Solution of Partial Differential Equations by electrical analogy

Save, Yogesh Dilip; Narayanan, Hariharan; Patkar, Sachin B.

doi:10.1016/j.jocs.2010.12.006

Cited by 16 publications

(8 citation statements)

References 16 publications

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“…It is worth pointing out that we have taken advantage of the Laplace transform for solving model (3), although it can also be calculated using the method of variation of constants or the integrating-factor method since it is a system of linear ordinary differential equations with a non-homogeneous term. However, we made the decision to apply the Laplace transform because later, we will deal with the case that the source term is defined via discontinuous functions such as the Dirac delta impulse (see Section 3.2).…”

Section: Formulation and Solutionmentioning

confidence: 99%

“…Differential equations are powerful tools for the mathematical modeling of physical phenomena because we can often observe and estimate the rate of change of a process without fully understanding its underlying mechanism. Despite their elementary form, ordinary and partial linear differential equations have remarkable efficacy in capturing the essence of real-world processes, encompassing applications within a great variety of scientific fields, such as chemical reactions [1], radioactive chains of decay [2], electrical networks [3], gene regulatory networks [4], or the absorption of medicine by various organs [5], just to mention a few. Linear differential equations also play a key role in the analytical and numerical analysis of models formulated via nonlinear differential equations [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic analysis of a class of compartmental models formulated by random differential equations

Bevia,

Carlos Cortés,

Luisovna Pérez

et al. 2024

Math Methods in App Sciences

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This paper deals with the probabilistic analysis of a class of compartmental models formulated via a system of linear differential equations with time‐dependent non‐homogeneous terms. For the sake of generality, we assume that initial conditions and rates between compartments are random variables with arbitrary distributions while the source terms defining the flows entering the compartments are stochastic processes. We then take extensive advantage of the so‐called random variable transformation (RVT) technique to determine the first probability distribution of the solution of such a randomized model under very general hypotheses. In the simplest but relevant case of time‐independent source terms, we also obtain the probability distribution of the equilibrium, which is a random vector. Furthermore, we first particularize the aforementioned results for different types of integrable source terms that permit obtaining an explicit solution of the compartmental model: random constants, a train of Dirac delta impulses with random intensities, and a Wiener process. Secondly, we show an alternative approach based on the Liouville–Gibbs equation, which is useful when dealing with source terms that do not admit a closed‐form primitive. All the previous theoretical results are first illustrated through several numerical examples and simulations where a wide range of different probability distributions are assumed for the model parameters. The paper concludes by applying a compartmental model that describes the dynamics of oral drug administration through multiple chronologically spaced doses using synthetic data generated according to pharmacological references.

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Section: Formulation and Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Probabilistic analysis of a class of compartmental models formulated by random differential equations

Bevia,

Carlos Cortés,

Luisovna Pérez

et al. 2024

Math Methods in App Sciences

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“…In addition to finite elements, thermal-electric analogies are also used [8]. For example, a thermal network model of a busbar system with lumped parameters was developed in [9].…”

Section: Introductionmentioning

confidence: 99%

Influence of the Skin and Proximity Effects on the Thermal Field in Flat and Trefoil Three-Phase Systems with Round Conductors

Jabłoński,

Zaręba,

Szczegielniak

et al. 2024

Energies

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The passage of current generates heat and increases the temperature of electrical components, which affects the environment, support insulators and contacts. Knowledge of the temperature allows for the determination of important operational parameters. Time-varying currents result in a nonuniform current density distribution due to the skin and proximity effects. As a result, temperature and energy losses are increased compared to the uniform DC current density case. In this paper, these effects are considered for three-phase systems with round conductors in flat and trefoil arrangements. In the first step, the analytical expressions for current distributions are determined and used to construct the heat source density. Then, a suitable Green’s function, which allows for obtaining temperature distribution in analytical form, is used to evaluate temperature at any point throughout the conductors. The temperature differences throughout individual wires are usually negligible, whereas noticeable differences can be observed between the wires. The impact of various parameters is examined, and an approximate closed formula is derived to assess the influence of the skin and proximity effects. When the skin depth is not smaller than the wire radius, the skin effect enlarges the temperature increase by around 2% compared to the DC case. As for the proximity effect, the additional increase can be neglected if the distance is above around 10 wire radii, but for closely spaced wires, it can reach up to around 17%, depending on the arrangement and the distance between the wires. Such an additional increase may result in exceeding the permissible temperatures, which damages particular components of the system; therefore, it is important to take it into account at the design stage.

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“…The circuit was shown and its responses in the time domain in addition to a comparison between an electrical circuit and a mass-spring-damper. Moreover, the solution of partial differential equations by electrical analogy has been reported in the literature [6].…”

Section: Introductionmentioning

confidence: 99%

Modelling and simulation of electrical analogous for permanent magnet materials

Fernandez,

Perigo,

de Faria Junior

2023

Phys. Scr.

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Expressions to simulate the intrinsic demagnetizing curve of permanent magnets are derived from the classical electrical analogy of a 2RLC circuit as an equivalent to a magnet under demagnetization in a closed magnetic circuit. Comparisons between experimental and theoretical intrinsic M x H curves were carried out for hard magnetic materials, and the possibility of using this analogous circuit with two components has also been investigated. The Stoner-Wohlfarth model theoretical curves have also been used as a comparison. At last, the electrical analogous parameters have been systematically varied in order to correlate them to the magnetic properties.

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Solution of Partial Differential Equations by electrical analogy

Cited by 16 publications

References 16 publications

Probabilistic analysis of a class of compartmental models formulated by random differential equations

Probabilistic analysis of a class of compartmental models formulated by random differential equations

Influence of the Skin and Proximity Effects on the Thermal Field in Flat and Trefoil Three-Phase Systems with Round Conductors

Modelling and simulation of electrical analogous for permanent magnet materials

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