Kirchhoff's Law Research Articles

Higher-order convergence analysis for interior and boundary layers in a semi-linear reaction-diffusion system networked by a $ k $-star graph with non-smooth source terms

<p>We investigated a nonlinear singularly perturbed elliptic reaction-diffusion coupled system having non-smooth data networked by a $ k $-star graph. We considered all possible boundary conditions at the free boundary located at the tail of the edge and imposed the continuity condition with Kirchhoff's junction law at the junction point of the $ k $-star graph to obtain a continuous solution for this coupled system. First, we showed the existence and uniqueness of the solution using the variational formulation approach. Then, we reformulated it into a minimization problem over a function space to conclude the uniqueness of the solution. For the approximation of the continuous problem, note that the upwind scheme for the flux condition at the free boundary leads to a parameter uniform first-order approximation. To obtain a higher-order uniform accuracy, we utilized a three-point scheme for first-order derivatives and a five-point approximation at the point of discontinuity. These approximations typically did not yield an M-matrix or strict diagonally dominant structure of the stiffness matrix. Hence, we provided a suitable transformation that could lead to a sufficient condition for preserving the strict diagonally dominant structure of the stiffness matrix. We performed a comprehensive convergence analysis to demonstrate the almost second-order uniform accuracy on each edge of the $ k $-star graph. Numerical experiments highly validate the theory on the $ k $-star graph.</p>

A computational framework for quantifying electrical conductance in metallic nanomesh using image processing and computer vision technologies.

This study introduces a computational framework for precisely quantifying electrical conductance in metallic nanomesh structures, leveraging advanced image processing and computer vision algorithms. Nanomesh images obtained via scanning electron microscopy are subjected to preprocessing operations, including threshold-based binary conversion and convolution techniques, to mitigate defects and delineate conductive pathways. A rigorous equivalent electrical path model is subsequently established through keypoint identification via mean-shift segmentation. Kirchhoff's current law is applied to the model to deduce the conductance of the nanomesh. The computationally estimated conductance results are stringently validated against experimental measurements, confirming the model's accuracy. Further, the framework is applied to ascertain the resistivity of nanoscale Ag films deposited on glass substrates, revealing a resistivity higher than that of bulk materials-a finding corroborated by both computational predictions and experimental data. The methodology can be a robust, automated analytical tool for assessing conductance in comparable nanostructured materials.

Numerical analysis and experimental validation of nonlinear broadband monostable and bistable energy harvesters

Vibration based piezoelectric energy harvesting has been receiving more and more attention for supplying usable electrical energy to low-power electronic devices. This type of energy can produce the desired voltage to power any low electronic device or wireless sensor. But most of them provide lower voltage and insufficient power. In this paper, the nonlinear magnetic field is introduced to broaden the effective resonant bandwidth for overcoming this issue. The dynamic linear and nonlinear model of magnetic coupling piezoelectric vibration energy harvester is established based on the Hamilton principle, Euler-Bernoulli beam theory, piezoelectric theory, and Kirchhoff's law and law of mechanics. Numerical solutions of nonlinear energy harvesting systems are studied by using the Runge-Kutta method. The bifurcation diagram, Poincare map, power spectrum, and phase trajectory of voltage output are investigated with different excitation amplitudes and frequencies. Simulation of linear and nonlinear model were illustrated at given excitation levels. Simulation results show the harvesting performance can be improved by proper external magnetic coupling and potential energy function. The theoretical harmonic balance analysis results verify the numerical solution and influence the mechanism of excitation levels and interface resistances. Experimental verification is carried out to measure the nonlinear restoring force and examine the performance of nonlinear bistable and monostable energy harvesters. The experiment results show the nonlinear bistable and monostable energy harvesters can provide larger voltage and more power.

Notes on the Use of Kirchhoff's Laws in Pharmacokinetics.

Recent publications by Benet and coworkers, Korzekwa and Nagar, and Rowland et al. signal disagreement regarding the use of Kirchhoff's laws in combining pharmacokinetic parameters, especially clearances and rate constants. Here, it is pointed out that Kirchhoff's laws as applied to pharmacokinetics simply assert that concentrations are well defined and that molar or mass balances hold. The real issue is how to combine parameters for clearance processes in sequence, which may be reversible, irreversible, or even active in either or both directions. It is also demonstrated that Kirchhoff's laws cannot be used to resolve contradictory results observed in liver transport and clearance. Finally, a simple argument is provided relating nonlinear clearance to apparently anomalous bioavailability observations.

Dynamic analysis of magnetorheological damper incorporating elastic ring in coupled multi-physical fields

The elastic ring assumes a multifunctional role, crucially providing support and reshaping oil-film thickness distribution in applications such as squeeze film dampers, demonstrating its practical efficacy. In this work, a magnetorheological damper (MRD) incorporating an elastic ring is proposed for the first time to improve the performance of damper. The innovative configuration of the elastic ring magnetorheological damper (ERMRD) is fabricated and integrated into a test platform of rotor system. The multi-filed coupling dynamic model of ERMRD is developed involving magnetic field interactions governed by Kirchhoff law, magnetorheological fluid flow dynamics derived from lubrication theory, and the elastic ring deformation based on thin plate theory. The intricate influence mechanisms of elastic ring and excitation current on oil-film characteristic of ERMRD, encompassing oil-film pressure, oil-film force, oil-film stiffness and damping, are investigated in detail. To substantiate the capabilities of ERMRD, it is implemented within the rotor system and a coupled dynamic model is established using Lagrange equation. This is followed by an in-depth analysis of the dynamic response using the Newmark-β method, including a comparative assessment with the conventional MRD. The results reveal that the elastic ring and excitation current influence oil-film pressure distribution in ERMRD from different perspectives, leading the oil-film force to present diverse variation characteristics. Compared to MRD, ERMRD exhibits weaker nonlinearity and superior damping performance.

Ultra-efficient machine learning design of nonreciprocal thermal absorber for arbitrary directional and spectral radiation

Development of nanophotonics has made it possible to control the wavelength and direction of thermal radiation emission, but it is still limited by Kirchhoff's law. Magneto-optical materials or Weyl semimetals have been used in recent studies to break the time-reversal symmetry, resulting in a violation of Kirchhoff's law. Currently, most of the work relies on the traditional optical design basis and can only realize the nonreciprocal thermal radiation at a specific angle or wavelength. In this work, on the basis of material informatics, a design framework of a multilayer nonreciprocal thermal absorber with high absorptivity and low emissivity at any arbitrary wavelength and angle is proposed. Through a comprehensive investigation of the underlying mechanism, it has been discovered that the nonreciprocal thermal radiation effect is primarily attributed to excitation of the cavity mode at the interface between the metal and the multilayer structure. Moreover, the impact of factors, such as layer count, incidence angle, extinction coefficient, and applied magnetic field on nonreciprocal thermal radiation, is thoroughly explored, offering valuable insights to instruct the design process. Additionally, by expanding the optimization objective, it becomes feasible to design fixed dual-band or even multi-band nonreciprocal thermal absorbers. Consequently, this study offers essential guidelines for advancing the control of nonreciprocal thermal radiation.

Extended Fan’s sub-ODE technique and its application to a fractional nonlinear coupled network including multicomponents — LC blocks

The present work deal with the improved Fan’s sub-ordinary differential equation (ODE) method and peruse abundant soliton solutions for a fractional nonlinear coupled network including multicomponents — LC blocks. The extended Fan’s sub-ODE technique is applied on a fractional nonlinear coupled electrical transmission network in addition — LC blocks and through some graphical representations we exhibit novelties. The integer version of the electrical circuit explored here is recently investigated but its fractional partner is weakly scrutinized. Then, we pay attention on the fractional nonlinear coupled electrical network including multicomponents — LC blocks and peruse peculiar voltage waves from the voltage wave equation governing their dynamics. The voltage waves dynamics equation is obtained by means of the Kirchhoff laws’ including the modified Riemann–Liouville derivatives. Through the fractional complex transform, we derive a nonlinear ordinary differential equation that is tackled by the suggested technique. The main gaps of the present investigation based not only on the use of the fractional version of the electrical model, but, also in the capacitor charge nonlinearity’s (the integer version used Qn,mt=C0Vn,m+b1Vn,m2, the fractional partner explored now Qn,mt=C0Vn,m+b2Vn,m3) and the proposed straightforward implemented. In addition, the technique performed here led us to discover new kind of voltage waves by using five auxiliary equation’s key parameters, more than two or three ones commonly involved into such straightforward method reported in the literature. We also prove the existence of our findings by examining the fixed points, phase portraits and related potentials according accurate electrical parameters ranges, coupling elements values wisely chosen. The current technique is reported in the present investigation in manner to be replicable to many other physical systems (electrical, mechanical, optics, acoustics to cite just a few) described by nonlinear evolution equations fractional or not.

Reliably and accurately estimate energy in super-capacitor via a model of cyclic voltammetry

As effective energy storage device super-capacitors have been widely applied in energy storage field. Cyclic voltammetry (CV) test is utilized to characterize the electrochemical performance of super-capacitors. Even if there are basic formulas to estimate specific capacitance by integral of CV, the integrable model of CV was not given in these literatures. Meanwhile, storage energy during one CV has not been known up to now. Researchers are keen to be able to calculate energy from CV. However, most current studies have not already provided integrable model of CV which is in any shape. The establishment of the accurate CV model is an important basis to realize the reliable estimation of energy density in super-capacitors via CV measurement, and also a necessary work to develop the super-capacitors management system. To fill this gap of knowledge, correct basic formula for calculation energy (density) is provided in this work for the first time in this work. To reliably and accurately calculate energy (density), a novel equivalent circuit model as dynamic model in explicit functional form of quasi ellipse shape of CV is established in this work. This quasi ellipse shape model of CV was validated on a set of thirty-five experimental CV curves, the results calculated from quasi ellipse model agree well with the experimental data because the essential novelty of the proposed model is that it is from Kirchhoff's current law and this law tells us how to calculate the total current density of a parallel circuit. Because this quasi ellipse shape model of CV is confirmed through experimental results and the integral of the model is also in explicit functional form, reliable and accurate energy (density) of each CV curve was also obtained. As another essential innovation of the proposed methodology is that quantitative relationship between the scan rate, potential window, intrinsic performance parameters of super-capacitor, measurement temperature, bending angle and energy (density) is quantitatively searched, this work makes a significant practical contribution and it makes impact on the research work on the research community. Hence, more scientific and practical significance of CV can be gained from the passage of this article.

Lattice Mie resonances and emissivity enhancement in mid-infrared iron pyrite metasurfaces.

High-refractive-index antennas with characteristic dimensions comparable to wavelength have a remarkable ability to support pronounces electric and magnetic dipole resonances. Furthermore, periodic arrangements of such resonant antennas result in narrow and strong lattice resonances facilitated by the lattice. We design iron pyrite antennas operating in the mid-infrared spectral range due to the material's low-energy bandgap and high refractive index. We utilize Kirchhoff's law, stating that emissivity and absorptance are equal to each other in equilibrium, and we apply it to improve the thermal properties of the iron pyrite metasurface. Through the excitation of collective resonances and manipulation of the antenna lattice's period, we demonstrate our capacity to control emissivity peaks. These peaks stem from the resonant excitation of electric and magnetic dipoles within proximity to the Rayleigh anomalies. In the lattice of truncated-cone antennas, we observe Rabi splitting of electric and magnetic dipole lattice resonances originating from the antennas' broken symmetry. We demonstrate that the truncated-cone antenna lattices support strong out-of-plane magnetic dipole lattice resonances at oblique incidence. We show that the truncated-cone antennas, as opposed to disks or cones, facilitate a particularly strong resonance and bound state in the continuum at the normal incidence. Our work demonstrates the effective manipulation of emissivity peaks in iron pyrite metasurfaces through controlled lattice resonances and antenna design, offering promising avenues for mid-infrared spectral engineering.

Enhancing the directional violation of Kirchhoff's law of thermal radiation with a nonreciprocal wire medium

Enhancing the directional violation of Kirchhoff's law of thermal radiation with a nonreciprocal wire medium

Using Four-Tier Test to Identify Prospective Elementary Teacher Students’ Misconception on Electricity Topic

The topic of electricity is one of the topics in the Advanced Physics course which has abstract dominant characteristics. The abstract nature of electrical material has the potential to be difficult to understand and has the potential for misunderstanding by students. The four-tier test is a type of test that can be used to identify student misconceptions. The research method used in this study is a quantitative descriptive research with a survey research type. The populations of this study were all first-year prospective elementary teacher students who took the advanced physics courses as many as 30 students. The sampling technique of this study used a saturated sample whose number is the same as that of the study population. The research instrument was in the form of a four-tier test related to electricity topics, totaling 20 questions and divided into the sub-topics of electric current, electromotive force and potential difference, resistance, energy and conductivity of electric current, dc electric circuits, and Kirchhoff's Laws. The characteristics of this four-tier test consist of four levels. The first level is a choice of answers by providing five choices. The second level is the level of the respondent's confidence in the answer choices. The third level is the choice of reasons for the answer chosen by the respondent. The fourth level is the level of confidence in the choice of reasons for the selected answer. Respondents' answer patterns were grouped into three categories, namely understanding the concept, not understanding, and misconceptions. The results showed that the percentage of students in the categories of not understanding concepts, understanding concepts, and misconceptions were respectively 49.65%, 29.38% and 20.97%. Overall, it can be concluded that the dominant first grade students do not understand the concept and some experience misconceptions. The findings of this study may have implications for efforts to improve debriefing in Advanced Physics lectures in the future so as to be able to reduce misconceptions and understand student concepts

Quantum Combinational Logics and their Realizations with Circuits

AbstractClassical combinational logic circuits (CCLCs) are widely used in various fields. Corresponding to the CCLCs, here schemes are given for some quantum combinational logic circuits (QCLCs) based on the quantum NAND tree. Three typical circuits, adder, comparator, and seven‐segment display decoder, are discussed in detail as examples. All the designs of the schemes are based on the quantum random walk theory. Furthermore, these QCLCs are mapped onto the classical circuit networks and design new types of CCLCs, and take advantage of the fact that there is a good correspondence between the voltage in the circuit satisfying Kirchhoff's law and the system wave function satisfying the Schrodinger equation. These CCLCs that are designed have exponential speedup functions compared with conventional ones, which have been demonstrated experimentally. Because classical circuit networks possess good scalability and stability, the realization of QCLCs on classical circuits is expected to have potential applications for information processing in the era of big data.

Multi-band tunable strongly nonreciprocal thermal radiation in topological edge state coupled mode

Violating Kirchhoff's law of thermal radiation can break the reciprocity constraints on spectral emissivity and absorptivity, which provides new capabilities for managing photonic heat flow and fundamentally improves energy harvesting systems' efficiency. Currently, most micro-nano structures that violate Kirchhoff's law are mainly confined to single- or dual-band models, significantly limiting applications such as photonic energy conversion and thermal management. Here, a scheme is proposed for a topological one-dimensional photonic crystal heterostructure consisting of multiple photonic crystals and Weyl semimetals, and its absorptivity and emissivity are theoretically calculated by the transfer matrix method. The results show that the multi-band nonreciprocity that completely violates Kirchhoff's law can persist over broad angular and frequency ranges without requiring any external magnetic field via tuning the relevant parameters. Furthermore, the electric field distribution reveals that the formation of such multiple bands originates from the coupling between topological edge states, and the significant enhancement of the local field near the interface of the heterostructure provides favorable conditions for the realization of strong nonreciprocity. Our work may contribute to the design and development of multiband nonreciprocal devices for energy conversion and thermal management and may also provide design ideas for multiband reciprocal absorbers, filters, optical switching, etc.

Thermodynamic Properties of 3- and 4-Ethoxyacetanilides between 80 and 480 K.

In this work, we present a comprehensive study of the thermodynamic properties of 3-and 4-ethoxyacetanilides. The heat capacities in crystalline, liquid, and supercooled liquid states from 80 to 475 K were obtained using adiabatic, differential scanning (DSC), and fast scanning (FSC) calorimetries. The fusion enthalpies at Tm were combined from DSC measurement results and the literature data. The fusion enthalpies at 298.15 K were evaluated in two independent ways: adjusted according to Kirchhoff's law of thermochemistry, and using Hess' law. For the latter approach, the enthalpies of the solution in DMF in crystalline and supercooled liquid states were derived. The values obtained by the two methods are consistent with each other. The standard thermodynamic functions (entropy, enthalpy, and Gibbs energy) between 80 and 470 K were calculated.

Pore scale analysis for flow and thermal characteristics in metallic woven mesh

Metallic woven mesh screens are representative porous media with periodic structures, which have great application prospects in emerging technology and industrial equipment. However, the effect of their pore structure on macroscopic properties is not clear, which limits their large-scale engineering application. In this paper, to investigate the influence mechanism of stacking patterns and wire contact conditions on flow and heat conduction from the pore scale, a representative elementary volume model of the square-shaped plain copper micromesh was reconstructed according to the geometric parameters obtained by the optical microscope and porosity test experiment. Furthermore, based on the understanding of microscopic mechanism, the theoretical calculation model for macroscopic characteristics was proposed. The results show that the flow characteristics in meshes are mainly affected by stacked patterns. When ReK is 0.08 and 0.28, the flow in single layer and staggered stacked woven meshes transitions from Darcy flow to Forchheimer flow. In Forchheimer flow regime, neglecting the inertia force causes a maximum 50 % error for permeability calculation. The permeability empirical correlations for Darcy and Forchheimer flow are proposed according to Kozeny-Carman and Kozeny-like model. The z-direction effective thermal conductivity of copper woven meshes is significantly affected by wire contact conditions, the maximum value is from 2.5 to 13.5 W/(m·K). The z-direction effective thermal conductivity of tangent and gap contact conditions can be described by the ZBS model, while the random model is suitable for that of overlapped contact conditions. The x-direction thermal conductivity is little affected by contact conditions, the maximum value is 50.3 W/(m·K), but the tortuosity effect of copper wires should be considered for calculation. The calculation model of anisotropic thermal conductivity for single-layer woven meshes is established according to Kirchhoff's law, which is also extended to the staggered stacked woven meshes by introducing a compactness factor.

Optimized Fault Location Identification in Power Distribution Systems With Inverter-Interfaced Distributed Generations

This article proposes a fault location identification method for radial power distribution systems with inverter-interfaced distributed generations (IIDGs). The proposed method is not restricted to any specific types of data. It can fully utilize all available data types in power distribution systems to enhance the accuracy of results. The dataset may include synchronized voltage and current measurements collected by micro-phasor measurement units (micro-PMUs) and/or unsynchronized measurements collected by legacy measuring devices, active and reactive power measurements, pseudo measurements of load values, and virtual measurements based on Kirchhoff's laws. The proposed method explicitly considers uncertainties in the dataset and is applicable to different load types. The article proposes a mathematical model for representing IIDGs in fault location identification applications that does not require any synchronized sampled data or during the fault period data collection. Simulation results on IEEE 34-node feeder demonstrate the accuracy of the proposed method.

Epsilon-near-zero thin film enhanced nonreciprocal thermal radiation in Weyl semimetal-based heterostructures

Violating Kirchhoff's radiation law plays a significant role in enhancing photonic energy conversion efficiency and controlling radiative heat transfer at the nanoscale. Here, we consider a heterostructure consisting of a phononic layer and a Weyl semimetal (WSM) interlayer sitting on a silver (Ag) substrate. We study the interaction of electromagnetic waves with the design and demonstrate that the epsilon-near-zero (ENZ) mode supported in ultra-thin aluminum nitride (AlN) can greatly improve the nonreciprocal response of the WSM layer. An attenuated total reflection (ATR) geometry in the classic Otto configuration is also considered. Our results demonstrate that the phononic thin layer can boost the difference between the emissivity and absorptivity in a broad range of wavelength as compared to an uncoated device. The nonreciprocity at resonance wavelength can reach near-unity with a small incident angle. By engineering the structural parameters, we reveal a surprising result of breaking Kirchhoff's law without requiring any surface patterning and external magnetic field, which identifies unique fundamental and technological prospects of WSMs for engineering thermal radiation with various requirements.

Ferroelectric-defined reconfigurable homojunctions for in-memory sensing and computing.

Recently, the increasing demand for data-centric applications is driving the elimination of image sensing, memory and computing unit interface, thus promising for latency- and energy-strict applications. Although dedicated electronic hardware has inspired the development of in-memory computing and in-sensor computing, folding the entire signal chain into one device remains challenging. Here an in-memory sensing and computing architecture is demonstrated using ferroelectric-defined reconfigurable two-dimensional photodiode arrays. High-level cognitive computing is realized based on the multiplications of light power and photoresponsivity through the photocurrent generation process and Kirchhoff's law. The weight is stored and programmed locally by the ferroelectric domains, enabling 51 (>5 bit) distinguishable weight states with linear, symmetric and reversible manipulation characteristics. Image recognition can be performed without any external memory and computing units. The three-in-one paradigm, integrating high-level computing, weight memorization and high-performance sensing, paves the way for a computing architecture with low energy consumption, low latency and reduced hardware overhead.

FEATURES OF THE ORGANIZATION OF LABORATORY WORKS IN THE STUDY OF PHYSICS OF ELECTRICAL PHENOMENA USING SOFTWARE SIMULATORS

The article shows the possibility of convenient use of software simulators of electric circuits in performing laboratory works in physics, theory of electric circuits and signals, and the basics of electronics. An example of studying Kirchhoffʼs laws in the NI Multisim 14 simulator as one of the simplest in terms of interface but very powerful in terms of capabilities is considered. The choice of NI Multisim is due to the fact that it is de-facto one of the industrial standards in the real design of electronic devices. Thus, students are introduced to not an educational software simulator for modeling electrical phenomena, but to industrial software that they may have to deal with as future electronics designers.The article describes the structure of a typical mini-project (laboratory work) on the study of Kirchhoff's laws, and shows that this approach to organizing training is related to the specifics of teaching students majoring in 172 – “Telecommunications and Radio Engineering”, 123 – “Computer Engineering” and 125 – “Cybersecurity”.As a result, students acquire the skills to develop and test models of electrical circuits with visualization of the results obtained, learn to use the methods of solving systems of linear equations acquired in the course of mathematics in practice.
 Keywords: educational technologies of distance learning; simulation of electrical circuits; analysis of processes in electrical systems; use of NI Multisim 14 software package for educational purposes; laboratory works in physics and electronics; Ohm’s law; Kirchhoff's laws; virtual learning environment.

A Novel Synchronous Rectification Scheme With Low Computational Burden for LLC Resonant Converter in EV Charger Applications

In EV charger applications, high voltage level and high computational burden caused by multiple charging modes bring serious challenges to the synchronous rectification (SR) of LLC resonant converter. Conventional SR schemes can be classified as current sensing-based, voltage sensing-based and sensorless, which are limited by high cost of current sensing, difficulty of high voltage sensing, narrow operating range or high computational burden, respectively. To deal with these problems, this paper proposes a novel SR scheme for LLC resonant converter in EV charger applications. In this scheme, SR control signals are tuned only by main control signal, output voltage and output current, which are naturally available from main controller in EV charger. To this end, no additional signal sensing is required and the cost for SR is reduced. Moreover, the SR tuning principle is on the basis of Kirchhoff's law and phase relationship between main control signal and secondary-side current, which no longer needs to calculate complicated models. Meanwhile, the foresaid tuning process of SR control signals can be implemented by analog circuits. With these effects, this scheme can tune SR control signals effectively over a wide operating range with low computational burden. Furthermore, a virtual current injection strategy is designed to suppress the inversion current of synchronous rectifier. It can guarantee no inversion current and low body diode conduction (BDC) loss. A 600-V input 200 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> 300-V output LLC prototype converter is built to verify the proposed SR scheme.