Topological Concepts Research Articles

Effect of Compositions of MRT System Route Maps on Cognitive Mapping

Route maps, common in public transportation systems, refer to thematic maps drawn according to topological concepts. To simplify complex route information, a transport network is represented using primary graphic elements. First used in 1931 with topological concepts, the octilinear design has influenced the compositions of traffic route maps to this day. The current study involved cognitive mapping research on a representative route map in Taiwan: the Metro Taipei Route Map. Through two task experiments, this study analyzed users’ cognitive behavior when using the route map and alternative route map representations. The results indicated that the route map composed of all curves resulted in higher user performance than maps using a hybrid system and the conventional octilinear system. The route map based on the hybrid system, which included a route in the shape of a perfect circle, was highly evaluated and subjectively preferred by the users. Thus, the addition of appropriate curves in route maps is beneficial for improving usability, cognitive memory, and subjective evaluation. Finally, adding travel time information to a route map effectively enhances users’ decision-making during route planning.

A comparison of two types of rough approximations based on Nj-neighborhoods

In 1982, Pawlak proposed the concept of rough sets as a novel mathematical tool to address the issues of vagueness and uncertain knowledge. Topological concepts and results are close to the concepts and results in rough set theory; therefore, some researchers have investigated topological aspects and their applications in rough set theory. In this discussion, we study further properties of Nj-neighborhoods; especially, those are related to a topological space. Then, we define new kinds of approximation spaces and establish main properties. Finally, we make some comparisons of the approximations and accuracy measures introduced herein and their counterparts induced from interior and closure topological operators and E-neighborhoods.

Homeomorphism and Quotient Mappings in Infrasoft Topological Spaces

In this paper, we contribute to infrasoft topology which is one of the recent generalizations of soft topology. Firstly, we redefine the concept of soft mappings to be convenient for studying the topological concepts and notions in different soft structures. Then, we introduce the concepts of open, closed, and homeomorphism mappings in the content of infrasoft topology. We establish main properties and investigate the transmission of these concepts between infrasoft topology and its parametric infratopologies. Finally, we define a quotient infrasoft topology and infrasoft quotient mappings and study their main properties with the aid of illustrative examples.

Comparative Analysis Deferent Topologies for Photovoltaic Based Grid-Tied Transformerless Inverters

Transformerless inverters are widely used in grid-tied photovoltaic (PV) generation systems, due to the benefits of achieving high efficiency and low cost. Various transformer less inverter topologies have been proposed to meet the safety requirement of leakage currents. In this paper, a family of H6 transformer less inverter topologies with low leakage currents is proposed, and the intrinsic relationship between H5 topology, highly efficient and reliable inverter concept (HERIC) topology, and the proposed H6 topology has been discussed as well. One of the proposed H6 inverter topologies is taken as an example for detail analysis with operation modes and modulation strategy. The power losses and power device costs are compared among the H5, the HERIC, and the proposed H6 topologies. A universal prototype is built for these three topologies mentioned for evaluating their performances in terms of power efficiency and leakage currents characteristics. Experimental results show that the proposed H6 topology and the HERIC achieve similar performance in leakage currents, which is slightly worse than that of the H5 topology, but it features higher efficiency than that of H5 topology.

Review on Photovoltaic Based Grid-Tied System using H6 Transformer Less Full-Bridge Inverters

Transformer less inverters are widely used in grid-tied photovoltaic (PV) generation systems, due to the benefits of achieving high efficiency and low cost. Various transformer less inverter topologies have been proposed to meet the safety requirement of leakage currents, such as specified in the VDE-4105 standard. In this thesis, a family of H6 transformer less inverter topologies with low leakage currents is proposed, and the intrinsic relationship between H5 topology, highly efficient and reliable inverter concept (HERIC) topology, and the proposed H6 topology has been discussed as well. One of the proposed H6 inverter topologies is taken as an example for detail analysis with operation modes and modulation strategy. The power losses and power device costs are compared among the H5, the HERIC, and the proposed H6 topologies. A universal prototype is built for these three topologies mentioned for evaluating their performances in terms of power efficiency and leakage currents characteristics. Experimental results show that the proposed H6 topology and the HERIC achieve similar performance in leakage currents, which is slightly worse than that of the H5 topology, but it features higher efficiency than that of H5 topology.

Active topolectrical circuits

The transfer of topological concepts from the quantum world to classical mechanical and electronic systems has opened fundamentally different approaches to protected information transmission and wave guidance. A particularly promising emergent technology is based on recently discovered topolectrical circuits that achieve robust electric signal transduction by mimicking edge currents in quantum Hall systems. In parallel, modern active matter research has shown how autonomous units driven by internal energy reservoirs can spontaneously self-organize into collective coherent dynamics. Here, we unify key ideas from these two previously disparate fields to develop design principles for active topolectrical circuits (ATCs) that can self-excite topologically protected global signal patterns. Realizing autonomous active units through nonlinear Chua diode circuits, we theoretically predict and experimentally confirm the emergence of self-organized protected edge oscillations in one- and two-dimensional ATCs. The close agreement between theory, simulations, and experiments implies that nonlinear ATCs provide a robust and versatile platform for developing high-dimensional autonomous electrical circuits with topologically protected functionalities.

Topologically protected optical signal processing using parity–time-symmetric oscillation quenching

AbstractThe concept of topology is universally observed in various physical objects when the objects can be described by geometric structures. Although a representative example is the knotted geometry of wavefunctions in reciprocal space for quantum Hall family and topological insulators, topological states have also been defined for other physical quantities, such as topologically distinct Fermi surfaces and enhanced lattice degrees of freedom in hyperbolic geometry. Here, we investigate a different class of topological states – topological geometry of dynamical state trajectories – in non-Hermitian and nonlinear optical dynamics, revealing topologically protected oscillation quenching mechanisms determined by parity–time (PT) symmetry. For coupled systems composed of nonlinear gain and loss elements, we classify the topology of equilibria separately for unbroken and broken PT symmetry, which result in distinct oscillation quenching mechanisms: amplitude death and oscillation death. We then show that these PT-symmetric quenching mechanisms lead to immunity against temporal perturbations, enabling the applications of topologically protected laser modulation and rectification. The observed connection between the topological geometry of dynamical states, oscillation quenching phenomena in dynamical systems theory, and PT symmetry provides a powerful toolkit for noise-immune signal processing.

Design, Simulation and Optimization of an Electrical Drive-Train

Today, design engineers engaged in the development of a high-performance electrical drive-train are challenged by the multitude of possible topological choices and numerous mutually interconnected physical phenomena. Development teams around the globe struggle with this challenge; usually they employ several tools for simulation and topology optimization and transfer multiple versions of their product models in a mainly manual process. The research presented in this paper aims to explore a holistic possibility to realize a sensible analysis-synthesis cycle that takes into consideration current developments in design, simulation and optimization processes. This kind of process can enhance the transparency of design decisions, can reduce the risk of design and process flaws and can support the approach toward a holistic optimum. The investigation starts with the development of the topological concept of the drive-train and continues over the interconnected simulation of several decisive properties of the drive-train. Obviously, these properties concern several domains (mechanical, electrical, thermal and the control domain). The optimization of the drive-train takes into consideration the main requirement—in the investigated example, which is a formula student drive-train—the lap time. The result is a holistic concept for a design, simulation and optimization approach that considers topological variety, interconnected multi-domain simulation and a continuous connection to the decisive requirements.

Topological Photonics on Superconducting Quantum Circuits with Parametric Couplings

AbstractTopological phases of matter are an exotic phenomenon in modern condensed matter physics, which has attracted much attention due to the unique boundary states and transport properties. Recently, this topological concept in electronic materials has been exploited in many other fields of physics. Motivated by designing and controlling the behavior of electromagnetic waves in optical, microwave, and sound frequencies, topological photonics emerges as a rapid growing research field. Due to the flexibility and diversity of superconducting quantum circuits system, it is a promising platform to realize exotic topological phases of matter and to probe and explore topologically‐protected effects in new ways. Here, theoretical and experimental advances of topological photonics on superconducting quantum circuits—via the experimentally demonstrated parametric tunable coupling techniques, including using of the superconducting transmission line resonator, superconducting qubits, and their coupled system—are reviewed. On superconducting circuits, the flexible interactions and intrinsic nonlinearity make topological photonics in this system not only a simple photonic analog of topological effects for novel devices, but also a realm of exotic but less‐explored fundamental physics.

Connectedness and Local Connectedness on Infra Soft Topological Spaces

This year, we introduced the concept of infra soft topology as a new generalization of soft topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We provide some descriptions for infra soft connectedness and elucidate that there is no relationship between an infra soft topological space and its parametric infra topological spaces with respect to the property of infra soft connectedness. We discuss the behaviors of infra soft connected and infra soft locally connected spaces under infra soft homeomorphism maps and a finite product of soft spaces. We complete this manuscript by defining a component of a soft point and establishing its main properties. We determine the conditions under which the number of components is finite or countable, and we discuss under what conditions the infra soft connected subsets are components.

Coexistence of zero-, one-, and two-dimensional degeneracy in tetragonal SnO2 phonons

Based on the dimension of degeneracy, topological electronic systems can roughly be divided into three parts: nodal point, line and surface materials corresponding to zero-, one- and two-dimensional degeneracy, respectively. In parallel to electronic systems, the concept of topology was extended to phonons, promoting the birth of topological phonons. Till date, few nodal point, line and surface phonons candidates have been predicted in solid-state materials. In this study, based on symmetry analysis and first-principles calculation, for the first time, we prove that zero-, one- and two-dimensional degeneracy co-exist in the phonon dispersion of one single realistic solid-state material SnO$_2$ with \textit{P}4$_2$/\textit{mnm} structure. In contrast to the previously reported electronic systems, the topological phonons observed in SnO$_2$ are not restricted by the Pauli exclusion principle, and they experience negligible spin-orbit coupling effect. Hence, SnO$_2$ with multiple dimensions of degeneracy phonons is a good platform for studying the entanglement among nodal point, line and surface phonons. Moreover, obvious phonon surface states are visible, which is beneficial for experimental detection.

Infra Soft Compact Spaces and Application to Fixed Point Theorem

Infra soft topology is one of the recent generalizations of soft topology which is closed under finite intersection. Herein, we contribute to this structure by presenting two kinds of soft covering properties, namely, infra soft compact and infra soft Lindelöf spaces. We describe them using a family of infra soft closed sets and display their main properties. With the assistance of examples, we mention some classical topological properties that are invalid in the frame of infra soft topology and determine under which condition they are valid. We focus on studying the “transmission” of these concepts between infra soft topology and classical infra topology which helps us to discover the behaviours of these concepts in infra soft topology using their counterparts in classical infra topology and vice versa. Among the obtained results, these concepts are closed under infra soft homeomorphisms and finite product of soft spaces. Finally, we introduce the concept of fixed soft points and reveal main characterizations, especially those induced from infra soft compact spaces.

Artificial bee colony algorithm based on multiple neighborhood topologies

In recent years, as an effective global optimization technique, artificial bee colony (ABC) algorithm has attracted increasing attention for its good performance yet easy implementation. However, the solution search equation of ABC emphasizes exploration over exploitation, which greatly affects the convergence speed and accuracy of ABC. To solve this problem, many ABC variants have been developed to enhance exploitation by using the superior individuals. However, the concept of neighborhood topology has rarely been considered, which has significant effect on the dissemination of search information among individuals. Hence, in this work, we propose a new ABC variant based on multiple neighborhood topologies (named ABC-MNT). In ABC-MNT, three kinds of neighborhood topologies are used for different individuals to perform diverse abilities of disseminating search information, contributing to a better balance between exploration and exploitation. Considering the characteristics of different neighborhood topologies, three modified solution search equations are assigned to the three neighborhood topologies, respectively, to generate offspring. Furthermore, to preserve search experience of the scout bee phase, the global neighborhood search and opposition-based learning techniques are used. Extensive experiments are carried out on two widely used test suites, and eight well-established ABC variants and five other evolutionary algorithms are included in the performance comparison. The comparison results verify that ABC-MNT can obtain better or at least comparable performance on most of the benchmark functions.

New Soft Structure: Infra Soft Topological Spaces

It is always convenient to find the weakest conditions that preserve some topologically inspired properties. To this end, we introduce the concept of an infra soft topology which is a collection of subsets that extend the concept of soft topology by dispensing with the postulate that the collection is closed under arbitrary unions. We study the basic concepts of infra soft topological spaces such as infra soft open and infra soft closed sets, infra soft interior and infra soft closure operators, and infra soft limit and infra soft boundary points of a soft set. We reveal the main properties of these concepts with the help of some elucidative examples. Then, we present some methods to generate infra soft topologies such as infra soft neighbourhood systems, basis of infra soft topology, and infra soft relative topology. We also investigate how we initiate an infra soft topology from crisp infra topologies. In the end, we explore the concept of continuity between infra soft topological spaces and determine the conditions under which the continuity is preserved between infra soft topological space and its parametric infra topological spaces.

Deterministic sampling from uniform distributions with Sierpiński space-filling curves

In this paper the problem of sampling from uniform probability distributions is approached by means of space-filling curves, a topological concept that has found a number of important applications in recent years. Departing from the theoretical fact that they are surjective but not necessarily injective, the investigation focused upon the structure of the distributions obtained when their domains are swept in a uniform and discrete manner, and the corresponding values used to build histograms, that are approximations of their true PDFs. This work concentrates on the real interval [0,1] and the Sierpiński space-filling curve was chosen because of its favorable computational properties. In order to validate the results, the Kullback–Leibler and other divergence measures are used when comparing the obtained distributions in several levels of granularity with other already established sampling methods. In truth, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. In this fashion, sequences resulting from this sort of process are not truly random. Despite this, and to be coherent with the literature, the expression “random number” will be used along the text to mean “pseudo-random number”.

Inverse design of indoor radiant terminal using the particle swarm optimization method with topology concept

Radiant air conditioning system could create thermal comfortable and energy saving indoor environment. However, previous studies indicated that the design scheme, such as the area, geometry, and installation position, of the radiant terminals have significant effects on indoor thermal environment. That is because the current radiant terminal design method is a trial-and-errors process, and this time-consuming method is very difficult to achieve the optimal design. To fix that problem, this study tried to develop an efficient inverse design method, the particle swarm optimization (PSO) method combined with the topology optimization, which can inversely identify the area, geometry, and installation position of the modularity radiant terminal based on the requirements. This investigation also explored the impact of some key factors on the inverse design results and finally the proposed method was used to design modularity radiant terminals for a multi-occupant's office. The results indicated that the proposed PSO method with the topology optimization could help with the design of high energy-efficiency radiant air conditioning system and the inversely identified modularity radiant terminal could create thermally comfort indoor environment.

Impact of Fracture Geometry and Topology on the Connectivity and Flow Properties of Stochastic Fracture Networks

AbstractIn a low permeability formation, connectivity of natural and induced fractures determines overall hydraulic diffusivity in fluid flow through this formation and defines effective rock permeability. Efficient evaluation of fracture connectivity is a nontrivial task. Here, we utilize a topological concept of global efficiency to evaluate this connectivity. We address the impact of key geometrical properties of stochastic fracture networks (fracture lengths, orientations, apertures, and positions of fracture centers) on the macro‐scale flow properties of a shale‐like formation. Six thousand different realizations have been generated to characterize these properties for each fracture network. We find that a reduced graph of a fracture network, which consists of the shortest paths from the inlet nodes (fractures) to all outlet nodes, contributes most to fluid flow. Three‐dimensional (3D) fracture networks usually have higher global efficiency than two‐dimensional (2D) ones, because they have better connectivity. All geometrical properties of fractures influence quality of their connectivity. Aperture distribution impacts strongly global efficiency of a fracture network and its influence is more significant when the system is dominated by large fractures. Fracture clustering lowers global efficiency in both 2D and 3D fracture networks. Global efficiency of 2D and 3D fracture networks also decreases with the increasing exponent of the power‐law distribution of fracture lengths, which means that the connectivity of the system decreases with an increasing number of small fractures. Realistic fracture networks, composed of several sets of fractures with constrained preferred orientations, share all the characteristics of the stochastic fracture networks we have investigated.

Isotropic topological second-order spatial differentiator operating in transmission mode.

Differentiation has widespread applications, particularly in image processing for edge detection. Significant advances have been made in using nanophotonic structures and metamaterials to perform such operations. In particular, a recent work demonstrated a topological differentiator in which the transfer function exhibited a topological charge, making the differentiation operation robust to variations in operating conditions. The demonstrated topological differentiator, however, operates in reflection mode at off-normal incidence and is difficult to integrate into compact imaging systems. In this work, we design a topological differentiator that operates isotropically in transmission mode at normal incidence. The device exhibits an optical transfer function with a symmetry-protected topological charge of ±2 and performs second-order differentiation. Our work points to the potential of harnessing topological concepts for optical computing applications.

Unprecedented pressure-driven metallization and topological charge transport in an anion radical salt

The hybrid inorganic/organic closed π-stacking and soft lattice of a copper anion radial (Copper-7,7,8,8-tetracyanoquinodimethane) renders its electrical conductivity and structural modifications, which are susceptible to temperature and pressure. The geometry of its metal-ligand construction contemplates the concept of topology with a charge-transfer instability. A pressure-induced ionic-neutral phase transition occurs and accompanies an anomalously large electrical conductivity, carries topological charges, and possesses a low energy gap smaller than the Coulomb gap. X-ray absorption spectroscopy of the metal establishes the high electrical conduction by the topological charges. X-ray diffraction and the first-principles calculations further suggest that the compression leads to an irreversible alteration in the metal coordination and rotation of the quinoid rings of the anion. The present observation demonstrates a close coupling of topological charges and lattice dynamics within a relatively low-pressure regime, which may expand a novel paradigm for the comprehensive topological charge transport phenomena including thermoelectric effects in future.

Availability-Based Selection of Electricity Delivery Network in Marine Conversion Systems Using Bayesian Network

Availability is an economically important metric used to assess the design of marine energy farms. Nowadays, three typical concepts of energy delivery network topologies have been proposed for marine energy conversion systems. Few research works assessing the availability of marine energy conversion systems have been published. Their methodology is only based upon time-consuming Monte Carlo simulations and only covers one maintenance strategy. The objective of this study is to consider different maintenance strategies and quantitatively assess the time-dependent availability of these typical energy delivery network topologies by investigating the working philosophy of these topologies and modelling the logic dependencies of them in a Bayesian network (BN). The working philosophy of each topology is investigated to obtain the logic dependencies of the units in the energy delivery network, by means of qualitative system analysis. A table-like data structure, called hierarchy, is introduced to store the information on the logic dependencies and serves as a basis for establishing the corresponding BN models. A logic gate in the hierarchy can be represented by a conditional probability table in the BN model. The availability of these topologies, as a function of time, can be estimated through the BN models. The optimal topology can be selected, based upon the time-dependent availability.