Electrical Circuit Network Research Articles

Hyperbolic Lattices and Two-Dimensional Yang-Mills Theory.

Hyperbolic lattices are a new type of synthetic quantum matter emulated in circuit quantum electrodynamics and electric-circuit networks, where particles coherently hop on a discrete tessellation of two-dimensional negatively curved space. While real-space methods and a reciprocal-space hyperbolic band theory have been recently proposed to analyze the energy spectra of those systems, discrepancies between the two sets of approaches remain. In this work, we reconcile those approaches by first establishing an equivalence between hyperbolic band theory and U(N) topological Yang-Mills theory on higher-genus Riemann surfaces. We then show that moments of the density of states of hyperbolic tight-binding models correspond to expectation values of Wilson loops in the quantum gauge theory and become exact in the large-N limit.

Human mobility description by physical analogy of electric circuit network based on GPS data

Human mobility in an urban area is complicated; the origins, destinations, and transportation modes of each person differ. The quantitative description of urban human mobility has recently attracted the attention of researchers, and it highly related to urban science problems. Herein, combined with physics inspiration, we introduce a revised electric circuit model (RECM) in which moving people are regarded as charged particles and analogical concepts of electromagnetism such as human conductivity and human potential enable us to capture the characteristics of urban human mobility. We introduce the unit system, ensure the uniqueness of the calculation result, and reduce the computation cost of the algorithm to 1/10,000 compared with the original ECM, making the model more universal and easier to use. We compared features including human conductivity and potential between different major cities in Japan to show our improvement of the universality and the application range of the model. Furthermore, based on inspiration of physics, we propose a route generation model (RGM) to simulate a human flow pattern that automatically determines suitable routes between a given origin and destination as a source and sink, respectively. These discoveries are expected to lead to new approaches to the solution of urban science problems.

Three-dimensional non-Abelian Bloch oscillations and higher-order topological states

Recently, higher-order topological insulators (HOTIs) have been introduced, and were shown to host topological corner states under the theoretical framework of Benalcazar-Bernevig-Hughes. Here we unveil some topological effects in HOTIs by studying the three-dimensional (3D) non-Abelian Bloch oscillations (BOs). In HOTIs, BOs with a multiplied period occur when a force with a special direction is applied due to the effect of the non-Abelian Berry curvature. Along the direction of the oscillations we find a higher-order topological state that goes beyond the theoretical framework of multipole moments. The emergence of such a higher-order topological state coincides with the appearance of the 3D non-Abelian BOs. That is, the 3D non-Abelian BOs can be used as a tool to probe higher-order topological states. These phenomena are observed experimentally with designed electric circuit networks. Our work opens up a way to detect topological phases theoretically and experimentally.

Electrical circuit realization of topological switching for the non-Hermitian skin effect

Non-Hermitian systems reveal rich physics beyond the Hermitian regime, and have aroused great interest. One remarkable physical phenomenon is the non-Hermitian skin effect. Recently, topological switching for the non-Hermitian skin effect has been theoretically proposed in cold-atom systems. However, experimental realization of such a phenomenon remains a great challenge. Here, we theoretically propose and experimentally demonstrate a topological switch for the non-Hermitian skin effect in electrical circuit networks. By controlling the operational amplifier and other electric components, the nonreciprocal transport of probability for electrical signals is observed when the switch is turned on. Furthermore, the robustness of such a topological switch is demonstrated both theoretically and experimentally when perturbations are added. Our study provides an avenue for controlling electrical signals in circuit networks, with potential applications in the field of integrated circuit design.

Observation of flat-band localization and topological edge states induced by effective strong interactions in electrical circuit networks

Flat-band topologies and localizations in noninteracting systems are extensively studied in different quantum and classical-wave systems. Recently, the exploration on the novel physics of flat-band localizations and topologies in interacting systems has aroused great interest. In particular, it is theoretically shown that the strong interaction could drive the formation of nontrivial topological flat bands; even dispersive trivial bands dominate the single-particle counterparts. However, the experimental observation of those interesting phenomena is still lacking. Here, we experimentally simulate the interaction-induced flat-band localizations and topological edge states in electrical circuit networks. We directly map the eigenstates of two correlated bosons in one-dimensional Aharonov-Bohm cages to modes of two-dimensional circuit lattices. In this case, by tuning the effective interaction strength through circuits' groundings, the two-boson flat bands and topological edge states are detected by measuring frequency-dependent impedance responses and voltage dynamics in the time domain. Our finding suggests a flexible platform to simulate the interaction-induced flat-band topology, and may possess potential applications in designing novel electronic devices.

A power consensus controller with overvoltage protection for meshed DC microgrids

A novel distributed power consensus control approach with overvoltage protection is proposed and analysed for meshed direct current (DC) microgrids (MGs) with constant power loads (CPLs). The DC MG considered herein consists of source and load nodes connected over an undirected weighted graph induced by the electrical circuit network, namely the conductance matrix. When deploying, the proposed controller features a second graph, that models the communication network over which the source nodes exchange information such as the instantaneous powers, and which is used to adjust the power injection accordingly to achieve power sharing. Additionally, one aims to maintain the voltage at each source below operator-set limits. This feature is critical given the power and voltage dependency. By addressing the occurrence of abnormal voltage values at different nodes in the network, one would guarantee a relatively safer power consensus policy and microgrid operation. To accommodate both objectives, we developed a nonlinear power consensus-based control system, with a voltage-limiting component, by means of Lyapunov analysis and ultimate boundedness theory. Asymptotic closed-loop stability is also established around a set of equilibria. Finally, numerical simulations align with and validate our theoretical findings.

Dissipativity, Reciprocity, and Passive Network Synthesis: From the Seminal Dissipative Dynamical Systems Articles of Jan Willems to The Present Day

The dissipativity concept sits at the intersection of physics, systems theory, and control engineering as a natural generalization of passive systems that dissipate energy. It relates the external behavior of systems to their internal state and connects the subjects of optimal control, algebraic Riccati equations, linear matrix inequalities, complex functions, and spectral factorization. Within control, its applications include the analysis and design of interconnected systems (such as cyberphysical systems), robustness, and the absolute stability problem as well as network synthesis (of electrical, mechanical, and multiphysics systems). Dissipativity emerged as a stand-alone concept following the seminal “Dissipative Dynamical Systems” articles of Jan Willems, which drew on the work of Kalman, Youla, Anderson, Yakubovich, Popov, and others. This article details recent developments in the treatment of dissipativity and the related concept of reciprocity for systems that are not necessarily controllable and need not lend themselves naturally to an input–state–output perspective, as is the case for many physical and passive systems. We illustrate these concepts using simple electric circuit and mechanical network examples. We also draw inspiration from the behavioral theory developed by Jan Willems and collaborators, a natural formalism for analyzing physical systems that need not be controllable and characterized in terms of inputs and outputs.

Effect of Different Types of Electric Drive Units on the Energy Consumption of Heavy Commercial Electric Vehicles

The increasing demand for electric vehicles (EVs) in the transportation industry, especially for efficient battery–electric trucks, has led to an increase in studies on the efficiency or energy consumption of commercial vehicles. In this paper, average energy consumption was investigated in terms of the effect of different transmission types in vehicle models considering three routes, and the effect of the number of gears on energy consumption for each transmission type was analyzed. Target performance specifications and packaging were also evaluated. The optimal design could be identified in terms of transmission type, the number of gears, vehicle performance, and packaging. Vehicle models with two types of electric drive units (EDUs) were developed in a MATLAB/Simulink environment. Driving cycles were obtained from collected road load data of municipal, intercity, and regional areas operated by heavy-duty trucks using nCode software. The battery model was developed based on the electric circuit network (ECN) modeling technique. The main research purpose of this study was to investigate the effect of multispeed and multimodal EDUs and the number of gears on the energy consumption of heavy commercial electric vehicles from actual road conditions in Turkey. The three-speed EDU was the optimal design, providing 7.83, 7.26, and 7.21% less energy consumption on the three routes, compared with three-mode electric drive units. Consequently, the energy consumption difference was 7.5% for combined real road conditions.

Constant intensity discrete diffraction in anti-PT-symmetric electric circuits

We theoretically investigate the time-domain dynamics in a non-Hermitian electric circuit network with anti-parity-time (anti-PT) symmetry, which is consisted of amplified resonant LRC circuits connected by resistors. The effective coupling strength and on-site potential can be flexibly tuned via controlling the resistance value and resonant frequencies of LRC circuits, respectively. Therein, we are able to realize all three symmetry phases of the system, including anti-PT symmetric, intermediate, and broken phases, which are distinguished from their band structures. We show the time evolution of the envelope of voltage is analogous to discrete diffraction as a single injection stimulates more and more channels over time. Specifically, the system exhibits constant intensity diffraction at the boundary between intermediate and broken phases as the voltages at different channels are of the same value during the evolution. The reason lies in the dispersionless band structure near exceptional points (EPs) and the related linear energy amplification. The results enrich the study of discrete diffraction and are helpful to further exploration of topological phenomena in anti-PT-symmetric systems.

Topological Defect Engineering and PT Symmetry in Non-Hermitian Electrical Circuits.

We employ electric circuit networks to study topological states of matter in non-Hermitian systems enriched by parity-time symmetry PT and chiral symmetry anti-PT (APT). The topological structure manifests itself in the complex admittance bands which yields excellent measurability and signal to noise ratio. We analyze the impact of PT-symmetric gain and loss on localized edge and defect states in a non-Hermitian Su-Schrieffer-Heeger (SSH) circuit. We realize all three symmetry phases of the system, including the APT-symmetric regime that occurs at large gain and loss. We measure the admittance spectrum and eigenstates for arbitrary boundary conditions, which allows us to resolve not only topological edge states, but also a novel PT-symmetric Z_{2} invariant of the bulk. We discover the distinct properties of topological edge states and defect states in the phase diagram. In the regime that is not PT symmetric, the topological defect state disappears and only reemerges when APT symmetry is reached, while the topological edge states always prevail and only experience a shift in eigenvalue. Our findings unveil a future route for topological defect engineering and tuning in non-Hermitian systems of arbitrary dimension.

Analysis of a rectangular prism n-units RLC fractional-order circuit network

It was demonstrated recently that ideal capacitors can not exist physically and that the behavior of real-world inductors and capacitors is characterized by fractional-order (FO) models. Therefore, the modeling and analysis of FO electrical circuit networks (FO-ECN) has gained considerable interest. This paper introduces the basic principles of a class of rectangular prism n-units (♢×n) RLC FO-ECN, including the mathematical modeling and the analysis of the impedance magnitude and phase. Three general formulas of the equivalent impedance between two nodes of the FO-ECN are obtained by the matrix transform method. The relationship between the impedance and the FO-ECN parameters, including the capacitance, inductance, number of circuit units and FO are investigated. Numerical simulations reveal dynamical phenomena not exhibited by ordinary ECN.

Chern insulators for electromagnetic waves in electrical circuit networks

Periodic networks composed of capacitors and inductors have been demonstrated to possess topological properties with respect to incident electromagnetic waves. Here, we develop an analogy between the mathematical description of waves propagating in such networks and models of Majorana fermions hopping on a lattice. Using this analogy we propose simple electrical network architectures that realize Chern insulating phases for electromagnetic waves. Such Chern insulating networks have a bulk gap for a range of signal frequencies that is easily tunable and exhibit topologically protected chiral edge modes that traverse the gap and are robust to perturbations. The requisite time reversal symmetry breaking is achieved by including a class of weakly dissipative Hall resistor elements whose physical implementation we describe in detail.

The wave concept iterative process (WCIP) method for electrical circuit network with triangular and hexagonal topology

SummaryThis paper deals with an RLC circuit network with triangular or hexagonal grid. It is about a planar equilateral triangular grid where the passive (resistor, capacitor, and inductor) or active (voltage source for example) components are located at the sides or/and at nodes attached to the ground. The planar graph is oriented by three main direction vectors phase shifted to 60° degrees. The wave concept iterative process (WCIP) method was employed to the theoretical formulation of the problem. In the formulation, the potential difference across each circuit component is represented by an auxiliary source defined in the spectral domain. The proposed theory is developed into two definition domains: a spectral domain in which periodicity and coupling between the circuit components are defined and a spatial domain describing the network topology and imposing the continuities conditions (Kirchhoff laws). The transition between the spectral and spatial domain is ensured by the so‐called fast hexagonal Fourier transform. Numerical applications demonstrate the ability of the method for solving the inhomogeneous triangular lattices. Various conceptions have been proposed including an RL, RC, and RLC triangular network circuit, a perturbed triangular RLC circuit, and a triangular circuit excited by many lumped sources.

Band structure engineering and reconstruction in electric circuit networks

We develop an approach to design, engineer, and measure band structures in a synthetic crystal composed of electric circuit elements. Starting from the nodal analysis of a circuit lattice in terms of currents and voltages, our Laplacian formalism for synthetic matter allows us to investigate arbitrary tight-binding models in terms of wave number resolved Laplacian eigenmodes, yielding an admittance band structure of the circuit. For illustration, we model and measure a honeycomb circuit featuring a Dirac cone admittance bulk dispersion as well as flat band admittance edge modes at its bearded and zigzag terminations. We further employ our circuit band analysis to measure a topological phase transition in the topolectrical Su-Schrieffer-Heeger circuit.

Numerical Analysis for Promoting Uniform Development of Simultaneous Multiple-Fracture Propagation in Horizontal Wells

Summary Multistage hydraulic fracturing, together with horizontal drilling, plays an important role in the economic development of unconventional reservoirs. However, according to field analysis of stimulation effectiveness, only a small percentage of perforation clusters contribute to most of the well production. One reason for this low effectiveness is that multiple fractures do not take the same amount of fluid and proppant because of the interaction between hydraulic fractures (i.e., stress-shadow effects). Unfortunately, how best to minimize the negative effects of stress shadowing is still not fully understood in the petroleum industry. In this paper, we analyze this problem to promote more-uniform fracture growth by use of a complex hydraulic-fracture-development model. We use our fracture-propagation model, which couples rock deformation and fluid flow in the fracture and horizontal wellbore. The model assumes homogeneous linear-elastic rock medium and does not consider proppant transport in multiple fractures. Partitioning of flow rate between multiple fractures is calculated by use of the principles of flow through an electric-circuit network. Fracture development is dominated by flow-rate distribution, which is controlled by flow resistance within the fractures. For simultaneous multiple-fracture propagation, nonuniform flow-rate distribution is induced because stress-shadow effects exert additional flow resistance on the interior fractures. To balance the extra resistance introduced by the effects, we investigated two adjustment approaches to promote uniform fracture development. The first approach was to adjust perforation number or diameter to increase flow resistance entering the exterior fractures. The second was to mitigate stress-shadow effects through management of nonuniform fracture spacing. We found that decreasing perforation diameter or the number of exterior fractures can divert fluid into the interior fractures and promote even fracture growth. Stress-shadow effects can be mitigated by moving the two interior fractures away from each other and toward the exterior fractures. The key mechanism is to maintain even flow resistance within each fracture and facilitate fractures to obtain the same amount of injection fluid. Furthermore, flow resistance is affected by near-wellbore fracture tortuosity, natural fractures, and stress heterogeneity in the reservoirs. These factors might also be effectively controlled by adding extra flow resistance to pass perforations, provided that this extra resistance is larger than the extra resistance introduced by the factors. This work analyzes the problem of uneven development of multiple fractures along the horizontal wellbore and provides new insights into how to control simultaneous multiple-fracture propagation. It offers potential approaches for engineers to apply in the field to optimize hydraulic-fracturing-treatment design, thereby maximizing well production cost-effectively.

Lightning-Induced Magnetic Field Distribution on Cable-Stayed Bridge Based on Modified Equivalent Circuit Method

In order to protect sensitive devices on the cable-stayed bridge against the effects of lightning electromagnetic pulse, detailed information about the lightning currents and the radiated electromagnetic fields are necessary. For this purpose, a modified equivalent electric circuit method is presented for evaluating the electromagnetic environment on a cable-stayed bridge during direct lightning strikes. The stayed cables of the bridge are modeled as cascade polylines to transform the internal metallic structure of the bridge into an equivalent electrical circuit network. Taking a bridge for example, the current distribution and the lightning-induced magnetic field distribution are calculated based on the proposed method. The guidelines for the protection of sensitive electrical and electronic equipment against lightning are provided.

Comparison of Methods for Permanent Magnet Eddy-Current Loss Computations With and Without Reaction Field Considerations in Axial Flux PMSM

This paper presents an analytical solution of the eddy currents in the permanent magnets (PMs) in the axial flux PM synchronous machine using a coupled solution of Maxwell’s equations and electric circuit network. This is based on calculating the axial field in an accurate way on the surface of the PM. This method is able to consider the effect of armature field and slots. The eddy currents are obtained by imposing this solution on the PM which is modeled by a simple electric network. This network is composed of simple resistances and inductances. The inductances are used to model the reaction field effect of the eddy currents flowing through the PM and also the skin effect. To show this effect, the machine is excited with different sources at different speeds. In addition, a variant of the model is made that neglects the inductances, in order to show in which conditions this low-frequency approximation is acceptable. It is concluded from this paper that inclusion of the reaction field is necessary when the machine is excited by a pulsewidth modulated (PWM) current, while for a sinusoidal excitation, the reaction field effect has minor contributions to the total eddy losses. In addition, the reaction field has major influence at higher speeds rather than lower speeds for PWM injection. In conclusions, for a preliminary design, the resistance model without the reaction field computation would be enough for the calculation of the PM losses. The circuit model is also capable of obtaining the solution with PM segmentation. In this paper, different PM segments were studied from the circuit model and the finite-element (FE) model point of view. Compared with the FE model, the circuit model has the advantage of flexibility in geometrical machine parameters, less CPU time, and accurate results for the PM losses up to 10%.

Identifying and characterizing key nodes among communities based on electrical-circuit networks.

Complex networks with community structures are ubiquitous in the real world. Despite many approaches developed for detecting communities, we continue to lack tools for identifying overlapping and bridging nodes that play crucial roles in the interactions and communications among communities in complex networks. Here we develop an algorithm based on the local flow conservation to effectively and efficiently identify and distinguish the two types of nodes. Our method is applicable in both undirected and directed networks without a priori knowledge of the community structure. Our method bypasses the extremely challenging problem of partitioning communities in the presence of overlapping nodes that may belong to multiple communities. Due to the fact that overlapping and bridging nodes are of paramount importance in maintaining the function of many social and biological networks, our tools open new avenues towards understanding and controlling real complex networks with communities accompanied with the key nodes.

Correspondence between the one-loop three-point vertex and the Y and Δ electric resistor networks

Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent (LI) hypergeometric functions of two variables F4. This result is not physically acceptable when it is embedded in higher loops, because all four hypergeometric functions in the triangle result have the same region of convergence and further integration means going outside those regions of convergence. We could go outside those regions by using the well-known analytic continuation formulas obeyed by the F4, but there are at least two ways we can do this. Which is the correct one? Whichever continuation one uses, it reduces a number of F4 from four to three. This reduction in the number of hypergeometric functions can be understood by taking into account the fundamental physical constraint imposed by the conservation of momenta flowing along the three legs of the diagram. With this, the number of overall LI functions that enter the most general solution must reduce accordingly. It remains to determine which set of three LI solutions needs to be taken. To determine the exact structure and content of the analytic solution for the three-point function that can be embedded in higher loops, we use the analogy that exists between Feynman diagrams and electric circuit networks, in which the electric current flowing in the network plays the role of the momentum flowing in the lines of a Feynman diagram. This analogy is employed to define exactly which three out of the four hypergeometric functions are relevant to the analytic solution for the Feynman diagram. The analogy is built based on the equivalence between electric resistance circuit networks of types Y and Δ in which flows a conserved current. The equivalence is established via the theorem of minimum energy dissipation within circuits having these structures.

Application of network simulation method to viscous flows: The nanofluid heated lid cavity under pulsating flow

In this paper, the Network Simulation Method (NSM) is used to model an unsteady, viscous, flow problem: the heated lid-driven filled with nanofluid and in the presence of a pulsating flow. Through this method is analyzed the influence of the amplitude, wave number and oscillation frequency of sinusoidal velocity waves at the lid on the convection performance of the cavity. It is stated that this method is simple and efficient for solving unsteady, viscous, Navier–Stokes equations, through the design and resolution of an electrical circuit network whose equations are formally equivalent to the ones of the fluid flow problem. Results show that, for the case of Pr=3.93, Re=50, Ri=11.82, sinusoidal velocity waves at the lid increase the time-averaged Nusselt number in the cavity with respect to the non-pulsating case up to a 16%. This is due to enhancement of the transport phenomena induced by the pulsating flow.