Topological Description Research Articles

Connections Between Topology and Macroscopic Mechanical Properties of Three-Dimensional Open-Pore Materials

This work addresses a number of fundamental questions regarding the topological description of materials characterized by a highly porous three-dimensional structure with bending as the major deformation mechanism. Highly efficient finite-element beam models were used for generating data on the mechanical behavior of structures with different topologies, ranging from highly coordinated bcc to Gibson–Ashby structures. Random cutting enabled a continuous modification of average coordination numbers ranging from the maximum connectivity to the percolation-cluster transition of the 3D network. The computed macroscopic mechanical properties – Young’s modulus, yield strength, and Poisson’s ratio – combined with the cut fraction, average coordination number, and statistical information on the local coordination numbers formed a database consisting of more than 100 different structures. Via data mining, the interdependencies of topological parameters and relationships between topological parameters with mechanical properties were discovered. A scaled genus density could be identified, which assumes a linear dependency on the average coordination number. Feeding statistical information about the local coordination numbers of detectable junctions with coordination number of 3 and higher to an artificial neural network enables the determination the average coordination number without any knowledge of the fully connected structure. This parameter serves as a common key for determining the cut fraction, the scaled genus density, and the macroscopic mechanical properties. The dependencies of macroscopic Young’s modulus, yield strength, and Poisson’s ratio on the cut fraction (or average coordination number) could be represented as master curves, covering a large range of structures from a coordination number of 8 (bcc reference) to 1.5, close to the percolation-cluster transition. The suggested fit functions with a single adjustable parameter agree with the numerical data within a few percent error. Artificial neural networks allow a further reduction of the error by at least a factor of 2. All data for macroscopic Young’s modulus and yield strength are covered by a single master curve. This leads to the important conclusion that the relative loss of macroscopic strength due to pinching-off of ligaments corresponds to that of macroscopic Young’s modulus. Experimental data in literature support this unexpected finding.

Phase-field modeling of fracture for quasi-brittle materials

This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topology. Within the computational mechanics community, several studies have treated the issue of modeling fracture using phase fields. Most of these studies have used an approach that implies the lack of a damage threshold. We herein explore an alternative model that includes a damage threshold and study how it compares with the most popular approach. The formulation is systematically explained within a rigorous variational framework. Subsequently, we present the corresponding three-dimensional finite element discretization that leads to a straightforward numerical implementation. Benchmark simulations in two dimensions and three dimensions are then presented. The results show that while an elastic stage and a damage threshold are ensured by the present model, good agreement with the results reported in the literature can be obtained, where such features are generally absent.

Fractal Topological Analysis for 2D Binary Digital Images

Fractal dimension is a powerful tool employed as a measurement of geometric aspects. In this work we propose a method of topological fractal analysis for 2D binary digital images by using a graph-based topological model of them, called Homological Spanning Forest (HSF, for short). Defined at interpixel level, this set of two trees allows to topologically describe the (black and white) connected component distribution within the image with regards to the relationship “to be surrounded by”. This distribution is condensed into a rooted tree, such that its nodes are connected components determined by some special sub-trees of the previous HSF and the levels of the tree specify the degree of nesting of each connected component. We ask for topological auto-similarity by comparing this topological description of the whole image with a regular rooted tree pattern. Such an analysis can be used to directly quantify some characteristics of biomedical images (e.g. cells samples or clinical images) that are not so noticeable when using geometrical approaches.

The Head Turning Modulation System: An Active Multimodal Paradigm for Intrinsically Motivated Exploration of Unknown Environments.

Over the last 20 years, a significant part of the research in exploratory robotics partially switches from looking for the most efficient way of exploring an unknown environment to finding what could motivate a robot to autonomously explore it. Moreover, a growing literature focuses not only on the topological description of a space (dimensions, obstacles, usable paths, etc.) but rather on more semantic components, such as multimodal objects present in it. In the search of designing robots that behave autonomously by embedding life-long learning abilities, the inclusion of mechanisms of attention is of importance. Indeed, be it endogenous or exogenous, attention constitutes a form of intrinsic motivation for it can trigger motor command toward specific stimuli, thus leading to an exploration of the space. The Head Turning Modulation model presented in this paper is composed of two modules providing a robot with two different forms of intrinsic motivations leading to triggering head movements toward audiovisual sources appearing in unknown environments. First, the Dynamic Weighting module implements a motivation by the concept of Congruence, a concept defined as an adaptive form of semantic saliency specific for each explored environment. Then, the Multimodal Fusion and Inference module implements a motivation by the reduction of Uncertainty through a self-supervised online learning algorithm that can autonomously determine local consistencies. One of the novelty of the proposed model is to solely rely on semantic inputs (namely audio and visual labels the sources belong to), in opposition to the traditional analysis of the low-level characteristics of the perceived data. Another contribution is found in the way the exploration is exploited to actively learn the relationship between the visual and auditory modalities. Importantly, the robot—endowed with binocular vision, binaural audition and a rotating head—does not have access to prior information about the different environments it will explore. Consequently, it will have to learn in real-time what audiovisual objects are of “importance” in order to rotate its head toward them. Results presented in this paper have been obtained in simulated environments as well as with a real robot in realistic experimental conditions.

PyPSA-Eur: An open optimisation model of the European transmission system

PyPSA-Eur, the first open model dataset of the European power system at the transmission network level to cover the full ENTSO-E area, is presented. It contains 6001 lines (alternating current lines at and above 220 kV voltage level and all high voltage direct current lines), 3657 substations, a new open database of conventional power plants, time series for electrical demand and variable renewable generator availability, and geographic potentials for the expansion of wind and solar power. The model is suitable both for operational studies and generation and transmission expansion planning studies. The continental scope and highly resolved spatial scale enables a proper description of the long-range smoothing effects for renewable power generation and their varying resource availability. The restriction to freely available and open data encourages the open exchange of model data developments and eases the comparison of model results. A further novelty of the dataset is the publication of the full, automated software pipeline to assemble the load-flow-ready model from the original datasets, which enables easy replacement and improvement of the individual parts. This paper focuses on the description of the network topology, the compilation of a European power plant database and a top-down load time-series regionalisation. It summarises the derivation of renewable wind and solar availability time-series from re-analysis weather datasets and the estimation of renewable capacity potentials restricted by land-use. Finally, validations of the dataset are presented, including a new methodology to compare geo-referenced network datasets to one another.

Decomposition of electric machines with particular emphasis of the squirrel-cage induction motors

Most of the descriptions and definitions of systems are based on flow charts or block diagrams. Such representation generates difficulties related to the structure complexity. The basic obstacle arises from the fact of the arbitrary representation of elements with complex relationships. Each system can be, however, described by the graphical representation provided through diagraphs (so-called topological description). From the point of view of failure propagation, analyses based on undirected graphs are not useful. On the other hand, such notation allows for simplification of the definition and analysis of relationships of the subsystems. A more useful representation is formalized notation in the field of directed graphs, because it allows to determine the direction of propagation of failures between the subsystems and identification of structural dependencies (in the case of functional structures). In such case the author used the FMECA methodology assumes the participation of professionals, whose main task is to provide the assessment of the failure impact on system operation.

An explicit optimization model for integrated layout design of planar multi-component systems using moving morphable bars

Layout design of multi-component systems has received ever-increasing attention over recent years. However, most of the current literature on the layout design of multi-component systems conducted are all carried out in an implicit way. In this paper, an explicit optimization model based on the moving morphable bars method is proposed. To this aim, topology description functions are used to describe the geometrical shapes of embedded components, while moving bars act as supporting structure that connects these embedded components. Different from traditional optimization methods, the geometric parameters used to describe the size, shape, location and orientation of the moving bars and embedded components are considered as design variables in this work. To avoid remeshing the grids and improve the efficiency of computation, the moving bars and embedding components are mapped into two density fields on a fixed grid using a smoothed Heaviside function. A discrete material interpolation scheme developed for orientation optimization problem is extended for the first time to the material parameterization of multi-component systems. Moreover, a single explicit constraint based on the volume and perimeter of embedded components is proposed for avoiding overlaps between the embedded components, and between each component and the design domain boundary. Several numerical examples are performed to show the effectiveness and flexibility of the presented optimization model in handling layout optimization of structures with multi-phase embedded components.

Optimal design of passive RC-damped LCL filter for grid-connected voltage source inverters

In this paper, a new and efficient global optimization method known as teaching–learning-based optimization is adopted to optimally design the parameters of a passive RC-damped LCL filter for grid-connected voltage source inverters. The novel proposed objective function of the optimization algorithm is to minimize the values of inductors and capacitors. The proposed design improves inverter efficiency and minimizes filter stored energy at a predefined operating and switching frequencies. Moreover, the proposed design procedure may reduce the complexity of the passive RC-damped LCL filter by removing one inductor or one capacitor. The optimal design procedure is built based on an accurate mathematical model and description of the filter topology. A detailed comparison between the results of the proposed work and related work in the literature is thoroughly discussed. The optimized filter is designed, built, and validated analytically and experimentally for verification based on a hardware prototype.

Safety monitor for train‐centric CBTC system

Train-centric communications-based train control (TcCBTC) system is a new solution for urban transit signalling. Compared to traditional train control systems, the on-board equipment is becoming more powerful and more complex. Due to its safety-critical nature, specialised technologies must be adopted to guarantee the safety of the system. To address the safety verification difficulty of the control logic for the new system, this study presents an innovative topology-based method for guaranteeing the train control safety. First, a railway network is described as a metric space, and then, topological spaces are introduced to express the movement authority and train trajectory. On the basis of the topological description, the safety rules are checked by performing a series computation of topology theorems. Finally, a case study has been carried out on a real metro line in China. The result shows that the proposed method strictly meets the safety verification and achieves excellent performance.

Bacterial expression, purification and biophysical characterization of the smallest plant reticulon isoform, RTNLB13

Reticulons are a large family of integral membrane proteins that are ubiquitous in eukaryotes and play a key role in functional remodelling of the endoplasmic reticulum membrane. The reticulon family is especially large in plants, with the Arabidopsis thaliana genome containing twenty-one isoforms. Reticulons vary in length but all contain a conserved C-terminal reticulon homology domain (RHD) that associates with membranes. An understanding of the structure and membrane interactions of RHDs is key to unlocking their mechanism of function, however no three-dimensional structure has been solved. We believe that this is, in part, due to difficulties in obtaining reticulon proteins in yields sufficient for structural study. To address this, we report here the first bacterial overexpression, purification, and biophysical investigation of a reticulon protein from plants, the RTNLB13 protein from A. thaliana. RTNLB13 is the smallest plant reticulon and is made up of a single RHD. We used circular dichroism, SDS-PAGE and analytical ultracentrifugation to reveal that RTNLB13 is 45% α-helical in a number of detergent environments, monomeric at low concentrations, and capable of self-association at higher concentrations. We used solution-state NMR to screen the effect of detergent type on the fold of isotopically-enriched RTNLB13, and found that ∼60% of the expected protein peaks were broadened due to slow dynamics. This broadening points toward a large network of protein-membrane interactions throughout the sequence. We have interpreted our results in light of current literature and suggest a preliminary description of RTNLB13 structure and topology.

An Efficient Topology Description Function Method Based on Modified Sigmoid Function

Optimal geometries extracted from traditional element-based topology optimization outcomes usually have zigzag boundaries, leading to being difficult to fabricate. In this study, a fairly accurate and efficient topology description function method (TDFM) for topology optimization of linear elastic structures is developed. By employing the modified sigmoid function, a simple yet efficient strategy is presented to tackle the computational difficulties because of the nonsmoothness of Heaviside function in topology optimization problem. The optimization problem is to minimize the structural compliance, with highest stiffness, while satisfying the volume constraint. The design problem is solved by a Sequential Linear Programming method. Convergent, crisp, and smooth final layouts are obtained, which can be fabricated without postprocessing, demonstrated by a series of numerical examples. Further, the proposed method has a rather higher accuracy and efficiency compared with traditional TDFM, when the classical topology optimization methods, such as bidirectional evolutionary structural optimization (BESO) and solid isotropic material with penalization (SIMP) method, are taken as benchmark.

Communication: Molecular-level description of constrained chain topologies in multiblock copolymer gel networks.

Network characteristics in physical gels composed of solvated block copolymers varying in molecular design are examined here by dynamic rheology and computer simulations. In two triblock copolymer series, one with chain length (N) varied at constant copolymer composition (f) and the other with f varied at constant N, we discern the dependence of equilibrium network metrics on both N and f. Increasing the block number in a linear multiblock series at constant N and f escalates conformational complexity, which dominates network connectivity classified according to a midblock conformation index.

Spoof Plasmonics: From Metamaterial Concept to Topological Description.

Advances in metamaterials have offered the opportunity of engineering electromagnetic properties beyond the limits of natural materials. A typical example is "spoof" surface plasmon polaritons (SPPs), which mimic features of SPPs without penetrating into metal, but only with periodic corrugations on metal surfaces. They hold considerable promise in device applications from microwaves to the far infrared, where real SPP modes do not exist. The original spoof SPP concept is derived from the description of corrugated surfaces by a metamaterial that hosts an effective plasma frequency. Later, studies have attempted to describe spoof SPP modes with the band structure by strictly solving Maxwell's equations, which can possess band gaps from polaritonic anticrossing principle or Bragg interference. More recently, as inspired by the development of topological framework in condensed matter physics, the topological description of spoof SPPs is used to propose topologically protected waveguiding phenomena. Here, the developments of spoof SPPs from both practical and fundamental perspectives are reviewed.

A new isogeometric topology optimization using moving morphable components based on R-functions and collocation schemes

This paper presents a new isogeometric topology optimization (TO) method based on moving morphable components (MMC), where the R-functions are used to represent the topology description functions (TDF) to overcome the C1 discontinuity problem of the overlapping regions of components. Three new ersatz material models based on uniform, Gauss and Greville abscissae collocation schemes are used to represent both the Young’s modulus of material and the density field based on the Heaviside values of collocation points. Three benchmark examples are tested to evaluate the proposed method, where the collocation schemes are compared as well as the difference between isogeometric analysis (IGA) and finite element method (FEM). The results show that the convergence rate using R-functions has been improved in a range of 17%–60% for different cases in both FEM and IGA frameworks, and the Greville collocation scheme outperforms the other two schemes in the MMC-based TO.

Wake flow analysis and control on a 47° slant angle Ahmed body

PurposeThe purpose of this paper is to present numerical investigations of the flow dynamic characteristics of a 47° Ahmed Body to identify wake flow control strategy leading to drag coefficient reduction, which could be tested later on sport utility vehicles.Design/methodology/approachThis study begins with a mean flow topology description owing to dynamic and spectral analysis of the aerodynamic tensor. Then, the sparse promoting dynamic modal decomposition method is discussed and compared to other modal approaches. This method is then applied on the wall and wake pressure to determine frequencies of the highest energy pressure modes and their transfers to other frequency modes. This analysis is then used to design appropriated feedback flow control strategies.FindingsThis dynamic modal decomposition highlights a reduced number of modes at low frequency which drive the flow dynamics. The authors especially notice that the pressure mode at a Strouhal number of 0.22, based on the width between feet, induces aerodynamic losses close to the rear end. Strategy of the proposed control loop enables to dampen the energy of this mode, but it has been transferred to lower frequency mode outside of the selected region of interest.Originality/valueThis analysis and methodology of feedback control shows potential drag reduction with appropriated modal energy transfer management.

A variational approach to the phase field modeling of brittle and ductile fracture

The modeling of the post-critical behavior of materials is still a scientific challenge. This is especially true when dealing with materials that undergo complex behavior, in which several mechanisms are combined. This physical complexity is reflected in the mathematics and the numerics of this kind of problems. In this work, we study the modeling of brittle and ductile fracture. We adopt regularized kinematics based on a phase field description of the fracture topology. In order to ensure mathematical soundness, we use a rigorous variational framework for dissipative rate-independent materials. This framework allows to introduce several dissipative mechanisms in a straightforward and clear manner. For instance, gradients for both damage and plasticity are introduced. This implies the existence of two internal length scales that control the degree of ductility of the macroscopic fracture mechanism. A finite element discretization allows to test the possibilities of the proposed model to describe different fracture behaviors with several benchmark numerical experiments. In addition, the variational framework naturally leads to a robust staggered algorithm. Despite the simplicity of the numerical solution, different types of fracture processes can be described as particular cases: quasi-brittle, elasto-plastic brittle, and ductile.

Non-deterministic Effects in a Realizability Model

We model non-deterministic effects for Turing computability by working in the assemblies of Kleene's first partial combinatory algebra. Two methods will be discussed, one using equivalence relations on trees and one using topological descriptions of powerdomains. We describe these models for a selection of non-deterministic paradigms: angelic, demonic, convex and probabilistic. Though the first approach has a connection to traditional non-deterministic computability, the second approach works better for combining non-determinism with recursion. We establish morphisms from the tree models to the powerdomain models, which are bijective at ground type and give isomorphisms for all but the demonic case. We also see that any of the powerdomain models can be interpreted as a sub-monad of a continuation monad.

Bifurcations of Liouville tori of a two fixed center problem

A complete description of the real phase topology of a two fixed center problem is introduced and studied. Moreover, all generic bifurcations of Liouville tori are determined theoretically and the periodic solution is presented. At the end of this paper, the phase portrait is studied.

Fifth-Order T-Type Passive Resonant Tanks Tailored for Constant Current Resonant Converters

Fifth-order T-type resonant converter (RC) topologies for constant current applications are introduced in this paper. Immittance property in passive resonant tanks (PRTs) of the RCs is the key feature for realizing this purpose. In comparison with the lower order PRTs, the fifth-order topologies have more inherent current robustness against load variation, less sensitivity to the parameters variation and current gain tuning ability. At first, resonant networks qualifying the PRT conditions are specified with their topological superiorities description. Without loss of generality, 28 immittance PRTs (IPRTs) are detected as possible candidates that can be used as a voltage source to current source converter. In addition, their immittance operating conditions are analyzed mathematically. For prototyping, a topology has been selected and designed using a method based on minimization of the IPRT elements size. Moreover, closed-form expressions of the output current and voltage/current stresses on the reactive elements are derived and verified for selecting the elements value. The designed prototype is a 150-W constant current RC with tight load regulation ability. Experimental results show that the ZVS operation with low reactive power on the switches as well as minimum losses on the rectifier diodes are achieved in a wide range of load variations.

Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening.

This work introduces a number of algebraic topology approaches, including multi-component persistent homology, multi-level persistent homology, and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. In contrast to the conventional persistent homology, multi-component persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for protein-ligand binding analysis and virtual screening of small molecules. Extensive numerical experiments involving 4,414 protein-ligand complexes from the PDBBind database and 128,374 ligand-target and decoy-target pairs in the DUD database are performed to test respectively the scoring power and the discriminatory power of the proposed topological learning strategies. It is demonstrated that the present topological learning outperforms other existing methods in protein-ligand binding affinity prediction and ligand-decoy discrimination.