On Semismooth∗ Path-Following Method for Parametric Inclusions

Continuous-time random walks (CTRWs) are generic models of anomalous diffusion and fractional dynamics in statistical physics. They are typically defined in the way that their trajectories are discontinuous step functions. In this paper, we propose alternative definition of CTRWs with continuous trajectories. We also give the scaling limit theorem for sequence of such random walks. In general case this result requires the use of strong Skorohod [Formula: see text] topology instead of Skorohod [Formula: see text] topology, which is usually used in limit theorems for ordinary CTRW processes. We also give additional conditions under which convergence of sequence of considered random walks holds in the [Formula: see text] topology.

Implantable intrabody communication (IBC) is a method that enables low-power, high-security communication between implanted in-body devices that could track biomedical signals and an on-body receiver by using the human body as a communication medium. As the human body consists of various tissues that each have different conductivity, this paper explores the effects of the conductivity of the communication medium on the channel gain over a wide frequency range from 10 MHz up to 300 MHz through the measurements and two models: an electrical circuit model and a FEM simulation model. Measurements are conducted using a liquid phantom with varying conductivity values from 0 S/m up to 1 S/m, covering most human tissues in the frequency range of interest. The circuit and FEM models are designed to mimic the measurement setup in order to verify the measurement results. Results show that the circuit model predicts the communication channel characteristics well at lower frequencies but cannot account for the influence of the measurement setup at higher frequencies. The influence of wire inductances, which can cause a resonant behavior when measuring at frequencies above 100 MHz, was observed using the FEM model. The results also show that the higher the conductivity of the tissue in which the device is implanted, the lower the gain of the signal, with the difference in gain being more prominent when capacitive termination with a high-impedance load is used instead of low-impedance termination. These findings provide valuable insight for selecting the appropriate interface (low-impedance vs. high-impedance termination) across specific frequency ranges for in-body to on-body (IB2OB) communication devices, while illustrating the effect of tissue conductivity on an IBC channel, thereby supporting the optimized design and implementation of reliable IB2OB communication systems.

This study deals with the analysis of Swarm vector magnetic data in order to create a circuit model of electric currents flowing in the Earth’s polar ionosphere and the inner magnetosphere. The model is composed of a system of two-dimensional electric currents representing the magnetic fields of three-dimensional ionospheric polar electrojets (PEJs), the field-aligned currents (FACs), magnetospheric ring currents (MRCs) and magnetospherically induced electric currents inside the Earth (MICs) for each Swarm track. The aim of this paper is to model PEJ and FAC magnetic fields in terms of electric currents on a track-by-track base, subtract those magnetic fields from along-track Swarm magnetic data and estimate the magnetospheric magnetic field (MMF) in discrete time bins. The proposed method is primarily intended to apply to Swarm signals recorded during magnetic storms. The electric circuit model is set up in three steps. After subtracting the main, lithospheric, Sq ionospheric and oceanic tidal magnetic fields from along-track Swarm magnetic signals, the residuals are grouped in 1-h time bins and adjusted by the magnetic field of a two-circular loop model of MRCs and MICs represented by 3times 2 parameters of the electric circular loops in the magnetosphere and the Earth. The adjustment is carried out for the X and Z magnetic field components only because the Y component contains a large signal due to FACs. In the second step, the modelled MRC–MIC magnetic field is removed from the original residuals and the reduced residuals are adjusted by the magnetic field of a system of two-dimensional electric circuits in the polar ionosphere and FACs. The circuit model is set up according to known geometry of PEJs and FACs. In the final step, the modelled magnetic fields of PEJs and FACs are subtracted from the original residuals and all three magnetic field components are adjusted by the MRC–MIC model, named MMC, in a similar way as in the first step. Reliability of the approach is demonstrated by the scatter plots of model MMC showing a significantly better agreement with Swarm magnetic field residuals than the existing MMFs.Graphical

A pumpless reactant recirculation system that offers several major advantages over conventional pump- or ejector-based recirculation systems is derived on the basis of the analogy between fluid flow and an electrical circuit. According to the electricity–fluid analogy, a fuel cell fluid system, including a cell and a reactant recirculation device, can be equivalently described in an electrical circuit model, in which voltage, current, and electrical capacitance correspond to pressure, reactant flow, and fluid volume, respectively, in a fluid flow. In the electrical circuit model, a switched capacitor (SC) circuit, a very popular electrical circuit, is incorporated as the recirculation device. The operation of the electrical circuit model of the recirculation system is mathematically generalized. Based on the analogy, the electrically described recirculation system using the SC is transformed into a fluid circuit, and the pumpless reactant recirculation system in a fluid flow that uses a flow controller and two check valves for reactant recirculation is derived. Experimental and simulation results in the fluid flow and electrical circuit model, respectively, were in good agreement, verifying that the electricity–fluid analogy and the operation of the derived pumpless recirculation system are appropriate. The experimental performance of a single cell in the derived pumpless recirculation system was stable and durable over 10 h, demonstrating that the water byproduct could be removed from the cell in the derived pumpless reactant recirculation system. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

In this study, we propose an electrical circuit model that will be useful for understanding of the mechanisms and dynamics of the human cardiovascular system, which is considered as a complex system in the field of physiology. The electrical circuit model, defined as the Windkessel model, plays an important role in the observation of the characteristic effect of the blood pressure on the arterial system. An electrical circuit model, which we have connected to the input terminals of the Windkessel model, ensures that the mean arterial blood pressure signals are observed within the expected range of values. The Windkessel circuit model that we have tried to develop in this study was constructed in a laboratory environment and the results were observed. It is thought that this study will contribute to the literature in terms of the development of the Windkessel model by increasing the number of parameters involved in the models of heart and arterial system.

Recent research has focused on vanadium redox flow batteries (VRFBs) to address the short lifetimes and fire risks associated with lithium battery systems. While VRFBs offer advantages in safety, they suffer from low energy density and efficiency compared with lithium batteries. To improve VRFB performance, studies are exploring improvements in materials such as anodes, cathodes, and separators and optimizing operations by controlling electrolyte flow rates. However, the impact of current magnitude on VRFB efficiency has been less studied, with few analyses addressing both current and flow rate effects. This research proposes an experimental procedure to evaluate charge/discharge efficiency, energy efficiency, and system efficiency across varying current magnitudes and electrolyte flow rates, using a 40 W VRFB stack composed of four 10 W cells in series. In addition, we introduce a design method for an electrical equivalent circuit model that simulates the VRFB stack, reflecting experimental findings. The model’s accuracy was validated by comparing it with data from 11 full charge/full discharge cycle tests, which varied current and electrolyte amounts.

The electrical equivalent circuit model (ECM) is widely employed for state of charge (SOC) estimation in lithium-ion batteries. Among ECM-based approaches, the Thevenin equivalent circuit model (TECM) is particularly favored due to its computational efficiency and ease of parameter identification. TECM can be implemented in various configurations, with 1RC, 2RC, and 3RC structures being the most common. In these configurations, each RC unit consists of a resistor (R) and a capacitor (C) connected in parallel and incorporated into the circuit branch in series. As the number of RC branches increases, the computational burden of SOC estimation also rises. However, the improvement in estimation accuracy does not scale proportionally with the increased model complexity. A critical factor influencing the accuracy of SOC estimation is the precise determination of ECM parameters. A widely accepted principle suggests that when a parameter can be directly computed from the available data, it is preferable to use the calculated value rather than an estimated one. In line with this principle, this study directly calculates the internal resistance parameter (R0), which is connected in series with the RC branches in TECM, using test data while estimating the remaining RC parameters. SOC estimation is conducted for 1RC, 2RC, and 3RC configurations, and results are compared with those obtained from ECMs where all parameters, including R0, are estimated. To ensure a rigorous comparison, all estimations are performed using the nonlinear least squares method (LSM). The study employs test data from the US06 and UDDS driving cycles, and performance evaluation is conducted based on error distributions (box plots), root mean square error (RMSE), mean absolute error (MAE), and computational cost. The results showed that there is no significant difference between the error values of the predictions made using the model in which R0 is directly calculated and those made using the model in which R0 is estimated. Specifically, for the 1RC model structure, the lowest MAE values are 6.2 and 6.1 millivolts, respectively. However, these values indicate that the nonlinear LSM can be effectively used for estimating the parameters of the battery electrical circuit model.

This paper investigates the index of differential‐algebraic equations (DAEs) that arise in modeling of electric circuits with gyrators. A gyrator is a two‐port network element whose constitutive equations are defined by a skew‐symmetric matrix. While the index analysis of DAEs in circuit simulation has been extensively studied, the existing characterizations are not applicable to circuits that include gyrators. For linear time‐invariant circuits with gyrators, we analyze the index of DAEs using a matroid‐theoretic approach. We show that the problem of determining whether DAEs arising from the hybrid analysis have index at most one or not is reduced to a linear matroid parity problem. We also provide a structural characterization for DAEs arising from the modified nodal analysis (MNA), and extend it to nonlinear circuits, generalizing a structural characterization that is well known in the index analysis of the MNA models.

The use of so-called “artificial lines” — i.e. miniature models of electric circuits — for experimental laboratory studies of transmission-line phenomena is well known. The miniature models are commonly made so as to represent, in true proportion, the electrical constants of a real line. Thus there are artificial telephone lines, artificial submarine cables, artificial long-distance power-transmission lines, etc. A miniature line is a true model of a real line to the extent that the miniature circuit has, for any desired degree of approximation, the same electrical behavior as the full-size circuit. Such laboratory models frequently permit — far more conveniently than the full-size circuit — the study of actual circuit phenomena in a practical and efficient manner. When their limitations are properly understood, miniature circuits may be of great value to transmission-line and operating engineers. Miniature electric circuits may for the present purpose be divided into two general classes: (1) Miniature circuits intended for the study of problems on long lines, such as lines having continuously distributed circuit constants. (2) Miniature circuits for the solution of problems involving complete system networks, inclusive of generating-station and substation apparatus. The following paper deals with a three-phase miniature a-c. system of the network type. The circuit includes synchronous machines, transformers, adjustable resistors, reactors, and condensers, for complete representation of generating stations, substations, lines and loads. The circuit connections are variable, so that any system having not more than the available number of circuit elements may be represented for the correct experimental solution of low-frequency problems. This miniature system has so far given about three years of service in the experimental analysis of transmission system behavior, for existing systems and for systems to be constructed. The problems solved have been within the realms of both the designing and the operating engineers, and have been applied to power systems in this country as well as abroad. One of the by-products of the miniature system is the confirmation and extension of the theory of transmission-line phenomena. Several prominent engineers have expressed the belief, and made the prediction, that after a few years of proper use of the miniature system, the theory and calculation of the present transmission problems will have been so well established that experimental solutions will no longer be necessary. In this paper are given (1) a brief discussion of some of the present problems calling for solutions by the miniature experimental method, (2) a full description of the miniature equipment, (3) an outline of the operating procedure in the solution of problems, and (4) an example illustrating the application of the miniature equipment.

The design of heterostructures that exhibit desired strain characteristics is critical for the realization of semiconductor devices with improved performance and reliability. The control of strain and dislocation dynamics requires an understanding of the relaxation processes associated with mismatched epitaxy, and the starting point for this analysis is the equilibrium strain profile, because the difference between the actual strain and the equilibrium value determines the driving force for dislocation glide and relaxation. Previously, we developed an electrical circuit model approach for the equilibrium analysis of semiconductor heterostructures, in which an epitaxial layer may be represented by a stack of subcircuits, each of which involves an independent current source, a resistor, an independent voltage source, and an ideal diode. In this work, we have applied the electrical circuit model to study the strain compensation mechanism and show that, for a given compositionally uniform device layer with fixed mismatch and layer thickness, a buffer layer may be designed (in terms of thickness and mismatch) to tailor the strain in the device layer. A special case is that in which the device layer will exhibit zero residual strain in equilibrium (complete strain compensation). In addition, the application of the electrical circuit analogy enables the determination of exact expressions for the residual strain characteristics of both the buffer and device layers in the general case where the device layer may exhibit partial strain compensation. On the basis of this framework, it is possible to develop design equations for the tailoring of the strain in a device layer grown on a uniform composition buffer.

We introduce Physics-Aware Normalizing Flows, a novel framework combining data-driven generative modeling with a physical layer based on an Electric Circuit Model, ensuring adherence to electricity laws, sample fidelity, and explainability.Four existing Normalizing Flow architectures, including Real-NVP and NSF, were adapted to our adversarial regime and evaluated with promising results for the ad hoc determination of value ranges of physical quantities and the generation of labeled measurements based on an unlabeled dataset.By extensive data generation according to our self-explainable approach, Random Forest regressions of underlying physical quantities could be improved significantly, compared to the original dataset including omitted ground truth labels. MotivationLately, generative artificial intelligence has attracted a high level of public attention.Despite the emergence of high-performing models, however, significant weaknesses in these methods have been revealed, such as hallucination [1] and violation of causal relationships and real-world conditions [2].Approaches that integrate explicitly represented knowledge with purely statistical generative techniques have therefore gained increasing interest recently [3].An important approach in this regard is the development of physics-aware generative modeling [2], which strengthens the credibility of the generated data as well as the explainability of the models themselves.To this end, invertible flow-based generative models, i.e.Normalizing Flows (NF) [4], deserve special attention due to their built-in self-explainability with support for both sampling and probability density estimation [5], as well as continuous improvements in modeling capacity and quality of the generated samples [6,7,5].One way to strengthen the integrity of generated data is to embed physical models in NFs.This allows ad hoc synthesis of labeled training data using the physical forward model and an unlabeled dataset.Particularly in the field of impedance spectroscopy, where electrical circuit models are used to explain observed measurements, the determination of the corresponding parameter values remains a challenge, but one that can be solved by supervised learning [8].In the following, a novel approach to combine NFs with physical models is presented, exemplary for electric circuits, but adaptable for a wide range of forward models.

Models of complex systems often consist of state variables with structurally similar dynamics that differ in the specific values of some parameters. Examples are multi-class epidemiological models, chemical reaction networks describing multiple components (e.g., binding sites) with equivalent functional behavior, and models of electric circuits with replicated designs. In these cases, the analysis may be expensive due to the model size. Here we consider models defined as systems of polynomial ordinary differential equations (ODEs) with positive solutions. We present an algorithm to reduce the computational cost by transforming the original ODE model into one for which we can compute an appropriate over-approximation on a smaller set of state variables. The algorithm is based on the theory of differential inequalities and consists of two steps. The first step computes a differential hull, which is an ODE system providing lower and upper bounds for each state variable. The hull is constructed such that variables with structurally similar dynamics but originally different parameters may now be represented by the same lower and upper bounds. Based on this, the second step exploits already developed notions of exact model reduction for ODEs to lump such variables. The algorithm is showcased on several case studies and its results are favourably compared against CORA, a well-known tool for reachability analysis of dynamical systems.KeywordsOrdinary differential equationsModel reductionReachability analysis

Тенденции развития науки и образования -39 -Зубарев А.В

Differential-algebraic equations (DAEs) provide an essential tool for system modeling and analysis within different fields of applied sciences and engineering. This book addresses modeling issues and analytical properties of DAEs, together with some applications in electrical circuit theory. Beginning with elementary aspects, the author succeeds in providing a self-contained and comprehensive presentation of several advanced topics in DAE theory, such as the full characterization of linear time-varying equations via projector methods or the geometric reduction of nonlinear systems.Recent results on singularities are extensively discussed. The book also addresses in detail differential-algebraic models of electrical and electronic circuits, including index characterizations and qualitative aspects of circuit dynamics. In particular, the reader will find a thorough discussion of the state/semistate dichotomy in circuit modeling. The state formulation problem, which has attracted much attention in the engineering literature, is cleverly tackled here as a reduction problem on semistate models.

A methodology of defect identification in linear DC circuits based on so called Virtual Distortion Method (VDM) will be presented. The proposed approach takes adventage of the analogy linking mechanical models of truss structures and electric circuits. In this paper we cover the issue of modelling defects in electric circuits by compatible state of distortions, next we introduce the concept of influence matrix Dij, which describes global sensitivity of the circuit and enables fast recalculation of system response, and we formulate a gradient method of defect identification (inverse problem) based on local current and voltage measurements. In the following analysis we focus on so-called impotent states of distortions, which are the source of ambiguity of solution. We show that these difficulties can be overcome by a proper measuring strategy.