Kirchhoff's Law Research Articles

Avoiding disc collisions and nonlinear vibration of unbalanced rotors by means of position control of the rotor journal mounted in magnetorheological hydrodynamic bearings

Rotors of rotating machines are often supported by hydrodynamic bearings. Imbalance, ground vibration, assembling inaccuracies, and eccentric position of the shaft journal in the bearing hole may result in collisions between the rotors and their casings if the gap between the rotating and stationary parts is narrow. This can be avoided by controlling the position of the rotor journal in the bearing hole by changing stiffness of the oil film. This method of controlling parameters of the lubricating layer is offered by application of magnetically sensitive fluids. A new design of magnetically controllable hydrodynamic bearing was developed. The magnetic flux is generated by an electric coil. It passes through the bearing housing, and the layer of lubricant and goes back to the coil core. Magnetic induction in the bearing gap is calculated by application of the Kirchhoff and Hopkinson laws. The pressure distribution in the oil layer is obtained by solving the Reynolds equation adapted to lubricants exhibiting yielding shear stress, the magnitude of which depends on magnetic induction. Results of the computational simulations showed that application of a magnetic field acting on magnetorheological lubricant in the bearing gap makes it possible to prevent impacts between the rotor and its casing in a certain velocity interval, or at least to reduce magnitude of the impact forces if collisions occur. The principal contribution of the conducted research is the proposal of a new approach based on semiactive principle to controlling position of rotors working in limited space and obtaining more information on interaction between the rotors and magnetically controllable hydrodynamic bearings during the operating conditions when collisions between the rotor and its stationary part take place.

Infrared spectral soot emission for robust and high-fidelity flame thermometry.

Spectral soot emission (SSE) in the visible spectrum is a popular technique for non-intrusive thermometry in sooting flames. However, its accuracy is restricted by uncertainties in the wavelength dependence of soot optical properties. We propose a novel infrared spectral soot emission method that successfully addresses this issue. Comprehensive light extinction experiments were firstly conducted to explore the spectral variation of soot optical property. The results indicated a wavelength independence of the soot absorption function provided the wavelength of the incident light is larger than 1000 nm, thereby indicating through the Kirchhoff law the potential of a robust thermometry using infrared (>1000 nm) spectral soot emissions. Proof-of-concept experiments were performed for sooting premixed flames of ethylene with different equivalence ratios. The results demonstrated that the new method provided more accurate temperature results compared with its visible-NIR counterpart, particularly at flame positions where nascent soot particles are present. The proposed method is, to our knowledge, the first infrared spectral soot emission-based thermometry, and is believed to offer a solution to improving the fidelity of SSE with a cost-effective optical setup.

New Absolute Cavity Pyrgeometer equation by application of Kirchhoff's law and adding a convection term

Abstract. An equation for the Absolute Cavity Pyrgeometer (ACP) is derived from application of Kirchhoff's law and the addition of a convection term to account for the thermopile being open to the environment, unlike a domed radiometer. The equation is then used to investigate four methods to characterise key instrumental parameters using laboratory and field measurements. The first uses solar irradiance to estimate the thermopile responsivity, the second uses a minimisation method that solves for the thermopile responsivity and transmission of the cavity, and the third and fourth revisit the Reda et al. (2012) linear least squares calibration technique. Data were collected between January and November 2020, when the ACP96 and two IRIS radiometers monitoring terrestrial irradiances were available. The results indicate good agreement with IRIS irradiances using the new equation. The analysis also indicates that while the thermopile responsivity, concentrator transmission and emissivity of an ACP can be determined independently, as an open instrument, the impact of the convection term is minor in steady-state conditions but significant when the base of the instrument is being subjected to rapid artificial cooling or heating. Using laboratory characterisation of the transmission and emissivity, together with use of an estimated solar calibration of the thermopile, generated mean differences of less than 1.5 Wm−2 to the two IRIS radiometers. A minimisation method using each IRIS radiometer as the reference also provided similar results, and the derived thermopile responsivity was within 0.3 µV W−1 m2 of the solar-calibration-derived infrared responsivity estimate of 10.5 µV W−1 m2 estimated using a nominal solar calibration and provide irradiances within ±2 % of the terrestrial irradiance measured by the reference pyrgeometers traceable to the International System of Units (SI). The calibration method using linear least squares regression introduced by Reda et al. (2012) that relies on rapid cooling of the ACP base but utilising the new equation was found to produce consistent results but was dependent on the assumed temperature of the air above the thermopile. This study demonstrates the potential of the ACP as another independent reference radiometer for terrestrial irradiance once the magnitude of the convection coefficient and any potential variations in it have been resolved.

Lithium-Ion Battery Cell Open Circuit Fault Diagnostics: Methods, Analysis, and Comparison

Battery fault diagnosis has great significance for guaranteeing the safety and reliability of lithium-ion battery (LIB) systems. Out of many possible failure modes of the series–parallel connected LIB pack, cell open circuit (COC) fault is a significant part of the causes that lead to the strong inconsistency in the pack and the reduction of pack life. Therefore, it is extremely important to diagnose COC faults in real time. Motivated by this fact, we propose Kirchhoff's law based method, short-time Fourier transform based method, the Pearson correlation coefficient based method, dual extended Kalman filter (DEKF) based method, and long short-term memory recurrent neural network based method for diagnosing COC fault. These diagnostic approaches do not rely on other sensor data except pack current and terminal voltages of modules composed of cells in parallel. Furthermore, several experiments on a 4S-3P battery pack are taken under time-varying ambient temperature conditions to evaluate and compare the computation cost, diagnostic delay, and accuracy of these approaches. Test results show that only the DEKF-based approach owns the weakest robustness, and Kirchhoff's law based method with the merit of the lowest diagnostic delay and computation cost is the most appropriate approach for online COC fault diagnosis.

Vaporization enthalpies of self-associated aromatic compounds at 298.15 K: A review of existing data and the features of heat capacity correction. Part I. Phenols

Vaporization, sublimation and fusion enthalpies of 39 phenol derivatives were thoroughly analyzed using Kirchhoff's and Hess's laws of Thermochemistry to derive the reliable ΔlgH°(298.15 K) values. During the analysis, the correction for non-ideality for the high-temperature vaporization enthalpies was performed. The crystal, liquid and gas heat capacities available from the literature were complemented with the additional experimental measurements of the condensed phases and the computations of the ideal gas properties. Analyzing the available information, we proposed a simple approach for the estimation of the temperature dependence of the vaporization enthalpy of phenol derivatives that showed high accuracy for compounds of various structure.

Controlling light emission by a thermalized ensemble of colloidal quantum dots with a metasurface.

We report an experimental and theoretical study of light emission by a patterned ensemble of colloidal quantum dots (cQDs). This system modifies drastically the emission spectrum and polarization as compared to a planar layer of cQDs. It exhibits bright, directional and polarized emission including a degree of circular polarization in some directions. We introduce a model of light emission based on a local Kirchhoff law which reproduces accurately all the features of the experiment. The model provides a figure of merit to assess quantitatively the emitted power. This work paves the way to the systematic design of efficient ultrathin light emitting metasurfaces with controlled polarization, spectrum and directivity.

In-situ estimate of coating by equivalent circuit for PEO of AZ31B

ABSTRACT The paper discusses an in-situ estimated methodology of coating using the equivalent circuit for the plasma electrolytic oxidation (PEO) process. An equivalent circuit of the second-order nonlinear structure can be proposed from the transient load waveform and the arc image recorded during pulsed bipolar PEO treatment. The transfer function of the linear part of the model was derived from Kirchhoff's law and Laplace's transformation rule; the nonlinear part of the model was fitted using Fitting Theory. Then the calculation method of each element value was derived in the equivalent circuit. The characterisation results of the coating properties show that the changes of different element values by the equivalent circuit can reflect the changes in coating thickness, coating density and discharge intensity. The relationship between the values of several elements and the microstructure of the coating is analysed comprehensively; a prediction method for the corrosion resistance of the coating is provided.

A proof of Kirchhoff's first law for hyperbolic conservation laws on networks

<abstract><p>In dynamical systems on networks, Kirchhoff's first law describes the local conservation of a quantity across edges. Predominantly, Kirchhoff's first law has been conceived as a phenomenological law of continuum physics. We establish its algebraic form as a property that is inherited from fundamental axioms of a network's geometry, instead of a law observed in physical nature. To this end, we extend calculus to networks, modeled as abstract metric spaces, and derive Kirchhoff's first law for hyperbolic conservation laws. In particular, our results show that hyperbolic conservation laws on networks can be stated without explicit Kirchhoff-type boundary conditions.</p></abstract>

A Data-Driven Linear Optimal Power Flow Model for Distribution Networks

The linearized power flow (PF) model is mainly used to make the optimal power flow (OPF) problem convex. However, existing data-driven linear PF models are not applicable for OPF calculation since the Kirchhoff's law (KCL) constraints are neglected. In this letter, we propose a data-driven linear PF model incorporating the KCL constraints and can be embedded in OPF for distribution networks (DNs). By combining the support vector regression (SVR) and ridge regression (RR) algorithms, the proposed method is robust against bad data in measurements. Numerical tests show that the proposed model has much higher accuracy than the existing linear models, especially for OPF calculation.

Tunable near-perfect nonreciprocal radiation with a Weyl semimetal and graphene.

A tunable near-perfect nonreciprocal thermal emitter, consisting of a dielectric plane and a monolayer graphene sandwiched between a subwavelength grating and a Weyl semimetal plane, is proposed and investigated. Near-complete nonreciprocal radiation can be achieved at resonance, breaking the traditional Kirchhoff's law. The underlying physical mechanism, resulting from a guided mode resonance, is disclosed by illustrating the magnetic field distribution. Moreover, the strong nonreciprocity remains well within a wide range of geometrical parameters. What's more, the performance of the near-perfect spectral nonreciprocity can be flexibly controlled in a wide spectral range through varying the Fermi level of graphene and the axial vector of the Weyl semimetal, which reduces the cost and should be interesting for real application. The conclusions of this paper should prompt the further development of tunable nonreciprocal thermal emitters.

Protein charge transfer far from equilibrium: a theoretical perspective.

Potential differences for protein-assisted electron transfer across lipid bilayers or in bio-nano setups can amount to several 100 mV; they lie far outside the range of linear response theory. We describe these situations by Pauli-master equations that are based on Marcus theory of charge transfer between self-trapped electrons and that obey Kirchhoff's current law. In addition, we take on-site blockade effects and a full non-linear response of the local potentials into account. We present analytical and numerical current-potential curves and electron populations for multi-site model systems and biological electron transfer chains. Based on these, we provide empirical rules for electron populations and chemical potentials along the chain. The Pauli-master mean-field results are validated by kinetic Monte Carlo simulations. We briefly discuss the biochemical and evolutionary aspects of our findings.

Theoretical investigation of injection-locked differential oscillator

A preliminary analysis of published works on this topic showed that at present there is no sufficiently substantiated theory of such devices, and the approximate approaches used are rough and do not always meet the requirements of practice. The proposed transition from a differential self-oscillator to an equivalent single-circuit oscillator has not received a convincing justification.
 This article presents a methodology for studying a synchronized differential oscillator using rigorous methods. A mathematical model of such oscillator is presented in the form of nonlinear differential equations obtained on the basis of Kirchhoff's laws. Their analysis made it possible to substantiate the transition to the model of a single circuit LC oscillator, equivalent to a differential one. A technique for such a transition is proposed, including the procedure for determining the nonlinear characteristics of the amplifying element of this self-oscillator, based on the nonlinear characteristics of two amplifying elements of the differential oscillator.
 The mathematical model of an equivalent oscillator is represented by a non-linear differential Van der Pol equation in a dimensionless form, it is simple and accurate. This form of representation made it possible to single out a small parameter and estimate its value. In the case of small values of the small parameter, as is known, traditional methods can be used for its analysis. Thus, the task of studying the synchronization process of a differential oscillator is reduced to the study of the synchronization process of a Van der Pol oscillator. The presented results can be useful in the development of various devices based on synchronized differential oscillators.

Designing of a quantum TIA to improve FSO signal reception

Free Space Optic Communication (FSO) is one of the communication systems chosen for 5G + / 6G backhaul. Many works were done to improve signal quality either at emission, transmission channel or at reception through photodetector. The aim of this work is to design a new transimpedance amplifier (TIA) to improve Free Space Optic Communication (FSO) photodetector performance. To achieve our purpose, a negative electrical resistance was introduced into conventional TIA. SPICE software and Kirchhoff's laws were used to design and analyze the circuit. The obtained results show that the new TIA has a better amplitude gain response and lower equivalent noise than conventional TIAs. High bandwidth and flat amplitude response in the pass band characterize our TIA. This characteristic is one of the two criteria for a photodetector to be considered as a quantum device. A 3D gain representation highlights different regions of positive and negative feedback resistors and frequencies to be used or avoided in order to ensure TIA stability.

Refinement and Generalization of Maxwell's Thermal Theorem

In the famous treatise on electricity and magnetism, J.K. Maxwell led to the conclusion that in a passive system of conductors, the current increases sharply in order to approach an increase in heating power. In such cases, Maxwell's thermal gain is valid only for passive electrical circuits when there are no electromotive forces (EMFs). We proposed to change the formulation of the theorem to the statement that the current is distributed in such a way as to minimize the loss of one second of the power for heating. This refinement allows, as shown in the article, to extend such a thermal theorem to active electrical circuits in which there may be sources of E.D.S. This allows us to make physically interpretable Lagrange multipliers of constraints expressing the first Kirchhoff law. The Lagrange multipliers under restrictions in this case coincide with the potentials in the nodes of the electric circuit. This refinement also leads to new interesting formulations of the thermal theorem including the distribution of voltages over the nodes of the electrical circuit.

Comprehensive Model for the Thermoelectric Properties of Two-Dimensional Carbon Nanotube Networks

Networks of semiconducting single-walled carbon nanotubes (SWCNTs) are interesting thermoelectric materials due to the interplay between CNT and network properties. Here, we present a unified model to explain charge and energy transport in SWCNT networks. We use the steady-state master equation for the random resistor network containing both intra- and intertube resistances, as defined through their one-dimensional density of states that are modulated by static Gaussian disorder. The tube-resistance dependence on the carrier density and disorder is described through the Landauer formalism. Electrical and thermoelectric properties of the network are obtained by solving Kirchhoff's laws through a modified nodal analysis, where we use the Boltzmann-transport formalism to obtain the conductivity, Seebeck coefficient, and electronic contribution to the thermal conductivity. The model provides a consistent description of a wide range of previously published experimental data for temperature and charge-carrier-density-dependent conductivities and Seebeck coefficients, with energetic disorder being the main factor to explain the experimentally observed mobility upswing with carrier concentration. Moreover, we show that, for lower disorder energies, the Lorentz factor obtained from the simulation is in accordance with the Wiedemann-Franz law for degenerate-band semiconductors. At higher disorder, deviations from simple band behavior are found. Suppressed disorder energy and lattice thermal conductivity can be the key to higher thermoelectric figures of merit, zT, in SWCNT networks, possibly approaching or even exceeding zT = 1. The general understanding of transport phenomena will help the selection of chirality, composition, and charge-carrier density of SWCNT networks to improve their efficiency of thermoelectric energy conversion.

Polarimetric analysis of thermal emission from both reciprocal and nonreciprocal materials using fluctuation electrodynamics

Coherent thermal emission for a given polarization has been observed in many metamaterials with micro/nanostructures. Emissivity is typically obtained based on the equivalence between absorptivity and emissivity according to Kirchhoff's law; however, such a relationship may be invalid for nonreciprocal media. This study aims at developing a more general approach, without the constraint of optical reciprocity, that is applicable to magneto-optical materials and magnetic Weyl semimetals. A polarimetric analysis is theoretically carried out based on fluctuation electrodynamics to provide a complete description of the emissivity for all polarization states. The Stokes parameters are calculated from the coherency matrix for a multilayered system, which may include anisotropic media and even nonreciprocal materials. It is demonstrated that thermal emission may be circularly or linearly polarized in selected directions and frequencies. The findings of this work are consistent with the modified Kirchhoff's law provided by several groups in recent years, and therefore, justify the appropriateness of both the direct and indirect methods. This study will help the design of desired thermal emitters for energy harvesting and thermal control.

Virtual Laboratory and Its Effect on Student Learning Outcomes in Physics Education

This study aims to determine the effect of using a virtual laboratory on student learning outcomes in Kirchhoff's law material at the physics education study program at HKBP Nommensen Pematangsiantar T.A. 2020/2021 by utilizing a virtual laboratory. This type of research is a true experiment with the research sample, namely the physics education study program group A as the experimental class and group B as the control class. The research instrument test was composed of 20 multiple-choice questions, the content validity was tested by a team of experts as validators as many as 2 people and student activity observation sheets. From the data analysis, the average post-test value for the experimental class was 78.46 with a standard deviation of 11.25 and the average post-test value for the control class was 66.50 with a standard deviation of 13.78. Normality and homogeneity tests at the level of =0.05 stated normal and homogeneous and one-party hypothesis testing t-stat > t-table (2.99> 1.67). Thus, it can be concluded that the use of a virtual laboratory can improve student learning outcomes in the basic physics practical subject of Kirchoff law

Методика проектирования асинхронных гребных электродвигателей с заданным коэффициентом мощности

The article considers the problem of improving the quality of electricity, in particular the power factor. The increased value of the power factor leads to decreasing the reactive component of the currents in the ship power network and, as a result, to a decreased power of converting equipment, generators and cable products. There is studied 
 a section in the methodology of designing ship electrical machines developed at the Department of Electric Drives and Electrical Equipment of Coastal Power Plants in Admiral Makarov State University of Maritime and Inland Shipping, which allows to evaluate the parameters of asynchronous electric motors at the design stage. Today, in designing electrical machines there are used the methods developed in the last century, which do not allow to carry out electromagnetic calculations subject to the required value of the power factor. The power factor is known to be determined by empirical formulas after setting the main parameters of the mechanism. The equivalent circuit of asynchronous electric motor containing the parameters of stator and rotor windings, and its mathematical description based on equations corresponding to Kirchhoff's laws are considered. Transformations of the equations describing the electromagnetic processes in the engine given for the static mode of operation in a complex form are made. There are given the expressions that allow determining the magnetizing current, magnetic conductivities, magnetizing forces, air gap and magnetic saturation coefficients, overall dimensions of the electric motor, and electromagnetic torque that it develops. Basing on the transformed equations describing an asynchronous electric motor there have been derived the regularities that help set the value of the power factor as initial data at the stage of design. The practical significance of the applied methodology and importance of the chosen subject have been analyzed.

Current Distribution in the Discharge Unit of a 10-Cell Vanadium Redox Flow Battery: Comparison of the Computational Model with Experiment.

Shunting currents are among the main problems of all-vanadium redox flow battery stacks since, in addition to capacity losses, they cause negative effects associated with the local destruction of electrodes and bipolar plates. The values of both the shunting currents and their destructive effects on materials can be reduced at the battery development stage by adjusting the resistance of the electrolyte supply channels. The solution to this problem can be found using a calculation model for current distribution based on the current balance in the nodes as well as voltage drops and electromotive force in internal circuits according to Kirchhoff's laws. This paper presents the verification of the model of current distribution in an all-vanadium redox flow battery stack of an original design that allows for the determination of membrane-electrode assembly resistances and electrolyte supply channels via direct measurements. Based on a comparison of the calculated and experimental values of the coulombic efficiency of charge-discharge cycles, the capacity fade associated with the crossover of vanadium compounds through the membrane has been determined.

Modeling and analysis of dual modules cantilever-based electrostatic energy harvester with stoppers

Based on the cantilever beam, this paper proposes and designs a novel electret-based electrostatic energy harvester (e-EEH) with dual modules: module I is a capacitor of nonparallel plate electrodes; module II is a multi-electrode array capacitor. Two stoppers are presented in concern with reliability by limiting the motion of proof mass to prevent capacitor breakdown and pull-in. Meanwhile the stoppers serve as a functional element to realize broadband harvesting. Considering the bending of the cantilever beam, the expression of the module Ⅰ capacitance is analytically derived as a function of the deflection. Conformal transformation is applied to obtain the expression of the module Ⅱ capacitance, simultaneously considering the change of distance and overlap area between movable and fixed electrodes. According to Hamilton's principle and Kirchhoff's circuit law, the electromechanical coupling nonlinear dynamics equations of the proposed energy harvesters are established. The output performance of the energy harvester is obtained and analyzed by numerical calculation. The results show that the double-model electrostatic energy harvester can output high power in low- frequency broadband.