Complicated Topological Structures Research Articles

A Region-growing GradNormal Algorithm for Geometrically and Topologically Accurate Mesh Extraction

With the prevalence of implicit shape processing and reconstruction, extracting a polygonal mesh of an isosurface from volume data, which plays an important role in these tasks, is receiving more and more attention. GradNormal, a recently proposed marching tetrahedra method, can effectively extract high-quality meshes from analytic functional shapes but suffers from detail loss and computational inefficiency issues. In this paper, we improve GradNormal from four aspects. First, we extend GradNormal from an analytic function to an arbitrary geometric domain equipped with the projection operation. Second, we select a seed tetrahedron and find only the tetrahedra intersecting the implicit surface, in a region-growing style, which helps save memory and accelerate calculation. Third, we invent a hierarchical tiling mechanism to enhance the recovery accuracy of the resulting mesh, unlike the uniform tiling used in GradNormal. Finally, we propose to accurately predict how the underlying surface goes through a tetrahedral element so that complicated topological structures such as thin plates and gaps can be well captured. Extensive experimental results on challenging shapes show that the improved GradNormal is able to quickly produce a feature-adapted triangle mesh that is more topologically and geometrically accurate than the state-of-the-art.

Adaptive Slicing of Implicit Porous Structure with Topology Guarantee

Adaptive slicing is an important step in 3D printing, where the thicknesses of slices are adaptively adjusted to achieve a trade-off between printing time reduction and surface quality improvement. However, in conventional slicing algorithms, the topological information inside the model is usually not considered, and then, they are not suitable for slicing porous structures with complicated inner topological structures. In this study, based on the persistent homology theory, a novel method is developed to adaptively slice implicit porous structures, which guarantees the topological correctness of the generated adaptive slice model. Given an implicit porous structure, we generate the finest slice model, and calculate the topological information of the finest slices, i.e., persistent diagram (PD) and Betti number. Next, the finest slice model is partitioned into parts based on the Betti number of the finest slices. In each part, the Betti numbers of the finest slices are the same. Moreover, in each part, we first determine the slices for printing by solving the ℓ0−norm optimization problem to optimize the printing time, and then, the thicknesses of the slices for printing are calculated by optimizing the surface quality. In this way, not only can the printing time and surface quality be optimized, but also the topological correctness of the adaptive slice model can be guaranteed. Experimental results show the effectiveness of the developed algorithm.

Ramified continua as global attractors of C 1-smooth self-maps of a cylinder close to skew products

In the paper we consider -smooth self-maps of a cylinder close to -smooth skew products (and satisfying some additional conditions). We study such geometric property of the maps, as existence of -smooth invariant local lamination, and apply this geometric property to the proof of the geometric integrability of maps under consideration. Using obtained results we construct the example of the family of -smooth maps close to skew products so that each map from this family admits the global attractor, which is a one-dimensional ramified continuum with a complicated topological structure. The global attractor of every map from the family under consideration consists of arcs of two types. On the unique circle (which is the arc of first type) the map is mixing; on arcs of second type of different lengths homeomorphic to a closed interval (the family of such arcs has continuum cardinality) the map is not mixing. The topological structure of the global attractor and dynamical properties of trajectories on the attractor lead to the property of dense intermittency (in the complement to the attractor) of attraction sets of different ω-limit sets, the union of which coincides with the global attractor.

A transitive homeomorphism on the Lelek fan

ABSTRACT Let X be a continuum and let be a homeomorphism. To construct a dynamical system with interesting dynamical properties, the continuum X often needs to have some complicated topological structure. In this paper, we are interested in one such dynamical property: transitivity. By now, various examples of continua X have been constructed in such a way that the dynamical system is transitive. Mostly, they are examples of continua that are not path-connected, such as the pseudo-arc or the pseudo-circle, or they are examples of locally connected continua (and every locally connected continuum is path-connected), Sierpiński carpet is such an example. In this paper, we present an example of a dynamical system , where φ is a homeomorphism on the continuum X and X is a path-connected but not locally connected continuum. We construct a transitive homeomorphism on the Lelek fan. As a by-product, a non-invertible transitive map on the Lelek fan is also constructed.

Hybrid Impulsive Pinning Control for Mean Square Synchronization of Uncertain Multi-Link Complex Networks with Stochastic Characteristics and Hybrid Delays

This study explores the synchronization issue for uncertain multi-link complex networks incorporating stochastic characteristics and hybrid delays. Unlike previous works, internal delays, coupling delays, and stochastic delays considered in our model change over time; meanwhile, the impulse strength and position change with time evolution. To actualize network synchronization, a strategy called hybrid impulsive pinning control is applied, which combines the virtue of impulsive control and pinning control as well as two categories of impulses (i.e., synchronization and desynchronization). By decomposing the complicated topological structures into diagonal items and off-diagonal items, multiple nonlinear coupling terms are linearly decomposed in the process of theoretical analysis. Combining inequality technology and matrix decomposition theory, several novel synchronization criteria have been gained to ensure synchronization for the concerning multi-link model. The criteria get in touch with the uncertain strengths, coupling strengths, hybrid impulse strengths, delay sizes, impulsive intervals, and network topologies.

Optimal Design of Asymmetric Rotor Pole for Interior Permanent Magnet Synchronous Motor Using Topology Optimization

As asymmetric interior permanent magnet synchronous motor (AIPMSM) has excellent performance but complicated topological structure, a novel high-resolution encoding and edge smoothing method is proposed for topology optimization of the asymmetric rotor of interior permanent magnet synchronous motor (IPMSM) in this study. This method aims to solve complex electromagnetic design problems with time-dependent performance through a multi-objective genetic algorithm (MOGA) integrated with a high-resolution encoding and edge smoothing method. The complex structure is represented by a high-resolution image-like matrix and then vectorized by the edge smoothing method. Therefore, the commonly used discrete binary encoded variables related to the finite element (FE) model are replaced with a vectorized topological structure and other control variables. In this sense, high-resolution matrix and edge smoothing methods are used for the first time to represent the rotor topology of AIPMSMs. Compared with the traditional topology optimization method, the proposed method has the advantage of expressing more complex and vectorized topological structures; meanwhile, the obtained performance is accurate and trustworthy using conventional FE simulation. Numerical results show that a stable convergence is achieved with the avoidance of checkerboards and material overlapping. It is shown that the proposed method can find solutions with better performances, in comparison with the reference model.

A Robustness Evaluation Method of Natural Gas Pipeline Network Based on Topological Structure Analysis

As the total mileage of natural gas pipeline network continues to increase, the topological structure of natural gas pipeline network will become more and more complex. The complicated topological structure of natural gas pipeline network is likely to cause inherent structural defects, which have serious impacts on the safe operation of natural gas pipeline network. At present, related researches mainly focused on the safe and reliable operation of natural gas pipeline network, which has become a research hotspot, but few of them considered the complexity of natural gas pipeline network and its potential impacts. In order to understand the complexity of natural gas pipeline network and its behaviors when facing structural changes, this paper studied the robustness of natural gas pipeline network based on complex network theory. This paper drew on the methods and experience of robustness researches in other related fields, and proposed a robustness evaluation method for natural gas pipeline network which is combined with its operation characteristics. The robustness evaluation method of natural gas pipeline network is helpful to identify the key components of the pipeline network and understand the response of the pipeline network to structural changes. Furthermore, it can provide a theoretical reference for the safe and stable operation of natural gas pipeline network. The evaluation results show that natural gas pipeline network shows strong robustness when faced with random disturbances represented by pipeline accidents or component failures caused by natural disasters, and when faced with targeted disturbances represented by terrorist disturbances, the robustness of natural gas pipeline network is very weak. Natural gas pipeline network behaves differently in the face of different types of random disturbances. Natural gas pipeline network is more robust when faced with component failures than pipeline accidents caused by natural disasters.

THE SEISMIC RESPONSE OF WATER SUPPLY NETWORKS IN RANDOM SEISMIC FIELDS BASED ON PHYSICAL MECHANISMS

Water supply networks are important components of lifeline engineering. Because of the influence of random earthquake motion fields, their seismic response and function also have obvious randomness. The influence of the complicated topological structure of water supply networks cannot be considered by the traditional seismic response analysis of buried pipelines. The traditional method is also difficult to be applied to analyze the random vibration of the nonlinear system. The physical response of pipelines has not been implemented into the functional analysis of water supply networks. To solve these three problems, this paper modifies the random physical model of seismic ground motion fields on the local engineering site, introduces a finite element method of buried pipe networks, combines the probability density evolution method, and realizes the random seismic response analysis of water supply networks. Furthermore, the transient flow theory is utilized, and the random seismic function analysis of water supply networks is completed. It lays foundation for the seismic reliability evaluation of water supply networks.

SSCA-Net: Simultaneous Self- and Channel-Attention Neural Network for Multiscale Structure-Preserving Vessel Segmentation.

Vessel segmentation is a fundamental, yet not well-solved problem in medical image analysis, due to the complicated geometrical and topological structures of human vessels. Unlike existing rule- and conventional learning-based techniques, which hardly capture the location of tiny vessel structures and perceive their global spatial structures, we propose Simultaneous Self- and Channel-attention Neural Network (termed SSCA-Net) to solve the multiscale structure-preserving vessel segmentation (MSVS) problem. SSCA-Net differs from the conventional neural networks in modeling image global contexts, showing more power to understand the global semantic information by both self- and channel-attention (SCA) mechanism and offering high performance on segmenting vessels with multiscale structures (e.g., DSC: 96.21% and MIoU: 92.70% on the intracranial vessel dataset). Specifically, the SCA module is designed and embedded in the feature decoding stage to learn SCA features at different layers, in which the self-attention is used to obtain the position information of the feature itself, and the channel attention is designed to guide the shallow features to obtain global feature information. To evaluate the effectiveness of our SSCA-Net, we compare it with several state-of-the-art methods on three well-known vessel segmentation benchmark datasets. Qualitative and quantitative results demonstrate clear improvements of our method over the state-of-the-art in terms of preserving vessel details and global spatial structures.

Automatic Crack Detection on Road Pavements Using Encoder-Decoder Architecture.

Automatic crack detection from images is an important task that is adopted to ensure road safety and durability for Portland cement concrete (PCC) and asphalt concrete (AC) pavement. Pavement failure depends on a number of causes including water intrusion, stress from heavy loads, and all the climate effects. Generally, cracks are the first distress that arises on road surfaces and proper monitoring and maintenance to prevent cracks from spreading or forming is important. Conventional algorithms to identify cracks on road pavements are extremely time-consuming and high cost. Many cracks show complicated topological structures, oil stains, poor continuity, and low contrast, which are difficult for defining crack features. Therefore, the automated crack detection algorithm is a key tool to improve the results. Inspired by the development of deep learning in computer vision and object detection, the proposed algorithm considers an encoder-decoder architecture with hierarchical feature learning and dilated convolution, named U-Hierarchical Dilated Network (U-HDN), to perform crack detection in an end-to-end method. Crack characteristics with multiple context information are automatically able to learn and perform end-to-end crack detection. Then, a multi-dilation module embedded in an encoder-decoder architecture is proposed. The crack features of multiple context sizes can be integrated into the multi-dilation module by dilation convolution with different dilatation rates, which can obtain much more cracks information. Finally, the hierarchical feature learning module is designed to obtain a multi-scale features from the high to low- level convolutional layers, which are integrated to predict pixel-wise crack detection. Some experiments on public crack databases using 118 images were performed and the results were compared with those obtained with other methods on the same images. The results show that the proposed U-HDN method achieves high performance because it can extract and fuse different context sizes and different levels of feature maps than other algorithms.

Lattice Boltzmann method simulations of the immiscible Rayleigh-Taylor instability with high Reynolds numbers

In this paper, an advanced phase-field lattice Boltzmann method based on the multiple-relaxation-time collision model is used to simulate the immiscible single-mode Rayleigh-Taylor instability with a moderate Atwoods number in a long tube, and we systematically analyze the effect of the Reynolds number on the interfacial dynamics and the late-time development stages of interface disturbance. The highest Reynolds number in the current simulation reaches up to 10000. The numerical results show that the Reynolds number significantly affects the development of the instability. For high Reynolds numbers, the instability undergoes a sequence of different growth stages, which include the linear growth, saturated velocity growth, reacceleration, and chaotic mixing stages. In the linear growth stage, the developments of the bubble and spike conform to the classical linear growth theory, and it is shown that the growth rate increases with the Reynolds number. In the second stage, the bubble and spike evolve with the constant velocities, and the numerical prediction for spike velocity is found to be slightly larger than the solution of the potential flow theory proposed by Goncharov [<i>Phys. Rev. Lett.</i> 2002 <b>88 </b> 134502], which can be attributed to the formation of vortices in the proximity of the spike tip. In addition, it is found that increasing the Reynolds number reduces the bubble saturated velocity, which then is smaller than the solution of the potential model. The nonlinear evolutions of the bubble and spike induce the Kelvin–Helmholtz instability, producing many vortex structures with different scales. Due to the interactions among the vortices, the instability eventually enters into the chaotic mixing stage, where the interfaces undergo the roll-up at multiple layers, sharp deformation, and chaotic breakup, forming a very complicated topology structure. Furthermore, we also measured the bubble and spike accelerations and find that the dimensionless values fluctuates around the constants of 0.045 and 0.233, indicating a mean quadratic growth. And for low Reynolds numbers, the heavy fluid will fall down in the form of the spike, and the interface in the whole process becomes very smooth without the appearances of the roll-up and vortices. The late-time evolutional stages such as the reacceleration and chaotic mixing cannot also be observed.

Rational design of crystalline two-dimensional frameworks with highly complicated topological structures

Constructing two-dimensional (2D) polymers with complex tessellation patterns via synthetic chemistry makes a significant contribution not only to the understanding of the emergence of complex hierarchical systems in living organisms, but also to the fabrication of advanced hierarchical materials. However, to achieve such tasks is a great challenge. In this communication we report a facile and general approach to tessellate 2D covalent organic frameworks (COFs) by three or four geometric shapes/sizes, which affords 2D COFs bearing three or four different kinds of pores and increases structural complexity in tessellations of 2D polymers to a much higher level. The complex tessellation patterns of the COFs are elucidated by powder X-ray diffraction studies, theoretical simulations and high-resolution TEM.

A new class of Hamiltonian conservative chaotic systems with multistability and design of pseudo-random number generator

• A new modeling method is employed to develop a class of high dimensional Hamiltonian conservative chaotic systems. • A new conservative hyperchaotic system is proposed and exhibits some behaviour previously unobserved. • Multistability including infinite-orbit and infinite-scroll is observed in the proposed systems. • For encryption, pseudo-random digital signal generators based on conservative chaotic systems are developed. Compared to dissipative chaotic system, conservative chaotic systems have some attractive features valuable for engineering applications, such as security communication. This paper proposes a method for constructing new high dimensional conservative chaotic systems, for instance 4 dimensional conservative chaotic systems and 5 dimensional conservative hyper-chaotic systems. The dynamic properties of the constructed systems are verified by the dynamical evolution map, equilibrium points, Lyapunov dimension, the volume of flow and the Hamiltonian energy. An interesting co-existence of quasi-period, chaos and hyper-chaos flows are observed in the developed conservative chaotic systems. With trigonometric transformation, parallel conservative chaotic systems are achieved with infinitely many scrolls. To accommodate the engineering application requirement, the security communication is considered as a case study. The proposed conservative chaotic systems passed the validation National Institute of Standard Statistic Test criteria for the pseudo-random property , which is the critical factor of security communication. Furthermore, the pseudo-random signal generator is developed using the Field Programmable Gate Array technique. Due to the complicated topology structure, such digital implementation was not commonly reported in literatures, instead most conservative chaotic systems were validated only by analog circuit simulation.

Single Crystal-Lattice-Shaped Chaotic and Quasi-Periodic Flows with Time-Reversible Symmetry

In the literature, there are few conservative chaotic systems which are not obviously conservative according to their equations. This paper reports a 3D time-reversible symmetric chaotic system without equilibrium. The matrix form of the new system shows that there exists a Hamiltonian, which can exhibit interesting spatial structures (isosurfaces) controlled by different initial conditions. Numerical results shows that different initial conditions lead to different dynamical behaviors, such as quasi-periodic motion and conservative chaos. Moreover, the chaotic trajectories, visually, entwine around a isosurface and form a complicated topological structure like a single crystal lattice.

Deployment accuracy analysis of cable-strut deployable mechanism with joint clearances and forces constrained

The effects on deployment accuracy of joint clearances and forces acting on the deployable mechanism are investigated. “A virtual massless link” is used to describe the joint clearance of the mechanism in the free state. Aiming at the following problems of multi-loop linkages mechanical system such as loop constraints coupling and complicated topology structure, the geometric relationships and the deploying error equations of deployable mechanism are provided based on Denavit-Hartenberg matrix by splitting multi-loop linkage into 3 single-loop linkages. In addition, with consideration of forces, “a virtual massless rope” is used instead of “virtual massless link” to describe the joint clearance for avoiding the extra singularities. And the criterion of mechanism in stable configuration is obtained by weighting coefficient method on the basis of minimum potential principle. The solving procedure of deploying error equations in the state of forces constrained is presented by combining Monte-Carlo method with genetic algorithm, it is an effective solution for the nonlinear objective function with multiple constraints and strong coupling. The results indicate that the appropriate forces acting on mechanism produce a significant effect on improving repeat accuracy, and the absolute accuracy can be improved with the future error compensation.

Degenerate Hopf bifurcation in a self-exciting Faraday disc dynamo

In order to further understand a self-exciting Faraday disc dynamo (Hide et al, in Proc. R. Soc. A 452, 1369 1996), showing chaotic attractors with very complicated topological structures, we present codimension one and two (degenerate) Hopf bifurcations and prove the existence of periodic solutions. In addition, numerical simulations are given for confirming the theoretical results.

ChemInform Abstract: Synthesis of Rotaxanes and Catenanes Using an Imine Clipping Reaction

AbstractReview: [73 refs.

Scalar multi-wormholes

In 1921 Bach and Weyl derived the method of superposition to construct new axially symmetric vacuum solutions of general relativity. In this paper we extend the Bach–Weyl approach to non-vacuum configurations with massless scalar fields. Considering a phantom scalar field with the negative kinetic energy, we construct a multi-wormhole solution describing an axially symmetric superposition of N wormholes. The solution found is static, everywhere regular and has no event horizons. These features drastically tell the multi-wormhole configuration from other axially symmetric vacuum solutions which inevitably contain gravitationally inert singular structures, such as ‘struts’ and ‘membranes’, that keep the two bodies apart making a stable configuration. However, the multi-wormholes are static without any singular struts. Instead, the stationarity of the multi-wormhole configuration is provided by the phantom scalar field with the negative kinetic energy. Anther unusual property is that the multi-wormhole spacetime has a complicated topological structure. Namely, in the spacetime there exist 2N asymptotically flat regions connected by throats.

Topological monsters in elliptic equations and spectral theory

In this paper we will discuss the appearance of complicated geometric and topological structures through the level sets of solutions to a wide range of elliptic equations. Applications to the analysis of nodal sets of eigenfunctions of Schrödinger operators will be discussed too.

Lattice Boltzmann simulation of three-dimensional Rayleigh-Taylor instability.

In this paper, the three-dimensional (3D) Rayleigh-Taylor instability (RTI) with low Atwood number (A(t)=0.15) in a long square duct (12W × W × W) is studied by using a multiple-relaxation-time lattice Boltzmann (LB) multiphase model. The effect of the Reynolds number on the interfacial dynamics and bubble and spike amplitudes at late time is investigated in detail. The numerical results show that at sufficiently large Reynolds numbers, a sequence of stages in the 3D immiscible RTI can be observed, which includes the linear growth, terminal velocity growth, reacceleration, and chaotic development stages. At late stage, the RTI induces a very complicated topology structure of the interface, and an abundance of dissociative drops are also observed in the system. The bubble and spike velocities at late stage are unstable and their values have exceeded the predictions of the potential flow theory [V. N. Goncharov, Phys. Rev. Lett. 88, 134502 (2002)]. The acceleration of the bubble front is also measured and it is found that the normalized acceleration at late time fluctuates around a constant value of 0.16. When the Reynolds number is reduced to small values, some later stages cannot be reached sequentially. The interface becomes relatively smoothed and the bubble velocity at late time is approximate to a constant value, which coincides with the results of the extended Layzer model [S.-I. Sohn, Phys. Rev. E 80, 055302(R) (2009)] and the modified potential theory [R. Banerjee, L. Mandal, S. Roy, M. Khan, and M. R. Guptae, Phys. Plasmas 18, 022109 (2011)]. In our simulations, the Graphics Processing Unit (GPU) parallel computing is also used to relieve the massive computational cost.