Intersection Of Surfaces Research Articles

Формування вимог до інформаційного супроводу виробництва аерокосмічних виробів для забезпечення їх якості

The aim of this study is informational support of the aerospace object production at the stages of their lifecycle. The purpose is to provide the necessary parameters of the aerospace products quality, which involves providing relevant information at each stage of the lifecycle in an easy-to-understand and complete form. The task is to create the analytical standard using the example of parts of precision and unit production. The model is based on the analytical standard of parts geometry developed using CAD/CAM-systems with the subsequent expansion of the models list to transfer the necessary information to all participants of the product lifecycle. According to the analysis, significant limitations of drawing documentation for informational support of aerospace industry objects at the stage of technology development are identified. The quality characteristics of the part are grouped according to the compliance degree with its nominal (reference) value of shape and dimensions (macrogeometry and microrelief), physical and chemical properties of the material and the surface layer, technological heredity and industrial purity. It is proposed to develop their models with the CAD/CAM-systems tools based on the analytical sample of geometry. Three necessary conditions for the correct formulation of the shaping problem regarding the implementation of quality management of serial products of machine-building enterprises are established. If at least one of them is violated, it is necessary to attract additional heuristic information to reproduce the correctness of the problem. The analytical standard creation and control implementation of an example of a mill that considers the geometry of the edges are shown, as well as a comparison of the reference geometry and geometry portrait. The scientific novelty of the obtained results consists of the concept introduction of an edge as a surface that connects the working “lines of two surfaces intersection” of a part. The representation of edges in the form of surfaces, not lines, on the one hand, and the selection of these surfaces from the totality of other working surfaces of the parts, on the other hand, creates an informational basis for developing the appropriate manufacturing technologies and maintenance of these parts elements during the product operation.

Concurrent optimization of topological configuration and continuous fiber path for composite structures — A unified level set approach

This study proposes a novel topology optimization approach for design of continuous steering fiber path for composite structures using a level set method. The radial basis function (RBF) is employed to construct the level set function (LSF). Fiber orientations are parameterized by LSF and fiber paths can be determined instinctively for the inherent advantages of the level set approach. Besides, the fast-marching method is employed to extrapolate the primary fiber paths to the secondary fiber paths, which can avoid the manufacturing drawbacks such as gaps and overlaps to a large extent. A detection and filtering technique is proposed here to alleviate the orientation disorder at the intersection of the diffusion surfaces. Two design schemes are developed to optimize both structural topology and fiber path. In a sequential procedure, topology optimization is conducted first with isotropic materials; and then fiber paths are optimized on the basis of fixed topological boundary. In a simultaneous optimization procedure, structural boundaries and fiber paths are optimized alternately through two inner loops. In this study, three numerical examples are presented to demonstrate the effectiveness of the proposed methods, and the results show that optimization of fiber path is beneficial to improvement of structural performance. In general, the simultaneous optimization scheme exhibits better optimal outcome in comparison with the sequential optimization scheme.

Elastoplastic Integration Method of Mohr-Coulomb Criterion

A new method for implicit integration of the Mohr-Coulomb non-smooth multisurface plasticity models is presented, and Koiter’s requirements are incorporated exactly within the proposed algorithm. Algorithmic and numerical complexities are identified and introduced by the nonsmooth intersections of the Mohr-Coulomb surfaces; then, a projection contraction algorithm is applied to solve the classical Kuhn–Tucker complementary equations which provide the only characterization of possible active yield surfaces as a special class of variational inequalities, and the actual active yield surface is further determined by iteration. The basic idea is to calculate derivatives of the yield and potential functions with the expressions in the principal stresses and perform the return manipulations in the general stress space. Based on the principal stress characteristic equation, partial derivatives of principal stresses are calculated. The proposed algorithm eliminates the error caused by smoothing the corner of Mohr-Coulomb surfaces, avoids the numerical singularity at the intersections in the general stress space, and does not require the stress transformation needed in the principal stress space method. Lastly, several numerical examples are given to verify the validity of the proposed method.

Hough transform based recognition of space curves

Given a set of points representing a curve embedded in the Euclidean space and a family of space curves, we face the problem of finding the curve of the family that best fits these points. For our purposes, we apply the Hough transform (HT), which allows the recognition of a template curve from a set of points and its exact representation. Our method directly applies to digital models of 3D objects and combines the HT based recognition of curves expressed in both implicit and parametric form in a single flow. Furthermore, we extend the number of space curves that can be recognised, by including also those curves whose profile P can be approximated as the intersection of a quadric surface and a cylinder generated by a plane curve.

Finding Valence Antibonding Levels while Avoiding Rydberg, Pseudo-continuum, and Dipole-Bound Orbitals.

Electronic structure methods are now widely used to assist in the interpretation of many varieties of experimental data. The energies and physical characteristics (e.g., sizes, shapes, and spatial localization) of valence antibonding π* and σ* orbitals play key roles in a variety of chemical processes including photochemical reactions and electron attachment reductions and are used in Woodward-Hoffmann-type analyses to probe reaction energy barriers and energy surface intersections leading to internal conversion or intersystem crossings. One's ability to properly populate such valence antibonding orbitals within electronic structure calculations is often hindered by the presence of other molecular orbitals having similar energies. These intruding orbitals can be of Rydberg, pseudo-continuum, or dipole-bound characteristic. This article shows how, within the most widely available electronic structure codes, one can avoid the pitfalls presented by these intruding orbitals to properly populate a valence π* or σ* orbital and how to subsequently use that orbital in a calculation that includes electron correlation effects and thereby offers the possibility of chemically useful precision. Special emphasis is given to cases in which the electronic state is metastable.

Nodule vascularity as novel radiomics imaging endpoint for lung cancer diagnosis and prognosis.

e20580 Background: The vascularization of lung nodules has been proven as severe risk factor for malignancy, and in lung cancer, indication of worse prognosis (1,2). For this reason, we developed a novel imagining endpoint based on the vasculature surrounding a lung mass and we tested this endpoint for the prediction of malignancy for lung nodules. Methods: The vasculature of the nodules (both arteries and veins) has been computed using the surface intersection between the nodule and the vascular structure 3D meshes. Both 3D structures were obtained by converting the segmentations of the nodule and of the vessels to meshes with a marching cubes algorithm. Nodule and vessels segmentation has been obtained with an in-house deep learning segmentation model. The features considered are the numbers of intersections, the total area of intersection and the mean area of intersection. These features have been used to predict nodule malignancy on thoracic CT scans from the Lung Image Database Consortium image collection (3). Quality controls on clinical data completeness and imaging parameters resulted in a cohort of 894 scans (715 for training and 179 for testing), from the original 1018 cases. The malignancy status is defined as high risk and low risk, based on the consensus classification of a panel of four radiologists. Firstly, an univariate analysis is performed to assess the variability of the features grouped by the malignancy score by using Mann-Whitney and ANOVA tests. After, seven combinations of features have been used to train generalized linear models (GLM) to predict nodule malignancy. To compare the models, the Area Under the Curve (AUC) is used as the main performance metric. Results: Univariate analysis of each feature grouped by the malignancy outcome showed that all the three features have good univariate discriminative power between high risk and low risk categories ( p value ≤ 0.05), with nb_connections as the most predictive singular feature ( p value of 1.343277 × 10-36). All the GLM models developed showed a good performance (AUC equal or higher than 0.7), with the best model in testing based on the combination of mean_area and sum_area (AUC of 0.84). Conclusions: The radiomics vascularity endpoint has been proven capable of predicting nodule malignancy with very good performance. The singular feature that is most related to malignancy is the number of vessels intersecting the nodule while the total area of intersection followed by the number of intersections are the most useful to model risk of malignancy. Wang et al., Lung Cancer 114: 38–43, 2017. Hamanaka et al., Diagn Pathol 10,17, 2015. G. Armato et al., Med. Phys., 38: 915-931, 2011.

A Flip‐book of Knot Diagrams for Visualizing Surfaces in 4‐Space

AbstractJust as 2D shadows of 3D curves lose structure where lines cross, 3D graphics projections of smooth 4D topological surfaces are interrupted where one surface intersects itself. They twist, turn, and fold back on themselves, leaving important but hidden features behind the surface sheets. In this paper, we propose a smart slicing tool that can read the 4D surface in its entropy map and suggest the optimal way to generate cross‐sectional images — or “slices” — of the surface to visualize its underlying 4D structure. Our visualization thinks of a 4D‐embedded surface as a collection of 3D curves stacked in time, very much like a flip‐book animation, where successive terms in the sequence differ at most by a critical change. This novel method can generate topologically meaningful visualization to depict complex and unfamiliar 4D surfaces, with the minimum number of cross‐sectional diagrams. Our approach has been successfully used to create flip‐books of diagrams to visualize a range of known 4D surfaces. In this preliminary study, our results show that the new visualization and slicing tool can help the viewers to understand and describe the complex spatial relationships and overall structures of 4D surfaces.

Tensor-Train Split-Operator KSL (TT-SOKSL) Method for Quantum Dynamics Simulations.

Numerically exact simulations of quantum reaction dynamics, including nonadiabatic effects in excited electronic states, are essential to gain fundamental insights into ultrafast chemical reactivity and rigorous interpretations of molecular spectroscopy. Here, we introduce the tensor-train split-operator KSL (TT-SOKSL) method for quantum simulations in tensor-train (TT)/matrix product state (MPS) representations. TT-SOKSL propagates the quantum state as a tensor train using the Trotter expansion of the time-evolution operator, as in the tensor-train split-operator Fourier transform (TT-SOFT) method. However, the exponential operators of the Trotter expansion are applied using a rank-adaptive TT-KSL scheme instead of using the scaling and squaring approach as in TT-SOFT. We demonstrate the accuracy and efficiency of TT-SOKSL as applied to simulations of the photoisomerization of the retinal chromophore in rhodopsin, including nonadiabatic dynamics at a conical intersection of potential energy surfaces. The quantum evolution is described in full dimensionality by a time-dependent wavepacket evolving according to a two-state 25-dimensional model Hamiltonian. We find that TT-SOKSL converges faster than TT-SOFT with respect to the maximally allowed memory requirement of the tensor-train representation and better preserves the norm of the time-evolving state. When compared to the corresponding simulations based on the TT-KSL method, TT-SOKSL has the advantage of avoiding the need to construct the matrix product state Laplacian by exploiting the linear scaling of multidimensional tensor-train Fourier transforms.

Thermal response of the fractured hot dry rocks with thermal-hydro-mechanical coupling effects

In order to efficiently exploit geothermal energy, the reasonable configuration of fracture network should ensure the minimum water loss, high flow rate, high production temperature, and good connectivity between injection wells and production wells. To achieve the above objectives, the operating parameters of the EGS project should be balanced with the reservoir characteristics. In this paper, the THM coupling model is established in the finite element solver, which analyzes the influence of formation stress, injection pressure, roughness of fracture surface, fracture intersection angle, and fracture connectivity on fluid seepage pressure and outlet temperature. The accuracy of the model was verified by comparison to analytical solutions. The results show that although the increased vertical stress, fracture surface roughness and intersection angle will increase the flow resistance, the temperature of fracture fluid will rise faster. On the contrary, the increase of injection pressure will expand the fracture aperture and lead to the temperature of the fracture fluid rises slowly. In addition, not all fractures contribute to the productivity of the hot dry rocks (HDRs) type of reservoirs, while only the interconnected fractures are effective. The flow rate of production will increase when fracture density increases under the condition of connecting the injection well and production well, but the production temperature will decrease. The relative importance of the individual parameter alone is not enough to directly measure the optimal engineering parameters, so considering the impact of multiple parameters comprehensively is crucial for EGS project development and directly affects its commercial viability.

Stereodynamics-Controlled Product Branching in the Nonadiabatic H + NaD → Na(3s, 3p) + HD Reaction at Low Temperatures.

Nonadiabatic processes play an important role at energies near or higher than conical intersection of adiabatic potential energy surfaces in chemical reactions. In this work, dynamics of the nonadiabatic H + NaD reaction at low temperatures are studied by using the quantum wave packet method based on an improved L-shaped grid. The nonadiabatic H + NaD reaction has two exothermic reaction channels: Na(3s) + HD and Na(3p) + HD; the latter can only occur via nonadiabatic transition. The dynamics results show that the product branching of the H + NaD reaction at collision energies ranging from 20 to 80 cm-1 is controlled by stereodynamics. The Na(3s) and Na(3p) reaction channels occur through collinear collision and side-on collision, respectively. When the collision energy is lower than 20 cm-1, the resonance-mediated reaction mechanism is dominant in both the Na(3s) and Na(3p) reaction channels.

INTERSECTIONS OF SURFACES OF REVOLUTION

In this paper, we deal with surfaces of revolution and their intersections. We start with the surfaces of revolution RS that have their axis along the x3–axis and find intersections with a line, a plane, and then intersection of two such RS. Furthermore, we apply formulas for the intersection with a line to determine the visibility of RS. Later we develop formulas for the intersection of two surfaces of revolution that have their axis along different arbitrary straight lines, and, as a special case, the intersections of two spheres and intersections of general surface of revolution with a sphere and a surface given by an equation. We apply our own software to the graphical representation of all the results we present.

Hardware-Accelerated Ray Tracing of CAD-Based Geometry for Monte Carlo Radiation Transport

Monte Carlo radiation transport (MCRT) methods have been used to simulate radiation environments for many decades by tracking individual particles through a model to accumulate statistical information. MCRT geometry is historically formed using the constructive solid geometry (CSG). Recently, significant work has been performed to support simulations using computer-aided design (CAD)-based tessellated surfaces to support highly complex geometries. Ray tracing acceleration data structures from the rendering and visualization community are applied to accelerate particle tracking in CAD-based models. Despite these efforts, CSG representations provide the superior performance in surface intersection operations during particle flight. Concurrently, pseudo Monte Carlo methods have become prevalent in rendering applications to support more realistic models for scattering media, motivating innovations that are advantageous for MCRT simulations. The authors’ work extends these innovations by employing Intel’s Embree ray tracing kernel within a geometry toolkit for Monte Carlo to improve the simulation performance using CAD-based models by factors of 1.5 to 2.

PSO-WELLSVM: An integrated method and its application in urban waterlogging susceptibility assessment in the central Wuhan, China

Urban waterlogging susceptibility assessment can be used in preventing urban waterlogging disaster, which can cause serious damage. An integrated method based on particle swarm optimization (PSO) and weakly labeled support vector machine (WELLSVM), is presented to assess urban waterlogging susceptibility for a certain rainstorm. This method incorporated twelve explanatory factors, including daily precipitation, 3-day cumulated rainfall prior to flood occurrences, elevation, slope, curvature, aspect, topographic wetness index, stream power index, distance to river, leaf area index, impervious surface percentage, distance to road, to perform waterlogging susceptibility analysis. The rainstorm on July 6, 2016 in the main districts of Wuhan, China was used as the scenario to test its feasibility. Cohen's kappa index, accuracy, precision, and recall were used to evaluate the performance of the proposed model. The accuracy of the proposed model (93.6% for training data and 90.1% for testing data) is higher than WELLSVM, support vector machine, and logistic regression, demonstrating the advantages of utilizing unlabeled data and optimized parameter selection. The proposed model can also well identify the waterlogging susceptibility zones. The highest waterlogging susceptibility areas are located in the area with high impervious surface percent, intersections, culverts and overpasses, lakeshore, and riverbank. Elevation and precipitation factors are the most influential factors to waterlogging susceptibility. The proposed model was also tested by the other two storms on July 7, 2013 and June 21, 2019, proving the validity of it. The proposed model is helpful for instant waterlogging susceptibility analysis and can help decision-making of urban waterlogging control.

Deformation characteristics of nanolayered dual-phase CrCoNi medium-entropy alloy nanowires

Due to the potential excellent mechanical properties of multicomponent alloys, the design of their microstructures and deformation mechanisms have attracted considerable attention. In this work, using molecular dynamics simulations, the mechanical behaviors of nanolayered face-centered cube/hexagonal close-packed (FCC/HCP) dual-phase CrCoNi medium-entropy alloys (MEAs) were investigated. The mechanical behaviors of the nanolayered dual-phase nanowires with various radii were studied and the effects of nanolayered dual-phase structure were evaluated. It was found that there are two different deformation modes mainly related to the dislocation nucleation position in the FCC phase or the HCP phase, of which in Model I dislocations nucleate from the intersection of phase boundary and surface, while in Model II dislocations nucleate on the surface of HCP phase. The deformation mode and strength change periodically with the variation of the surface disorder degree against radius. Annealing in the temperature range of 600–800 K can optimize the dual-phase structure, change the deformation mode and improve the mechanical performance.

On Incremental Structure from Motion Using Lines

Humans tend to build environments with structure, which consists of mainly planar surfaces. From the intersection of planar surfaces arise straight lines. Lines have more degrees of freedom than points. Thus, line-based structure-from-motion (SfM) provides more information about the environment. In this article, we present solutions for SfM using lines, namely, incremental SfM. These approaches consist of designing state observers for a camera’s dynamical visual system looking at a 3-D line. We start by presenting a model that uses spherical coordinates for representing the line’s moment vector. We show that this parameterization has singularities, and, therefore, we introduce a more suitable model that considers the line’s moment and shortest viewing ray. Concerning the observers, we present two different methodologies. The first uses a memory-less state-of-the-art framework for dynamic visual systems. Since the previous states of the robotic agent are accessible—while performing the 3-D mapping of the environment—the second approach aims at exploiting the use of memory to improve the estimation accuracy and convergence speed. The two models and the two observers are evaluated in simulation and real data, where mobile and manipulator robots are used.

Mechanical properties of room-temperature injection molded, pressurelessly sintered boron carbide

Boron carbide (B4C) is of interest in the armor community due to its combination of extreme hardness and low density. However, it is difficult to utilize these properties in many applications due to the challenges associated with forming near-net shapes of B4C, combined with its low inherent sinterability without the application of external pressure. In this study, highly loaded (51 vol. %) aqueous B4C suspensions were developed and injection molded at room temperature followed by pressureless sintering up to 2075 °C. Three different sintering aids (Y2O3, Al, and Al2O3) were used to aid the densification process. B4C parts were sintered to high density (up to 97.7% relative density) and high hardness values (up to 3200 Vickers). The flexural strength of the samples was limited by grain pullout during polishing of the tensile surface; the strength was correlated to the maximum grain pullout flaw measured at the intersection of the tensile surface and the fracture surface (R2 > 0.98). The robust performance of the B4C suspensions and their resulting densities and hardness demonstrate the room-temperature injection molding process as a viable alternative for low-cost near-net shaping of B4C components.

The Influence of Wind Shielding and Train‐Induced Wind on the Vibration of a Train‐Bridge System

The aerodynamic forces of the system were obtained based on a 3D aerodynamic model, and a dynamic analysis model of the train‐bridge coupling system was established to compare the vibration responses of the train and bridge with and without a wind barrier to fully consider the wind shielding effect and train‐induced wind effect on the vibration of a train‐bridge system. The results show that the combined wind direction and the direction of the operating train are at an angle. Although the shape of the leading and trailing cars is the same, their wind load values are not the same due to the influence of the train wind. Because of the perforations, the vortex between the wind barrier and the train’s windward surface varies in a complicated fashion. The airflow traveling through the holes has a negative value because it circulates at the intersection of the windward surface and the top surface of the car body. The vehicles’ lateral wheel force, derailment factor, offload factor, and overturning factor are all lowered when the wind barrier is erected. The shielding effect of the wind barrier on the head car is more noticeable when it comes to lateral wheel force and derailment factor. With a wind barrier installed, the wind field surrounding the bridge is very complex, resulting in a modest decrease in vertical displacement.

Dual quaternion-based osculating circle algorithm for finding intersection curves

Abstract The intersection of surfaces is a fundamental process in computational geometry and computer-aided design applications to build and interrogate complex shapes in the computer. This paper presents a novel and simple dual quaternion-based osculating circle DQOC algorithm to find the intersection curve of two regular surfaces based on the osculating circle concept and dual quaternions. Additionally, we expressed the natural equations of the intersection curve. We have also demonstrated the superiority of our method through numerical examples.

An enhanced semi-implicit particle method for simulating the flow of droplets with free surfaces

The accurate modeling of the surface-tension on free surfaces remains a challenging problem in meshfree particle methods. Recently, Matsunaga et al. (2020) have made an important step forward toward addressing this issue by introducing a moving surface mesh to represent the free-surface boundary in 2D. However, the surface mesh makes it difficult to extend this methodology to 3D and to treat topological changes in free surfaces. This study aims to extend this methodology to 3D and restore the capability of the model to simulate topological changes by carefully detecting the free-surface particles. In this situation, the problems regarding fluctuated free-surface boundaries and the dynamic intersection of a free surface with a wall boundary arise. To resolve these problems, a new particle shifting method in the surface normal direction is proposed for the free-surface particles to reduce fluctuations. A new contact angle model is proposed to compute the intersection point of a free surface and a wall boundary. In this manner, an enhanced particle method suitable for simulating the dynamics of liquid droplets with possible topological changes in 3D is developed. Eight numerical examples verified the developed method and demonstrated the enhancement of the new particle shifting technique.

Theory and analysis of acoustic-gravity waves in a free-surface compressible and stratified ocean

Waves propagate in a free-surface ocean due to compressibility and gravity (and surface tension at much smaller scale). Analytical solutions have long been derived independently for acoustic and gravity waves, i.e., acoustic waves or internal-gravity waves in an unbounded ocean, surface-gravity waves in a free-surface-ocean, and acoustic or internal modes in a bounded ocean. In the present study, surface tension and earth-rotation are neglected and a simple, unified model based on inner and boundary dispersion relations is derived for waves propagating in a compressible, stratified, free-surface ocean. Branches of acoustic gravity wave solutions are identified and visually analysed in phase-space. Taylor developments are then carried out with respect to small parameters describing stratification and compressibility and are compared with numerical approximations of the intersection of inner and boundary dispersion surfaces. Finally, the model recovers the known approximations for swell, long-surface waves, internal-gravity waves, internal modes, acoustic waves or acoustic modes, and also provides information on the modifications of these solutions due to stratification and compressibility and on the coupling of acoustic and gravity waves. Two peculiar regions of the acoustic-gravity wave phase-space are more specifically highlighted and studied in detail: one for long waves shedding new light on the distinction between surface waves and low-order internal modes, the other for marginally stable surface waves of intermediate length-scale.