Topological Entities Research Articles

Generating Analysis Topology using Virtual Topology Operators

Virtual topology operations have been utilized to generate an analysis topology definition suitable for downstream mesh generation. Detailed descriptions are provided for virtual topology merge and split operations for all topological entities, where virtual decompositions are robustly linked to the underlying geometry. Current virtual topology technology is extended to allow the virtual partitioning of volume cells. A valid description of the topology, including relative orientations, is maintained which enables downstream interrogations to be performed on the analysis topology description, such as determining if a specific meshing strategy can be applied to the virtual volume cells. As the virtual representation is a true non-manifold description of the sub-divided domain the interfaces between cells are recorded automatically. Therefore, the advantages of non-manifold modelling are exploited within the manifold modelling environment of a major commercial CAD system without any adaptation of the underlying CAD model. A hierarchical virtual structure is maintained where virtual entities are merged or partitioned. This has a major benefit over existing solutions as the virtual dependencies here are stored in an open and accessible manner, providing the analyst with the freedom to create, modify and edit the analysis topology in any preferred sequence.

Non‐Nuclear Attractor in a Molecular Compound under External Pressure

AbstractThe dimeric magnesium(I) compound [{(DipNacnac)Mg}2] [1, DipNacnac = (DipNCMe)2CH, Dip = 2,6‐diisopropylphenyl] has previously been shown to exhibit a non‐nuclear attractor (NNA) between the two Mg atoms in the molecular ground state by both experimental and theoretical electron‐density studies. To study the stability and characteristics of this topological entity, we have determined the molecular structure of 1 in the pressure range from 0.4 to 1.9 GPa by high‐pressure single‐crystal X‐ray diffraction. The central Mg–Mg bond contracts significantly in this range to 97 % of the value at ambient pressure and a temperature of 100 K. High‐level single‐point theoretical calculations with the resulting atomic coordinates show that the NNA is persistently present in the topology at all pressures and that the difference between the value of the electron density at the NNA and the Mg–NNA bond critical point (bcp) is close to a maximum at the Mg–Mg separation that is found experimentally.

Small Angle Neutron Scattering Studies of Skyrmion Lattices

Skyrmion lattices in chiral magnets can be regarded as macroscopic lattices formed by topological entities with particle like properties where the particle-like character of the Skyrmions is reflected in the integer winding number of their magnetization [1]. Caused by their topology, Skyrmions cannot be destroyed or created by a smooth deformation of a trivial spin texture. Skyrmion lines can be seen as magnetic whirls – sharing strong similarities with vortices of type II superconductors. Analogous to the large variety of different phases of superconducting vortex matter, Skyrmion lattice melting transitions, Skyrmion liquids and Skyrmion glass phases are expected to exist in the various B20 materials. The structure of Skyrmion matter thereby sensitively reflects the underlying physical properties of the material carrying the Skyrmions. Moreover, due to their topology, Skyrmion lattices in chiral magnets provide an excellent showcase for the investigation of topological stability and phase conversion [2]. A further consequence of the special topological properties of Skyrmions is called emergent electrodynamics: While moving through the Skyrmion lattice, conduction electrons collect a Berry´s phase in real space which leads to a very efficient coupling of transport current and magnetic structure. This leads to considerable spin transfer torque effects at current densities as low as 10^6 A/m2 [3]. Small angle neutron scattering (SANS) has played a central role in the investigation of Skyrmion lattices. We show how SANS can be used for a detailed investigation of the structure, stability, transport properties and topological decay of Skyrmion lattices in B20 compounds. *Work in collaboration with: T. Adams, A. Bauer, H. Berger, P. Böni, S. Buhrandt, A. Chacon, S. Dunsiger, L. Eng, K. Everschor-Sitte, M. Garst, R. Georgii, M. Janoschek, F. Jonietz, J. Kindervater, P. Milde, A. Neubauer, C. Pfleiderer, A. Rosch, C. Schütte, J. Seidel, J. Waizner, W. Wünzer

Toward a Consistent Interpretation of the QTAIM: Tortuous Link between Chemical Bonds, Interactions, and Bond/Line Paths

Currently, bonding analysis of molecules based on the Quantum Theory of Atoms in Molecules (QTAIM) is popular; however, "misinterpretations" of the QTAIM analysis are also very frequent. In this contribution the chemical relevance of the bond path as one of the key topological entities emerging from the QTAIM's topological analysis of the one-electron density is reconsidered. The role of nuclear vibrations on the topological analysis is investigated demonstrating that the bond paths are not indicators of chemical bonds. Also, it is argued that the detection of the bond paths is not necessary for the "interaction" to be present between two atoms in a molecule. The conceptual disentanglement of chemical bonds/interactions from the bonds paths, which are alternatively termed "line paths" in this contribution, dismisses many superficial inconsistencies. Such inconsistencies emerge from the presence/absence of the line paths in places of a molecule in which chemical intuition or alternative bonding analysis does not support the presence/absence of a chemical bond. Moreover, computational QTAIM studies have been performed on some "problematic" molecules, which were considered previously by other authors, and the role of nuclear vibrations on presence/absence of the line paths is studied demonstrating that a bonding pattern consistent with other theoretical schemes appears after a careful QTAIM analysis and a new "interpretation" of data is performed.

Drive geometry construction method of machining features for aircraft structural part numerical control machining

Feature-based manufacturing methodologies offer opportunity for numerical control machining effectively and efficiently. However, the loss of drive geometries caused by the complex shape and machining process of aircraft structural parts undercuts the advantage of feature-based manufacturing tools. To better address the gap between the process planning and tool path generation for aircraft structural part, a drive geometry construction approach based on the topological relationships and machining process of machining features for process planning are proposed. The created drive geometries correspond with the optimized machining process. The drive geometries that define the machining areas of machining features are categorized into guide lines and guide faces in accord with the machining mode, such as 2.5- to 3-axis machining and multi-axis machining. In contrast to the traditional performing of intersection operations with a series of slice planes and the part model manually, the drive geometries are constructed by extracting the existing topological entities and creating some auxiliary topological entities automatically. The drive geometry preparing time and the consumption of computer memory are reduced significantly. The proposed approach has been tested and used in a pilot feature-based programming system that is developed for some aircraft manufacturers in China.

Hyperbolic spin vortices and textures in exciton–polariton condensates

From cosmology to the microscopic scales of the quantum world, the study of topological excitations is essential for the understanding of phase conformation and phase transitions. Quantum fluids are convenient systems to investigate topological entities because well-established techniques are available for their preparation, control and measurement. Across a phase transition, a system dramatically changes its properties because of the spontaneous breaking of certain continuous symmetries, leading to generation of topological defects. In particular, attention is given to entities that involve both spin and phase topologies. Exciton-polariton condensates are quantum fluids combining coherence and spin properties that, thanks to their light-matter nature, bring the advantage of direct optical access to the condensate order parameter. Here we report on the spontaneous occurrence of hyperbolic spin vortices in polariton condensates, by directly imaging both their phase and spin structure, and observe the associated spatial polarization patterns, spin textures that arise in the condensate.

Optical generation, templating, and polymerization of three-dimensional arrays of liquid-crystal defects decorated by plasmonic nanoparticles

Defects in liquid crystals are used to model topological entities ranging from Skyrmions in high-energy physics to early-universe cosmic strings, as well as find practical applications in self-assembly of diffraction gratings and in scaffolding of plasmonic nanoparticles, but they are hard to control and organize into three-dimensional lattices. We laterally scan focused laser beams to produce periodic arrays of twist-stabilized defects forming either linear (fingers) or axially symmetric (torons) configurations in partially polymerizable liquid crystal films. Polymerization allows for stabilization of these structures and the formation of three-dimensional arrays of defects by stacking of the thin cholesteric films on top of each other. In the process of fabrication of such arrays, we polymerize the liquid crystal film with an array of torons or fingers and then sequentially produce and photopolymerize new liquid crystal layers on top of it, thus obtaining a three-dimensional structure of twist-stabilized defects in a layer-by-layer fashion. Templating by the polymerized layer spontaneously yields ordered organization of fingers and torons in the new cholesteric layer, thus enabling a three-dimensional ordered structure of defects. Nondestructive three-dimensional imaging of director fields by use of three-photon excitation fluorescence polarizing microscopy reveals the nature of topological singularities and physical underpinnings behind the observed templating effect. Three-dimensional patterning of defects templates the self-assembly of plasmonic nanoparticles into individual singularities and their arrays, laying the groundwork for potential applications in nanophotonics, plasmonics, metamaterial fabrication, and nanoscale energy conversion.

A method for topological entity matching in the integration of heterogeneous CAD systems

Topological entities are always used as reference or operation objects in the feature modeling procedure. Hence, to achieve the integration of heterogeneous CAD systems, the corresponding topological entities must be found in the target CAD system to

Name matching method using topology merging and splitting history for exchange of feature-based CAD models

A feature is generated by referring to topological entities in a solid model. It is essential to persistently name the topological entities referenced by the feature. This problem is known as the persistent naming problem. The persistent naming problem is divided into naming and name matching. The persistent naming problem is an important issue in the exchange of feature-based CAD models through a neutral format. If a CAD model contains only construction history, the naming of the topological entities is required during translation. However, if a CAD model contains modification history as well, name matching is also required. In a previous study, the authors proposed a naming method for exchanging feature-based CAD models. In this study, a solution to the name matching problem is proposed and its technical details are discussed. The proposed name matching method is based on the local matching technique, using topology merging and splitting history. The feasibility of the proposed name matching method has been demonstrated through experiments with a prototype CAD model translator.

Formula omitted]-Complex: Efficient non-manifold boundary representation with inclusion topology

The interpretation of auxiliary entities as boundary entities in previous non-manifold boundary (NMB) representations may change a model’s intended topology and increase the complexity of the corresponding data structure. In this paper, entities appearing in a modeling process are classified into boundary and non-boundary entities. Non-boundary entities are usually embedded into embedding-space entities. These embedding relationships are described by inclusion topology. To support inclusion topology, a new mathematical framework—quasi-cell-complex, as well as a topological data structure—Q-Complex, are proposed. Quasi-cell-complex is an extension of cell-complex with inclusion topology supported. Q-Complex is an NMB representation, in which a new topological entity—embedder is created for inclusion topology and zone/disk is adopted to capture the complete adjacencies around a vertex. Thus, Q-Complex allows full adjacencies, incidence-ordering, and inclusion relationships to be derived, and the efficiency of most basic queries is several times faster than most state-of-the-art NMB representations, without increasing storage. Additionally, the benefits of inclusion topology for shape modeling and feature modeling are explored.

A New Mechanism of Naming Topological Entities for Semantic Feature Operations

Naming topological entities and the validity maintenance of model are two important issues in Computer Aided Design, which can make a semantic feature model conform to all constraints correctly. In this paper, a new mechanism of naming topological entities based on face features is proposed. Based on the corresponding mechanisms for naming topological entities, the methods of coding entities, sub-entities and virtual entities are given. The mechanisms for maintaining the validity of semantic feature operations are described. Sub-edges, sub-faces, virtual faces and virtual sub-edges are applied to process the problem of face obliteration. Sub-edges and virtual edges are used to process the problem of edge obliteration. After the mechanisms for naming topological entities and the methods of validity maintenance are applied to HUST-CAID system, its modeling performance is improved and the feasibility of the proposed mechanisms and methods above is also proved.

Boolean operations on multi-region solids for mesh generation

An algorithm for Boolean operations on non-manifold models is proposed to allow the treatment of solids with multiple regions (internal interfaces) and degenerate portions (shells and wires), in the context of mesh generation. In a solid modeler, one of the most powerful tools to create three-dimensional objects with any level of geometric complexity is the Boolean set operators. They are intuitive and popular ways to combine solids, based on the operations applied to point sets. To assure that the resulting objects have the same dimension as the original objects, without loose or dangling parts, a regularization process is usually applied after a Boolean operation. In practice, the regularization is performed classifying the topological elements and removing internal or lower-dimensional structures. However, in many engineering applications, the adopted geometric model may contain idealized internal parts, as in the case of multi-region models, or lower-dimensional parts, as in the case of solids that contain dangling slabs that are represented as zero-thickness surfaces or wireframes in the model. Therefore, the aim of this work is the development of a generic algorithm that allows the application of the Boolean set operations in a geometric modeling environment applied to finite and boundary element mesh generation. This environment adopts a non-manifold boundary representation that considers an undefined number of topological entities (group concept), and works with objects of different dimensions and with objects not necessarily plane or polyhedral (parametric curved surfaces). Numerical examples are presented to illustrate the proposed methodology.

Spin-to-orbital angular momentum conversion in semiconductor microcavities

We experimentally demonstrate a technique for the generation of optical beams carrying orbital angular momentum using a planar semiconductor microcavity. Despite being isotropic systems, the transverse electric - transverse magnetic (TE-TM) polarization splitting featured by semiconductor microcavities allows for the conversion of the circular polarization of an incoming laser beam into the orbital angular momentum of the transmitted light field. The process implies the formation of topological entities, a pair of optical half-vortices, in the intracavity field.

Quasi-two-dimensional Skyrmion lattices in a chiral nematic liquid crystal

Skyrmions are particle-like topological entities in a continuous field that have an important role in various condensed matter systems, including two-dimensional electron gases exhibiting the quantum Hall effect, chiral ferromagnets and Bose-Einstein condensates. Here we show theoretically, with the aid of numerical methods, that a highly chiral nematic liquid crystal can accommodate a quasi-two-dimensional Skyrmion lattice as a thermodynamically stable state, when it is confined to a thin film between two parallel surfaces imposing normal alignment. A chiral nematic liquid crystal film can thus serve as a model Skyrmion system, allowing direct investigation of their structural properties by a variety of optical techniques at room temperatures that are less demanding than Skyrmion systems discussed previously.

Adaptive dynamic cohesive fracture simulation using nodal perturbation and edge‐swap operators

AbstractDependence on mesh orientation impacts adversely the quality of computational solutions generated by cohesive zone models. For instance, when considering crack propagation along interfaces between finite elements of 4k structured meshes, both extension of crack length and crack angle are biased according to the mesh configuration. To address mesh orientation dependence in 4k structured meshes and to avoid undesirable crack patterns, we propose the use of nodal perturbation (NP) and edge‐swap (ES) topological operation. To this effect, the topological data structure TopS (Int. J. Numer. Meth. Engng 2005; 64: 1529–1556), based on topological entities (node, element, vertex, edge and facet), is utilized so that it is possible to access adjacency information and to manage a consistent data structure in time proportional to the number of retrieved entities. In particular, the data structure allows the ES operation to be done in constant time. Three representative dynamic fracture examples using ES and NP operators are provided: crack propagation in the compact compression specimen, local branching instability, and fragmentation. These examples illustrate the features of the present computational framework in simulating a range of physical phenomena associated with cracking. Copyright © 2010 John Wiley & Sons, Ltd.

Analysis of Leading-Edge Separation Bubbles on Rotating Blades

T HE regions of separated flow that form on blades govern the blade stall characteristics and the loading of wind turbine blades. The nature and extent of these regions are determined primarily (except for the airfoil shape, incidence, andReynolds number) by the two most important parameters that trigger three-dimensional (3-D) effects, and they are the radius by chord ratio r=c and the rotation parameter Vw= r defining the ratio of the wind velocity to the tangential velocity. The rotation parameter shows the interaction between the axial flow (wind) and the rotational flow induced by the rotor blades. The physical mechanism driving the 3-D effects is in conjunction with the interaction between the wind speed higher than the designvelocity and the flow induced by constant-rotational speed rotors. If the rotation parameter is less than unity along the entire span (Vw= r 1 at the inner part of the span producing both strong centrifugal andCoriolis forces that involve the separation of the boundary layer on the blade. Larger rotation parameters mean enhanced rotational flow that reduces the negative pressure peak from the leading edge and produces leading-edge separation bubbles (not leading-edge stall). On the other hand, the Coriolis forces contribute to stall delay by a favorable chordwise pressure gradient. The occurrence of what is termed inboard stall delay, characterized by an abrupt increase in lift and drag, can be attributed to the sudden suck of air from the separation bubble at the leading edge of the blade that is directed toward the radial direction. Of concern here are the small separation bubbles that form near the leading edge of the inboard sections of the blade, at r=c 1. At extreme inboard locations, separation bubble initiation and aft progression are closely associated with poststall lift force magnitudes that exceed those exhibited by nonrotating blades. The flow in the vicinity of the leading edge of a blade section subject to leading-edge stall is as sketched in Fig. 1. The laminar boundary layer, extending from the stagnation point over the leading edge, separates just downstream of the point of minimum pressure. Transition to turbulent flow occurs in the free-shear layer a short distance downstream of the separation point. The flow then reattaches to the section surface, with a turbulent boundary layer extending from the reattachment point to the trailing edge. If the r=c ratio is decreased, the bubble becomes slightly shorter and ultimately coalesces in a singular topological entity [1]. The interaction between the viscous and inviscid flows in the vicinity of the bubble is taken into account through a simplified procedure in the sequel.

Volumetric Topological Analysis: A Novel Approach for Trabecular Bone Classification on the Continuum Between Plates and Rods

Trabecular bone (TB) is a complex quasi-random network of interconnected plates and rods. TB constantly remodels to adapt to the stresses to which it is subjected (Wolff's Law). In osteoporosis, this dynamic equilibrium between bone formation and resorption is perturbed, leading to bone loss and structural deterioration. Both bone loss and structural deterioration increase fracture risk. Bone's mechanical behavior can only be partially explained by variations in bone mineral density, which led to the notion of bone structural quality. Previously, we developed digital topological analysis (DTA) which classifies plates, rods, profiles, edges, and junctions in a TB skeletal representation. Although the method has become quite popular, a major limitation of DTA is that it provides only hard classifications of different topological entities, failing to distinguish between narrow and wide plates. Here, we present a new method called volumetric topological analysis (VTA) for regional quantification of TB topology. At each TB location, the method uniquely classifies its topology on the continuum between perfect plates and perfect rods, facilitating early detections of TB alterations from plates to rods according to the known etiology of osteoporotic bone loss. Several new ideas, including manifold distance transform, manifold scale, and feature propagation have been introduced here and combined with existing DTA and distance transform methods, leading to the new VTA technology. This method has been applied to multidetector computed tomography (CT) and micro-computed tomography ( μCT) images of four cadaveric distal tibia and five distal radius specimens. Both intra- and inter-modality reproducibility of the method has been examined using repeat CT and μCT scans of distal tibia specimens. Also, the method's ability to predict experimental biomechanical properties of TB via CT imaging under in vivo conditions has been quantitatively examined and the results found are very encouraging.

An approach to recognize interacting features from B-Rep CAD models of prismatic machined parts using a hybrid (graph and rule based) technique

This paper presents a new hybrid (graph + rule based) approach for recognizing the interacting features from B-Rep CAD models of prismatic machined parts. The developed algorithm considers variable topology features and handles both adjacent and volumetric feature interactions to provide a single interpretation for the latter. The input CAD part model in B-Rep format is preprocessed to create the adjacency graphs for faces and features of associated topological entities and compute their attributes. The developed FR system initially recognizes all varieties of the simple and stepped holes with flat and conical bottoms from the feature graphs. A new concept of Base Explicit Feature Graphs and No-base Explicit Feature Graphs has been proposed which essentially delineates between features having planar base face like pockets, blind slots, etc. and those without planar base faces like passages, 3D features, conical bottom features, etc. Based on the structure of the explicit feature graphs, geometric reasoning rules are formulated to recognize the interacting feature types. Extracted data has been post-processed to compute the feature attributes and their parent–child relationships which are written into a STEP like native feature file format. The FR system was extensively tested with several standard benchmark components and was found to be robust and consistent. The extracted feature file can be used for integration with various downstream applications like CAPP.

Tracking topological changes in parametric models

In current parametric CAD systems, the relation between the values of the parameters of a model and the topology of the model is often not clear to the user. To give the user better control over the topology of the model, this relation should be made explicit. A method is presented here that determines the parameter values for which the topology of a model changes, i.e. the critical values of a given variant parameter. The considered model consists of a system of geometric constraints, which relates parameters and feature geometries, and a cellular model, which partitions space into volumetric cells determined by the intersections of the feature geometries and represented by topological entities. Our method creates a new system of geometric constraints to relate the parameters of the model to the topological entities. For each entity that is dependent on the variant parameter, degenerate cases are enforced by specific geometric constraints. Solving the resulting constraint systems yields the critical parameter values. Critical values can be used to compute parameter ranges corresponding to families of objects, i.e. all parameter values which correspond to models that satisfy a given set of geometric and topological constraints.

Reconstruction automatique des entités d’un modèle BREP à partir d’un maillage déformé

Nowadays, the integration of the different steps of mechanical design process (Design, analysis and manufacturing) is a necessity to reduce the time of design and optimization. This tendency of integrating CAD/CAM/Analysis and automation of the corresponding processes requires shared data between the various tasks using an integrated product model. Our research is oriented to CAD/CAM/Analysis integration by rebuilding the CAD model (BREP) starting from the FE results (deformed mesh). This paper presents techniques for rebuilding the geometrical and topological entities of the CAD model starting from a deformed mesh.