Kirchhoff's Law Research Articles

Burgers’ Equation Revisited: Extension of Mono-Dimensional Case on a Network

The paper deals with the analysis of Burgers’ equation on acyclic metric graphs. The main goal is to establish the existence of weak solutions in the TV—class of regularity. A key point is transmission conditions in vertices obeying the Kirchhoff law. First, we consider positive solutions at arbitrary acyclic networks and highlight two kinds of vertices, describing two mechanisms of flow splitting at the vertex. Next we design rules at vertices for solutions of arbitrary sign for any subgraph of hexagonal grid, which leads to a construction of general solutions with TV—regularity for this class of networks. Introduced transmission conditions are motivated by the change of the energy estimation.

Thermal Vertical Emitter of Ultra‐High Directionality Achieved Through Nonreciprocal Magneto‐Optical Lattice Resonances

AbstractKirchhoff's law shows that reciprocal materials have equal spectral emissivity at two symmetric polar angles, which is a fundamental limit for a thermal emitter to achieve a small angular divergence in the normal direction. Nonreciprocal materials allow violation of Kirchhoff's law as the emissivity at the two symmetric polar angles can be different. However, achieving strong nonreciprocal thermal radiation near zero angle is challenging. In this work, to reduce the power consumption of a light source for e.g. gas sensing, an ultra‐high‐directional nonreciprocal thermal vertical emitter is proposed, with a periodic structure of magneto‐optical material. When B = 3 T or 1.5 T, magneto‐optical lattice resonances enable the near‐perfect emissivity at 22.36 µm or 22.99 µm at zero angle. The strong nonreciprocity contributed by the collective modes allows for a near‐complete violation of Kirchhoff's law at small angles of ±1°. The nonreciprocal emitters have a very small angular divergence (≈1°), which is better than that of the state‐of‐the‐art thermal emitters. The highly directional nonreciprocal thermal emission is robust despite ±25% change in material loss and ±5% fluctuation in structural parameters. This work should inspire the design of high‐directional nonreciprocal thermal emitters and their applications in high‐resolution thermal imaging, infrared gas sensing, biomedical breath monitoring, and so on.

Modeling of Relative Humidity-Dependent Impedance of Polymer Electrolyte Membrane Fuel Cells

1. IntroductionPolymer electrolyte membrane fuel cells (PEMFCs) are highly efficient devices that utilize hydrogen energy. The large overpotential of PEMFCs, particularly under low relative humidity (R.H.) conditions [1], is a challenge. Equivalent circuit modeling is an effective technique for impedance analysis, in which circuit elements are used to simulate electrode reactions [2]. The transmission line model (TLM) is often used for porous electrodes including PEMFCs [3]. In this study, a TLM was constructed considering the resistance distribution in the cathode catalyst layer (CCL), and the dependence of the impedance on R.H. was investigated.2. ModelingFigure 1 shows a TLM. The proton potential Xl was set as a parameter for each triple phase boundary (TPB), where an oxygen reduction reaction (ORR) occurs. At a certain TPB, Equation 1 holds based on Kirchhoff's current law [4]. Rion is the proton conduction resistance; Rct is the resistance of charge transfer in the ORR; Tct and P are parameters of the constant phase element. In this study, Rct was made a function of proton potential using Equation 2, where i0 is the exchange current density of the cathode and n is the number of exchanged electrons. The potential X0 of the TPB on a Nafion membrane was specified as the boundary condition. Subsequently, the model impedance was calculated by varying the frequency f from 106 to 0.1 Hz.Using the proposed model, a simulation was performed by varying Rion to be similar to the measured impedance spectra in the next section. For comparison, a simulation was performed under the same conditions using a conventional TLM in which Rct is a constant value.3. ExperimentalA membrane electrode assembly (MEA) was prepared by spraying a catalyst ink with an ionomer/carbon weight ratio of 0.92 onto a Nafion membrane. For both the cathode and anode, the electrode area was 1 cm2 and the Pt loading was 0.4 mgpt cm-2. Power generation tests were conducted at a cell temperature of 80 °C. Gases flowing at 200 sccm were supplied to the cathode at an oxygen partial pressure of 0.2 atm and to the anode at a hydrogen partial pressure of 0.4 atm. The impedance spectra of the MEA were measured under various R.H. conditions by electrochemical impedance spectroscopy [5] in the potentiostatic mode at 0.7 V. The distribution of relaxation times (DRT) analysis [6] was conducted on the impedance spectra.4. Results and discussionFigure 2 shows the experimental and simulation results. The left and right columns show the impedance spectra and the DRT analysis results, respectively.Based on the analysis of DRT peaks by Heinzmann et al. [7], the peak in the mid-frequency range, PM, is associated with the resistance of charge transfer in the ORR, whereas the peak group in the high-frequency range, PH, is associated with the resistance of proton conduction. The PH of the DRT of the measured impedance increases as R.H. decreases. This indicates that a decrease in R.H. promotes a decrease in proton conductivity. The increase in Rion in the simulation represents a decrease in proton conductivity, which increases the PH as shown in both simulation results. As the proton conductivity decreases, the PM of the DRTs of the measured impedance and the calculated impedance using the proposed model increases. However, the PM of the DRT of the calculated impedance using the conventional model does not change. This indicates that the proposed model can accurately simulate the actual phenomena in the CCL. The reason for the increase in PM caused by the decrease in proton conductivity could be that the local charge transfer resistance increases by a decrease in the proton potential at each TPB.5. ConclusionsA TLM was constructed to predict the dependence of impedance on R.H. Experimental results showed that an unsatisfactory proton conductivity resulted in an increase in the charge transfer resistance. The results of the simulation with varying proton conduction resistances using the proposed model are consistent with the experimental trend. In future studies, circuit parameters should be appropriately determined by fitting the model to the measured impedance spectra.

Nodal conservation principle of potential energy flow analysis for energy flow calculation in energy internet

The energy internet analysis method based on energy flow analysis can be used to analyze complex flow phenomena of material and energy effectively. However, there is a lack of general conservation principles for energy flow modeling when analyzing the coupling of energy flow with different types of material and energy. Hence, it is necessary to explore the general transmission principles of energy flows based on the physical mechanism. The objective of this paper is to obtain the conservation principles of energy flow at the node and the state parameters characteristics, then develop an effective energy flow calculation method. Firstly, concepts of potential parameters are extended to the general physical potentials, such as voltage, pressure, temperature, and concentration. Then, the application limitations of Kirchhoff's loop law from circuit calculation to energy network analysis are analyzed. The nodal conservation principle of potential energy flow (PEF) and the nodal mixing principle of potential is proposed. Finally, a general PEF calculation method suitable for energy internet is proposed. The results of the 14-node heating solution network show that the general PEF calculation method can effectively analyze the heating solution network, and the number of iterations does not increase with the increase of PEF types.

Limitations of the St. Venant–Kirchhoff material model in large strain regimes

The St. Venant–Kirchhoff law is a widely used constitutive relation in engineering applications. However, its limitation to small strains is frequently mentioned in the literature but rarely elaborated on. Therefore, we present a comprehensive study discussing the St. Venant–Kirchhoff law and its shortcomings in large stain regimes, focusing on compressive loading based on one-dimensional stress and strain states. The linear stress–strain relation in combination with the associated Green–Lagrange strain yields a nonphysical structural behavior for large compressive strains, which is reflected in instabilities and nonphysical softening. Common misconceptions concerning the St. Venant–Kirchhoff law and alternative constitutive models are presented and evaluated based on a two-bar snap-through problem.

Strong nonreciprocal thermal radiation by optical Tamm states in Weyl semimetallic photonic multilayers

The almost-complete violation of Kirchhoff's law possesses various potential applications, such as nonreciprocal thermal emitters, thermal routers, and other logic devices. Recently, Weyl semimetal materials have attracted wide attention. It exhibits a very unusual and extremely large gyroscopic optical response within the mid IR without an external magnetic field, which is due to its unique topologically nontrivial electronic state and inherent time-reversal symmetry breaking. Here, we show a planar multilayer structure composed of Weyl semimetals, which can achieve an almost-complete violation of Kirchhoff's law at an incident angle of 18° without applying any external magnetic field. By tuning the thickness of the ITO layer, the angle of incidence, and the axial vector of the WSM, an almost complete violation of Kirchhoff's law can persist over a wide range of angles (18°–52.3°) and wavelengths (6.6 μm–7.2 μm). Furthermore, through the study of the electric field distribution, it is revealed that this enhanced nonreciprocity is due to the local field-enhancing properties of TPPs. Our work may contribute a practical design scheme for constructing strongly nonreciprocal thermal emitters.

Development, validation and application of an energy model for energy efficient operation of parallel pump systems

Parallel pumps are commonly applied in chilled water and hot water systems to handle broad water flow variation. The application of variable frequency drives leaves the sequencing control of parallel pumps a tricky problem, especially if the pumps have various sizes or/and experience various speeds. The objective of this paper is to develop and validate an energy model to optimize the operation of parallel pump systems. First a comprehensive energy model is developed based on the affinity and Kirchhoff Laws. The pump installed head is applied to eliminate the impact of the pump fittings and the drive efficiency is considered to obtain the true electrical power. Then, the energy model is constructed and validated for a parallel pump system, which has three 284 L/s pumps with one as a backup pump and each powered by a 150 kW motor. Finally, the validated model is applied to identify the energy efficient operation. The results reveal that one-pump operation outperforms two-pump operation at lower flow range with the switchover flowrate decreasing from 300 L/s to 240 L/s as the controlled pump installed head varies from a constant setpoint to a reset variable setpoint. Moreover, faulty various speed settings result in the electrical power waste of 20 kW for the lower-speed pump.

A generalized external circuit model for electrostatic particle-in-cell simulations

A fully self-consistent second order accuracy model for coupling a generalized external circuit and a one-dimensional bounded electrode-driven plasma was proposed in this paper. The plasma was embedded in the circuit as a non-linear element with a potential difference. Based on Kirchhoff's voltage law and the definition of current, the problem of solving the generalized external circuit was transformed into an initial value problem of a set of first-order ordinary differential equations which can be discretized numerically by the second-order backward differential formula. The charge conservation equation at the electrode plate was coupled to the above equation, and the voltage, current, and surface charge density at the next moment were solved by a differential equation solver. Dirichlet boundary conditions of Poisson's equation were obtained through the surface charge density σ0 of the generalized external circuit equation and the plasma density ρ of the Particle-in-Cell (PIC) model. The spatial distribution of plasma potential was solved by using the second-order central difference scheme. The obtained potential at the electrode plate can be used as the Robin boundary condition of the system of generalized external circuit equations. In this model, the loose coupling between the generalized external circuit and plasma was realized by the boundary condition, and the system was fully self-consistent based on the charge conservation law and energy conservation law. We simulated the capacitively coupled plasmas (CCP) under different external circuits as the example and verified the performance of the model. This model can be used to study the influence of different external circuit structures and parameters on plasma discharge, and can be used for any plasma sources driven by electrodes, like CCP, some vacuum electronic devices, and Z-Pinches.

Mechanism analysis and unified calculation model of exergy flow distribution in regional integrated energy system

A regional integrated energy system (RIES) involves many different forms of energy, which can use exergy as a measure of energy quality. Based on the multi-energy flow, this paper analyses the exergy flow distribution mechanism of the network, and puts forward a unified calculation model of the exergy flow of RIES. Firstly, the exergy flow distribution mechanism of the regional heat network is analysed. Taking the return network as the reference system, the exergy flow model of a single-layer regional heat network is established, and the equivalence rationality of the regional heat network is verified by the exergy flow balance analysis. Next, the concept of exergy-voltage is proposed based on exergy-potential difference, and the exergy flow calculation model of the equivalent region heat network is established. The relevant laws are extended to other energy links, the concepts of exergy-voltage of electric and gas distribution networks are proposed, and the exergy flow model is established. The energy station is equivalent to the exergy loss node. Based on exergy flow balance, the generalized Kirchhoff's first law of node exergy flow is proposed. Then, the concept of exergy-impedance is put forward. The exergy-circuit model and exergy flow unified calculation model of RIES are established. Lastly, the energy quality of a typical RIES in China is studied using the present method. Through the exergy flow distribution, it is expedient to determine the effective energy of the energy network and the energy quality characteristics of the entire system. This research demonstrates that the quantity and quality of energy and the overall and local energy quality may exhibit different characteristics. It is found that factors including improving energy structure, adopting reasonable network topology, selecting appropriate equipment, and operation mode for energy station may enhance the system energy quality.

Optimal design of classic RCD absorption circuit in transient electromagnetic transmitter

Abstract The classic RCD absorption circuit has been applied to shorten the turn-off time of transmitters. The current way to determine the resistor and capacitor values of the classic RCD circuit is inefficient. In this paper, an intelligent optimization method to design the classic RCD absorption circuit is proposed. First, based on Kirchhoff's law, the working principles of the RCD absorption circuit at three phases are mathematically analyzed. The formulations of current and voltage at each phase are derived. Next, the shortest turn-off time and its corresponding capacitance and resistance are determined using modeling. Finally, tests are carried out with the transmitting board and antenna to verify the simulation results. Compared with existing method, this new method is easier to operate, and it is more efficient at getting a accurate minimum turn-off time for a given transmitter loop.

Modeling dynamics of chemical reaction networks using electrical analogs: Application to autocatalytic reactions

Modeling complex chemical reaction networks has inspired a considerable body of research and a variety of approaches to modeling nonlinear pathways are being developed. Here, a general methodology is formulated to convert an arbitrary reaction network into its equivalent electrical analog. The topological equivalence of the electrical analog is mathematically established for unimolecular reactions using Kirchhoff's laws. The modular approach is generalized to bimolecular and nonlinear autocatalytic reactions. It is then applied to simulate the dynamics of nonlinear autocatalytic networks without making simplifying assumptions, such as use of the quasi-steady state/Bodenstein approximation or the absence of nonlinear steps in the intermediates. This is among the few papers that quantify the dynamics of a nonlinear chemical reaction network by generating and simulating an electrical network analog. As a realistic biological application, the early phase of the spread of COVID-19 is modeled as an autocatalytic process and the predicted dynamics are in good agreement with experimental data. The rate-limiting step of viral transmission is identified, leading to novel mechanistic insights.

Flexible design method for multiple loads inductive power transfer system with equal power distribution

AbstractAn inductive power transfer (IPT) system for powering multiple sensor nodes placed at various distances is proposed, in which the relay coil not only performs as a power relay to enhance the magnetic field along the power transfer route but also supplies energy to the local load. Based on Kirchhoff's law, the equivalent circuit model of the multi‐load IPT system is established, and the relationship between power distribution and mutual inductance of adjacent coils is investigated. Aiming at practical applications, a flexible design method for the adjacent coil distance is proposed to adjust the mutual inductance and regulate the power distribution. Experimental results show that the equal power distribution is achieved for five loads across a transfer distance of 60.9 cm. Each load dissipates about 0.78 W with a power variation within 6.3%. The results indicate the feasibility of the proposed design method in the multiple‐load wireless sensor network (WSN) applications.

Short-Circuit Calculations in LV Cold Ironing Systems: Characteristic Currents Method CCM and IEC Method

This article presents the calculation procedure of short circuits adopting the characteristic currents method (CCM). In a previous paper by the author G. Parise, the CCM has been upgraded with the introduction of “characteristic” countercurrents and the generalization of the Kirchhoff laws. For illustrating the calculation procedure, the selected case study deals with a low voltage cold ironing system where multiple ships are allowed to operate simultaneously on one shore power transformer and, so, a comparison has been developed between the IEC approach of the short-circuit calculation and the CCM.

Analytical model for fluid flow distribution in an Enhanced Geothermal Systems (EGS)

Enhanced geothermal system (EGS) is often envisioned to consist of at least two wells spaced sufficiently apart and connected by hydraulic fractures that serve as flow paths. All the flow paths must be utilized efficiently to ensure the system is operated at its highest potential. However, building an efficient and sustainable EGS is a complicated process as the fluid always chooses the path of least resistance, which can lead to uneven flow distribution. This study focuses on several critical parameters related to well designs, which can potentially allow for optimized flow distribution. An analytical model (written in Python) is developed based on Kirchhoff's law to calculate the flow distribution in any doublet EGS. Wellbore perforations, the completed wellbores and the fractures are simulated as resistance while the fluid is simulated as a current analog. The model solves the pressure at each node, analogous to voltage, using pipe flow equations and Darcy's law. Three different doublets EGS designs (parallel, anti-parallel and non-parallel) were simulated using the model, and a detailed sensitivity study was performed. Anti-parallel doublet systems perform the best in terms of better fluid distribution and at a lower frictional loss. It was also observed that the flow distribution in a doublet system can be affected by fracture permeability, perforation size and flow rate. Higher permeability fracture leads to poor fluid distribution. Smaller perforation size improves the fluid distribution, but it leads to huge frictional losses. Low flow rates also help with optimized fluid distribution but would eventually lead to low heat output.

Leveraging heat accumulation of district heating network to improve performances of integrated energy system under source-load uncertainties

The multiple uncertainties in renewable energy and loads and the thermoelectric coupling characteristic of the integrated energy system (IES) restrict the accommodation of renewable energy. The IES contains massive pipelines in its district heating network, which signifies the heat storage potential. This paper incorporates the dynamic performance of the district heating network into the multi-scenario optimization model to improve IES's operational performance. Herein, the graph theory and Kirchhoff law are employed to construct the dynamic model of district heating network from the single pipeline and network viewpoints, which characterizes the thermal accumulation performance. The stochastic scenarios are generated by combining Latin hypercube sampling for the initial scenarios and scenario curtailment 0–1 algorithm based on Wasserstein probability distance for the curtailment scenarios to capture the uncertainties. Then, a stochastic multi-scenario optimization method is proposed, which is implemented into a case study to analyze the influences of critical parameters and the performance improvement resulted from the network thermal accumulation. The results show that the scenario curtailment 0–1 algorithm can obtain stable and repeatable scenarios. Considering the heat accumulation characteristics of the district heating network can improve the economic performance by 2.41% and wind energy accommodation by 5.51%.

Metal-Dielectric Thin Film Structure Metamaterial for Obtaining High Equilibrium Temperature Under Direct Solar Optical Radiation

Metal-dielectric thin film structure metamaterials can be designed to absorb solar light radiation over a wide spectral band. By using Kirchhoff's law, metal-dielectric thin film metamaterials are investigated for obtaining high equilibrium temperatures under direct solar light radiation at normal incidence. It is found that among all metal-dielectric thin film structures, the dielectric layer on metal (DLM) surface structure is the optimal structure for producing the highest thermal equilibrium temperature under direct solar optical radiation.

A novel model concerning the independence of emissivity and absorptivity for enhancing the sustainability of radiant cooling technology.

Radiant cooling technology is a sustainable technology for improving built environment. The past research only studied the thermal performance (e.g., radiant heat flux) based on Kirchhoff's law while the accuracy and its reasons were seldom analyzed. This article points out that it is necessary to analyze the precondition before applying Kirchhoff's law directly, because emissivity may not be equal to absorptivityon radiant surfaces. The independence ofthe emissivity and absorptivity is considered in the new model based on the inapplicability of Kirchhoff's law. The analysis of sensitivity and relative deviation are performed to investigate the reasons for errors. The sensitivity of emissivity is about 20%-40% more sensitive to radiant heat flux than the absorptivity.Furthermore, the deviation of the heat flux can reach up to 20% when the absorptivity is in the range from 0.4 to 0.9. This deviation is close to the error range of 21.8%estimated in the past. Thence, the discussion based on the theoretical analysis, shows that the errors in past studies were highly caused by the oversimplified preconditions for applying Kirchhoff's law and the impact of surface absorption was ignored. Additionally, the validation in the past experiments was highly coincidence, since the key independent tests of the absorptivity and radiant heat flux were neglected. Comprehensively, the new model is valuable to provide a reliable solution for future design and analysis of radiant heat exchange when a radiant surface is not locally equilibrium.

Effects of porosity variation in different linear and combination modes in the electrode on the performance of all‑vanadium flow battery

To improve the performance of all‑vanadium flow battery, the electrode porosity is arranged in different linear variations and combination forms, in which the electrolyte flow in the electrode, polarization characteristics, system efficiency (SE), energy efficiency (EE) and dissipative power ratio (DPR) are investigated among the sixteen combined electrodes with the porosity variation in range of ε = 0.9–0.5 and inlet velocity of Q = 10 ml/min in simulations. A novel electrode with the variable porosity in the diagonal direction along flow channel is developed to favor the permeation of electrolyte in the porous electrode. The change amplitude and offset of activation overpotential at 50% state of charge (SOC) are related to the porosity variation in electrode, and the lower concentration overpotential occurs in the area with larger porosity due to more electrolyte supply for the electrochemical reactions under lower permeation resistance. The Kirchhoff's Current law (KCL) in equivalent circuit model is employed to analyze the capacity variation with different porosity combinations in the electrode accounting for the effective capacity ratio of electrode in the consideration of porosity gap at the junction. The 66.9% system efficiency and 16.2% dissipative power ratio occur in the mode with combined electrode of horizontal linear increasing porosity and vertical linear increasing porosity, in which the higher system efficiency and lower dissipative power ratio can be obtained than those of other mentioned modes.

β-Lactoglobulin–fucoidan nanocomplexes: Energetics of formation, stability, and oligomeric structure of the bound protein

Interaction of β-lactoglobulin (BLG) with a sulfated polysaccharide isolated from the brown alga Fucus vesiculosus (fucoidan, FVF), was studied by nephelometry, high-sensitivity differential scanning calorimetry, and sedimentation velocity as a function of pH and the polysaccharide/protein ratio. FVF–BLG complexes were found over the pH 2.5–6.0 range. The complexation was accompanied by the decrease in the conformational stability of BLG at pH < pI 5.2 of the protein where FVF and BLG were oppositely charged. Near pI of the protein and at the pH values larger a bit than pI, where BLG has a large dipole moment or carries a small negative charge, the complexation appeared as changes in the oligomeric state of the protein. Binding curves of BLG to FVF were obtained at pH 3.0 and 6.0 according to the DSC and sedimentation velocity data. Binding constants were evaluated: 3.6 × 103 M−1 at pH 3.0 and 2 × 104 M−1 at pH 6.0. Correlations between the denaturation enthalpy and temperature for the free and bound protein in terms of Kirchhoff's law indicated that the denaturation of both forms of the protein is associated with comparable changes in the accessible surface area of the BLG molecule. It means that the binding of BLG to FVF does not perturb the hydrophobic core of the protein.

Transverse electronic transport through nucleobase-pairs of a DNA wire

Simulations of charge transport through DNA wires face many challenges due to limitations in the description of coherent tunneling, environmental influence and lead-molecule contacts. This article proposes a novel pathway of observing transverse transport through nucleobase-pairs of a DNA molecule to avoid most of these challenges. A total of six single and parallel base-pair systems are considered from the Dickerson's (1981) B-DNA dodecamer series for investigation. The single base-pair G-C and its parallel circuit (G-C||C-G) are observed to show superior transport in this series. Constructive quantum interference is observed in the G-C||C-G system making it the best transport device in the present report. In comparison with a short DNA molecule, the parallel base-pair circuits reveal an advantage of quantum interference to enhance transport in general by satisfying Kirchhoff's circuit law. The superior transport through G-C in comparison with the A-T base-pair is understood through the analysis of electron delocalization functions, electrostatic potentials, and density functional descriptors.