relatively large extent. However, these also have a great influence on the properties and applicability of clinching. The effect of process disturbances on the clinched joint are investigated with numerical and experimental methods. The investigated process variations are the history of the sheets using the pre-hardening of the material, different sheet thicknesses, sheet arrangements and punch strokes. For the consideration of the material history, a specimen geometry for pre-stretching specimens in uniaxial tension is used, from which the pre-stretched secondary specimens are taken. A finite element model is set up for the numerical investigations. Suitable clinching tools are selected. With the simulation, selected process influences can be examined. The effort of the numerical investigations is considerably reduced with the help of a statistical experimental design according to Taguchi. To confirm the simulation results, experimental investigations of the clinch point geometry by using micrographs and the shear strength of the clinched joint are performed. The analysis of the influence of difference disturbance factors on the clinching process demonstrate the importance of the holistic view of the clinching process.

IT Technology for Establishing Borders of Reserved Territories in the Conditions of Land Reform in Ukraine

The existence of only a paper outline scheme in the National Nature Park Project does not allow to unambiguously interpret the boundaries of the object. Purpose. Development of technique for establishing the boundaries of protected areas. Methods. Cartographic using the ArcGIS geographic information system Results. The basic cartographic document for the study was a scanned map at a scale of 1:50 000 showing the boundaries of the Gomilshansky Forests National Park from the National Nature Park (NNP) Project. The main problem was the lack of elements of its mathematical basis on the map. The IT technology of geo-linking the scanned map of the park boundaries in the GIS environment includes the following actions: linking topographic map sheets at a scale of 1: 50,000 in the ArcGIS geographic information system, saving the relevant geo-linked, transformed copies of the image; visualization of digital geodata with geometry and coordinates of points of boundaries of forest areas (quarters); download the scanned map of the boundaries of the NNP from the Project of creation without geographical reference and perform the procedure of sequential addition of control points of reference; image transformation and saving the result in geotiff format. After that, a polygonal vector layer of * shp format was created and the park territory was digitized according to the NNP Project. The result of the research was a map of the boundaries of the Gomilshansky Forests National Park in geotiff format, geographically linked in the ArcGIS environment, as well as a vector layer of the National Park's territory based on it. Conclusions. The use of the developed technology allows to determine the location of any land plots in relation to the national nature park, knowing their coordinates or uploading the Public Cadastral Map of Ukraine to the GIS project.

Quantum chemical study of reaction mechanism between plutonium and nitrogen.

The study of the reaction between plutonium and nitrogen is helpful in further understanding the interaction between plutonium and air molecules. Currently, there is no research on the microscopic reaction mechanism of plutonium nitridation reactions. Therefore, the microscopic mechanism of the Pu with N2 gas phase reaction is explored in this study, based on density functional theory (DFT) using different basis functions. In this paper, the geometry of stationary points on the potential energy surface is optimized. In addition, the transition states are verified by frequency analysis and intrinsic reaction coordination (IRC). Finally, we obtained the reaction potential energy curve and micro reaction pathways. Analysis of the reaction mechanism shows that the reaction of Pu with N2 has two pathways. Pathway 1 (Pu + N2 → R1 → TS1 → PuN2) has a T-shaped transition state and pathway 2 (Pu + N2 → R2 → TS2 → PuN + N) has an L-shaped transition state. Both transition states have only one imaginary frequency. According to the comparison of the energy at each stagnation point along the two pathways, and the heat energy emitted by the two reaction paths, we found that pathway 1 is the main reaction pathway. The nature of Pu-N bonding evolution along the pathways was studied by atoms in molecules (AIM) and electron localization function (ELF) topological approaches. In order to analyze the role of the plutonium atom 5f orbital in the reaction, the variation in density state along the pathways was measured. Results show that the 5f orbital mainly contributes to the formation of Pu-N bonds, and the influence of temperature on the reaction rate is revealed by calculating the rate constants of the two reaction pathways.

A Novel Extrinsic Calibration Method of Mobile Manipulator Camera and 2D-LiDAR via Arbitrary Trihedron-Based Reconstruction

Mobile manipulators are increasingly applied to improve the efficiency in industrial manufacturing. As a typical system using multi-sensor fusion technology, accurate extrinsic calibration of manipulator’s exteroceptive sensors like camera and 2D-LiDAR is essential for mobile manipulators to perform complicated task such as mobile assembly. However, most existing camera-LiDAR calibration methods require sophisticated artificial calibration targets, leading to implementation restrictions. In this paper, by reconstructing an arbitrary trihedron that existed in the general human-made environment, a novel method is presented to estimate the transformation between the manipulator camera and the 2D-LiDAR coordinate system. The proposed method is based on the use of point, line, and plane geometry constraints between the segmented 2D-LiDAR scan and the reconstructed trihedron features. Considering the metric of reconstruction, the extended hand-eye calibration framework is implemented to recover the scale factor and hand-eye parameters. Then, a new optimization model is presented to reconstruct the key features of arbitrary trihedron in a preset global coordinate system. Finally, with only one 2D-LiDAR measurement, camera-LiDAR transformation can be calculated by constructing point-to-line and line-to-plane geometric constraints. Further, the transformation between the manipulator kinematic base and 2D-LiDAR can also be calibrated. Both simulation and real-world experiments show that the proposed method can provide robust and accurate results.

Islands in multiverse models

We consider multiverse models in two-dimensional linear dilaton-gravity theories as toy models of false vacuum eternal inflation. Coupling conformal matter we calculate the Von Neumann entropy of subregions. When these are sufficiently large we find that an island develops covering most of the rest of the multiverse, leading to a Page-like transition. This resonates with a description of multiverse models in semiclassical quantum cosmology, where a measure for local predictions is given by saddle point geometries which coarse-grain over any structure associated with eternal inflation beyond one’s patch.

Theoretical studies of the reactions of 1,2-Ethanediol with triplet oxygen and hydrogen atoms

An direct kinetics study of the (CH2OH)2 + O(3P) and (CH2OH)2 + H reactions was performed over the temperature range of 300–1500 K. The geometries of all stationary points were optimised at the M06-2X/cc-pVQZ level of theory. The electronic energies were refined by CCSD(T)/CBS and QCISD(T)/cc-pVTZ methods. The rate coefficients were calculated using canonical variational transition state theory (CVT) with small-curvature tunneling (SCT) correction. The results showed that the channels of hydrogen abstraction from the CH2 group were most kinetically favourable at the temperature less than 1300 K and have positive temperature dependence. The OH-transfer channels were ignorable.

Semi-Implicit Finite Volume Procedure for Compositional Subsurface Flow Simulation in Highly Anisotropic Porous Media

Subsurface multiphase flow in porous media simulation is extensively used in many disciplines. Large meshes with non-orthogonalities (e.g., corner point geometries) and full tensor highly anisotropy ratios are usually required for subsurface flow applications. Nonetheless, simulations using two-point flux approximations (TPFA) fail to accurately calculate fluxes in these types of meshes. Several simulators account for non-orthogonal meshes, but their discretization method is usually non-conservative. In this work, we propose a semi-implicit procedure for general compositional flow simulation in highly anisotropic porous media as an extension of TPFA. This procedure accounts for non-orthogonalities by adding corrections to residual in the Newton-Raphson method. Our semi-implicit formulation poses the guideline for FlowTraM (Flow and Transport Modeller) implementation for research and industry subsurface purposes. We validated FlowTraM with a non-orthogonal variation of the Third SPE Comparative Solution Project case. Our model is used to successfully simulating a real Colombian oil field.

The Role of Zero-Point Vibration and Reactant Attraction in Exothermic Bimolecular Reactions with Submerged Potential Barriers: Theoretical Studies of the R + HBr → RH + Br (R = CH3, HO) Systems.

The dynamics of the reactions CH3 + HBr → CH4 + Br and HO + HBr → H2O + Br have been studied using the quasiclassical trajectory method to explore the interplay of the vibrational excitation of the breaking bond and the potential energy surface characterized by a prereaction van der Waals well and a submerged barrier to reaction. The attraction between the reactants is favorable for the reaction, because it brings together the reactants without any energy investment. The reaction can be thought to be controlled by capture. The trajectory calculations indeed provide excitation functions typical to capture: the reaction cross sections diverge when the collision energy is reduced toward zero. Excitation of reactant vibration accelerates both reactions. The barrier on the potential surface is so early that the coupling between the degrees of freedom at the saddle point geometry is negligible. However, the trajectory calculations show that when the breaking bond is stretched at the time of the encounter, an attractive force arises, as if the radical approached a HBr molecule whose bond is partially broken. As a result, the dynamics of the reaction are controlled more by the temporary “dynamical”, vibrationally induced than by the “static” van der Waals attraction even when the reactants are in vibrational ground state. The cross sections are shown to drop to very small values when the amplitude of the breaking bond’s vibration is artificially reduced, which provides an estimate of the reactivity due to the “static” attraction. Without zero-point vibration these reactions would be very slow, which is a manifestation of a unique quantum effect. Reactions where the reactivity is determined by dynamical factors such as the vibrationally enhanced attraction are found to be beyond the range of applicability of Polanyi’s rules.

Gravitational and gravitoscalar thermodynamics

Gravitational thermodynamics and gravitoscalar thermodynamics with S2 × ℝ boundary geometry are investigated through the partition function, assuming that all Euclidean saddle point geometries contribute to the path integral and dominant ones are in the B3 × S1 or S2 × Disc topology sector. In the first part, I concentrate on the purely gravitational case with or without a cosmological constant and show there exists a new type of saddle point geometry, which I call the “bag of gold(BG) instanton,” only for the Λ > 0 case. Because of this existence, thermodynamical stability of the system and the entropy bound are absent for Λ > 0, these being universal properties for Λ ≤ 0. In the second part, I investigate the thermodynamical properties of a gravity-scalar system with a φ2 potential. I show that when Λ ≤ 0 and the boundary value of scalar field Jφ is below some value, then the entropy bound and thermodynamical stability do exist. When either condition on the parameters does not hold, however, thermodynamical stability is (partially) broken. The properties of the system and the relation between BG instantons and the breakdown are discussed in detail.

Theoretical investigation on the addition reaction of the germylenoid H2GeLiCl with acetone.

In this work, theoretical calculations were performed on the addition reaction of the germylenoid H2GeLiCl with acetone. The DFT M06-2X method was used to optimize the geometries of the whole stationary points on the potential energy surfaces and the QCISD method to calculate the single-point energy. The results reveal that the addition reaction of H2GeLiCl with acetone firstly generates an oxagermacyclopropane c-H2GeOC(CH3)2 and then c-H2GeOC(CH3)2 further reacts with acetone along two possible pathways, pathway I and pathway II, in which the 2,4-dioxagermolane is formed at the end of pathway I and 2,5-dioxagermolane is formed at the end of pathway II, respectively. According to the calculated barrier heights, we can deduce that the pathway I is more favorable than pathway II. The computational results suggest that this reaction model can provide new inspiration for the synthesis of heterocyclic germanium compounds.

Black hole black string phase transition in Einstein-Gauss-Bonnet gravity

We investigate the presence of a black hole black string phase transition in Einstein Gauss Bonnet (EGB) gravity in the large dimension limit. The merger point is the static spacetime connecting the black string phase with the black hole phase. We consider several ranges of the Gauss-Bonnet parameter. We find that there is a range when the Gauss-Bonnet corrections are subordinate to the Einstein gravity terms in the large dimension limit, and yet the merger point geometry does not approach a black hole away from the neck. We cannot rule out a topology changing phase transition as argued by Kol. However as the merger point geometry does not approach the black hole geometry asymptotically it is not obvious that the transition is directly to a black hole phase. We also demonstrate that for another range of the Gauss-Bonnet parameter, the merger point geometry approaches the black hole geometry asymptotically when a certain parameter depending on the Gauss-Bonnet parameter $\alpha$ and on the parameters in the Einstein-Gauss-Bonnet black hole metric is small enough.

Операция пересечения на комплексной плоскости

Two plane algebraic curves intersect at the actual intersection points of these curves’ graphs. In addition to real intersection points, algebraic curves can also have imaginary intersection points. The total number of curves intersection points is equal to the product of their orders mn. The number of imaginary intersection points can be equal to or part of mn. The position of the actual intersection points is determined by the graphs of the curves, but the imaginary intersection points do not lie on the graphs of these curves, and their position on the plane remains unclear. This work aims to determine the geometry of imaginary intersection points, introduces into consideration the concept of imaginary complement for these algebraic curves in the intersection operation, determines the form of imaginary complements, which intersect at imaginary points. The visualization of imaginary complements clarifies the curves intersection picture, and the position of the imaginary intersection points becomes expected.

Операция пересечения на комплексной плоскости

Two plane algebraic curves intersect at the actual intersection points of these curves’ graphs. In addition to real intersection points, algebraic curves can also have imaginary intersection points. The total number of curves intersection points is equal to the product of their orders mn. The number of imaginary intersection points can be equal to or part of mn. The position of the actual intersection points is determined by the graphs of the curves, but the imaginary intersection points do not lie on the graphs of these curves, and their position on the plane remains unclear. This work aims to determine the geometry of imaginary intersection points, introduces into consideration the concept of imaginary complement for these algebraic curves in the intersection operation, determines the form of imaginary complements, which intersect at imaginary points. The visualization of imaginary complements clarifies the curves intersection picture, and the position of the imaginary intersection points becomes expected.

PERFORMANCE PROPERTIES OF THREAD SEAMS OF KNITTED-BASED MEMBRANE MATERIALS

The article is devoted to the study of the strength and wear resistance of thread seams of membrane materials on a knitted basis. The characteristics of the composite membrane three-layer material are given and the modes of its stitching and the test method are substantiated. Investigations of material cutting through with a needle were carried out and the geometry of the sewing needle point was chosen. The results of the study of the strength of thread seams made along of the front layer of the material before and after modelling the operational tensile loads along and across the seam are presented. 15000 load-unload cycles were simulated, stretching the sample by 10 % of the seam length. As a result of a full factorial experiment, it was found that the linear density of the threads and the diameter of the needle have the greatest effect on the strength and wear resistance of the thread seams of the composite material. The influence of the sewing frequency is ambiguous for the parameter of the wear resistance of the seam when stretched along and across the line.