Three Dimensional Electric Circuits with Multiple Capacitors and Resistors

Two cubical 3D electric circuits with single and double capacitors and twelve ohmic resistors are considered. The resistors are the sides of the cube. The circuit is fed with a single internal emf. The charge on the capacitor(s) and the current distributions of all twelve sides of the circuit(s) vs. time are evaluated. The analysis requires solving twelve differential-algebraic intertwined symbolic equations. This is accomplished by applying a Computer Algebra System (CAS), specifically Mathematica. The needed codes are included. For a set of values assigned to the elements, the numeric results are depicted.

3D_Multi Resistor Electric Circuit

This report addresses the issues concerning the analysis of an electric circuit composed of multiple resistors configured in a 3-Dimension structure. Noting, all the standard textbooks of physics and engineering irrespective of the used components are circuits assembled in two dimensions. Here, by deviating from the “norm” we consider a case where the resistors are arranged in a 3D structure;e.g., a cube. Although, independent of the dimension of the design the same physics principles apply, transitioning from a 2D to a 3D makes the corresponding analysis considerably challenging. In general, with no exception, depending on the used components the analysis faces with solving a set of either algebraic or differential-algebraic equations. Practically, this interfaces with a Computer Algebra System (CAS). The main objective is symbolically to identify the current distributions and the equivalent resistor (s) of cubically assembled resistors.

Analyzing Electric Circuits with Computer Algebra

This report shows how starting from classic electric circuits embodying commonly electric components we have reached semi-complicated circuits embodying the same components that analyzing the signal characteristics requires a Computer Algebra System. Our approach distinguishes itself from the electrical engineers’ (EE) approach that relies on utilizing commercially available software. Our approach step-by-step shows how Kirchhoff’s rules are applied conducive to the needed circuit information. It is shown for the case at hand the characteristic information is a set of coupled differential equations and that with the help of Mathematica numeric solutions are sought. Our report paves the research road for unlimited creative similar circuits with any degree of complications. Occasionally, by tweaking the circuits we have addressed the “what if” scenarios widening the scope of the investigation. Justification of the accuracy of our analysis for the generalized circuits is cross-checked by arranging the components symmetrizing the circuit leading to an intuitively predictable reasonable result. Mathematica codes are embedded assisting the interested reader in producing and extending our results.

Seamlessly-integrated Textile Electric Circuit Enabled by Self-connecting Interwoven Points

Flexible,breathable and lightweight electronic textiles hold great promise to change the ways we intact with electronics.Electrical connections among functional components are indispensable for system integrations of electronic textiles.However,it remains challenging to achieve mechanically and electrically robust connections to fully integrate with interwoven architecture and weaving process of textiles.Here,we reported a seamlessly-integrated textile electric circuit by weaving conductive fibers with self-connecting capacity at the interwoven points.Selfconnecting conductive fibers(SCFs)were prepared by coating modified polyurethane conductive composites onto nylon fibers.Electrical connections were achieved at interwoven points in less than 5 s once the weft and warp SCFs were woven together,due to the designed dynamic bonds of aromatic disulfide metathesis and hydrogen bonds in the modified polyurethane(MPU).The self-connecting point was electrically stable(varied by less than 6.7%in electrical resistance)to withstand repeated deformations of bending,pressing and even folding.Such a selfconnecting strategy could be generalized to weave full-textile electronics capable of receiving signals and displaying with enhanced interfacial stability,offering a new way to unify fabrication of electronics and weaving of textiles.

Performance of beam-type piezoelectric vibration energy harvester based on ZnO film fabrication and improved energy harvesting circuit

We demonstrate a piezoelectric vibration energy harvester with the ZnO piezoelectric film and an improved synchronous electric charge extraction energy harvesting circuit on the basis of the beam-type mechanical structure,especially investigate its output performance in vibration harvesting and ability to generate charges.By establishing the theoretical model for each of vibration and circuit,the numerical results of voltage and power output are obtained.By fabricating the prototype of this harvester,the quality of the sputtered film is explored.Theoretical and experimental analyses are conducted in open-circuit and closed-circuit conditions,where the open-circuit mode refers to the voltage output in relation to the ZnO film and external excitation,and the power output of the closed-circuit mode is relevant to resistance.Experimental findings show good agreement with the theoretical ones,in the output tendency.It is observed that the properties of ZnO film achieve regularly direct proportion to output performance under different excitations.Furthermore,a maximum experimental power output of 4.5 mW in a resistance range of 3 kΩ-8 kΩis achieved by using an improved synchronous electric charge extraction circuit.The result is not only more than three times the power output of classic circuit,but also can broaden the resistance to a large range of 5 kΩunder an identical maximum value of power output.In this study we demonstrate the fundamental mechanism of piezoelectric materials under multiple conditions and take an example to show the methods of fabricating and testing the ZnO film.Furthermore,it may contribute to a novel energy harvesting circuit with high output performance.

Symmetric bursting behaviour in non-smooth Chua's circuit

The dynamics of a non-smooth electric circuit with an order gap between its parameters is investigated in this paper. Different types of symmetric bursting phenomena can be observed in numerical simulations. Their dynamical behaviours are discussed by means of slow-fast analysis. Furthermore, the generalized Jacobian matrix at the non-smooth boundaries is introduced to explore the bifurcation mechanism for the bursting solutions, which can also be used to account for the evolution of the complicated structures of the phase portraits. With the variation of the parameter, the periodic symmetric bursting can evolve into chaotic symmetric bursting via period-doubling bifurcation.

Border collision bifurcations in 3D piecewise smooth chaotic circuit

A variety of border collision bifurcations in a three-dimensional （3D） piecewise smooth chaotic electrical circuit are investigated. The existence and stability of the equilibrium points are analyzed. It is found that there are two kinds of non-smooth fold bifurcations. The existence of periodic orbits is also proved to show the occurrence of non-smooth Hopf bifurcations. As a composite of non-smooth fold and Hopf bifurcations, the multiple crossing bifurcation is studied by the generalized Jacobian matrix. Some interesting phenomena which cannot occur in smooth bifurcations are also considered.

A Comparative Study of Analytical Solutions to the Coupled Van-der-Pol’s Non-linear Circuits Using the He’s Method(HPEM)and(BPES)

In this paper, the He’s parameter-expanding method (HPEM) and the 4q-Boubaker Polynomials Expansion Scheme (BPES) are used in order to obtain analytical solutions to the non-linear modified Van der Pol’s oscillating circuit equation. The resolution protocols are applied to the ordinary Van der Pol equation, which annexed to conjoint delayed feedback and delay-related damping terms. The results are plotted, and compared with exact solutions proposed elsewhere, in order to evaluate accuracy.

Habitat Suitability &Connectivity of Alborz Wild Sheep in the East of Tehran, Iran

Habitat loss and fragmentation of the wildlife species due to anthropogenic developments have been becoming serious issues in biological conservation. Alborz wild sheep, listed as threatened by IUCN, is distributed in relatively small and isolated patches in an increasingly human dominated landscape in the north-central Iran and east of Tehran. We used maximum entropy modeling to identify habitat areas of the wild sheep, across Jajrud protected area and its neighbouring protected areas including varjin, lar, koohsefid and the surroundings. Regarding to seasonal variation of the species home range, winter, summer and multi seasonal (annual) habitats were predicted. To estimate habitat connectivity, we used models of connectivity based in electrical circuit theory. Applying core areas of multi season for connectivity analysis, movement pattern of the species was predicted and important connective areas for conservation were identified. Species distribution maps revealed that the summer and winter habitats were approximately occurred in similar areas. Distance to eco-guards’ post was the most important predictor for both habitat models of summer and winter. The annual model, which is a combination of summer and winter, shows that the largest suitable habitat patches are located in the north, south and west of the study area. Maximum current flow map demonstrates that the areas among patch pairs are covered in low current, reflecting low rates of the species dispersal. This map presented bottlenecks to the species movement across major roads and along extending human settlements. Cumulative current flow map displayed that current was highest in Jajrud north of Mamloo extending to the northern Jajrud. Overall, our study demonstrated a prediction of habitat suitability and connectivity for Alborz wild sheep in east of Tehran, which can be used to direct conservation endeavours dealing with maintenance of the wild sheep metapopulation dynamics.

Enhancement of Large Renewable Distributed Generation Penetration Levels at the Point of Common Coupling

The occurrence of distortion and over voltage at the Point of Common Coupling(PCC)of Renewable Distributed Generation(RDG)limits its penetration levels to the power system and the RDG integration is expected to play a crucial role in power system transformation.For its penetrations to be sustained without disconnection from the system,there must be a solution to the voltage rise,distortion,unbalanced current and grid reactive power control strategy at PCC.It is an IEEE-1547 requirement that RDG integration to the power system should be regulated at PCC to avoid disconnection from the network due to power quality criteria.RDG integration must meet up with this specification to uphold power quality and avoid damage to the sensitive equipment connected at PCC.In this paper,voltage rise,unbalanced current,reactive power and distortion are being managed at PCC while Distribution Network(DN)accepts more RDG penetration levels without violation of the IEEE and South Africa grid code act.Active Power Filter and Full Bridge Multi-Level Converter(FBMC)are considered to safeguard power quality to the grid,they are modelled in MATLAB/SIMULINK and the results obtained shown that the proposed strategy can successfully regulate voltage rise,distortion,unbalanced current and continuously improve power quality with RDG integration at PCC.The proposed method’s key innovation is the strategic generation and absorption of reactive power to curtain an overvoltage,reverse power flow,and distortion at the PCC,allowing more RDG penetration levels to the grid without disconnection while maintaining the standard requirement for power quality at the PCC.The simulation outcomes validate the superiority of the FBMC over the active power filter with respect of reactive power generation/absorption,dynamic response,and damping capability.

Modeling and Simulations in Symmetrical Supercapacitors Using Time Domain Mathematical Expressions

This study presents the deduction of time domain mathematical equations to simulate the curve of the charging process of a symmetrical electrochemical supercapacitor with activated carbon electrodes fed by a source of constant electric potential in time ε and the curve of the discharge process through two fixed resistors. The first resistor RCo is a control that aims to prevent sudden variations in the intensity of the electric current i1(t) present at the terminals of the electrochemical supercapacitor at the beginning of the charging process. The second resistor is the internal resistance RA of the ammeter used in the calculation of the intensity of the electric current i1(t) over time in the charging and discharging processes. The mathematical equations generated were based on a 2R(C + kUC(t)) electrical circuit model and allowed to simulate the effects of the potential-dependent capacitance (kUC(t)) on the charge and discharge curves and hence on the calculated values of the fixed capacitance C, the equivalent series resistance (ESR), the equivalent parallel resistance (EPR) and the electrical potential dependent capacitance index k.

Traveling chimera states in locally coupled memristive Hindmarsh-Rose neuronal networks and circuit simulation

Chimera states have been found in many physiology systems as well as nervous systems and may relate to neural information processing. The present work investigates the traveling chimera states in memristive neuronal networks of locally coupled Hindmarsh-Rose neurons, with both excitation and inhibition considered. Various traveling chimera patterns and firing modes are found to exist in the networks. Particularly, for excitatory connection, two kinds of traveling chimera states appear in opposite directions. Besides, a new type of chimera state composed of traveling chimera state and incoherent state is observed, named the semi-traveling chimera state. Multi-head traveling chimera states with several incoherent groups are also observed. For excitatory-inhibitory connection, the network is observed to exhibit an imperfect coherent state under the synergistic effect of strong excitatory and weak inhibitory coupling. Moreover, a firing pattern named mixed-amplitude bursting state is witnessed,consisting of two bursts of different amplitudes in a time sequence. Furthermore, an electric circuit is designed and built on Multisim to realize the above phenomena, suggesting that traveling chimera states could be generated in real circuits. Our findings can deepen the understanding of the electromagnetic induction effect in regulating the dynamics of neuronal networks and may provide useful clues for constructing artificial neural systems.

Algorithm for solving problems related to the natural vibrations of electro-viscoelastic structures with shunt circuits using ANSYS data

An algorithm for numerical realisation of a mathematical statement of the natural vibrations problem for electro-viscoelastic bodies with passive external electric circuits(i.e.shunting circuits)with an arbitrary configuration using the finite element method is proposed in the present paper.The proposed algorithm allows considering the viscoelastic properties of materials using the model of linear hereditary viscoelasticity with complex dynamic moduli and is used to solve 3D solid structure problems that are compatible for ANSYS package element types.This technique implies the usage of the global assembled matrices of stiffness and mass,formed in the ANSYS package.The basis of the algorithm is a novel approach that allows performing decomposition of the global assembled stiffness matrix formed in the ANSYS software package into constituents that are needed for calculation of the natural vibration frequencies of the objects under study.These matrix components are used in the program that was written in FORTRAN(Formula Translation)language.This problem could be efficiently applied for analysis of the dynamic processes in smart systems based on piezoelectric materials and could also form a basis for the development of numerical finite element algorithms for optimization of the dissipative characteristics of electromechanical systems with shunted piezoelectric elements.

Charging process simulation of a coil by a self-regulating high-T_(c)superconducting flux pump

Self‐regulating high‐temperature superconducting(HTS)flux pumps enable direct current injection into a closed‐loop superconducting coil without any electrical contact.In this work,the process of charging a coil by a self‐regulating HTS flux pump is examined in detail by numerical modeling.The proposed model combines an H‐formulation finite element method(FEM)model with an electrical circuit,enabling a comprehensive evaluation of the overall performance of self‐regulating HTS flux pumps while accurately capturing local effects.The results indicate that the proposed model can capture all the critical features of a self‐regulating HTS flux pump,including superconducting properties and the impact of the secondary resistance.When the numerical results are compared to the experimental data,the presented model is found to be acceptable both qualitatively and quantitatively.Based on this model,we have demonstrated how the addition of a milliohm range,normal‐conducting secondary resistance in series with the charging loop can improve the charging process.In addition,its impact on the charging performance is revealed,including the maximum achievable current,charging speed,and the generated losses.The modeling approach employed in this study can be generalized to the optimization and design of various types of flux pumps,potentially expediting their practical application.