Neuro-monte carlo solution of electrostatic problems

Garcia, R.C.; Sadiku, Matthew N. O.

doi:10.1016/s0016-0032(96)00115-9

Cited by 8 publications

(4 citation statements)

References 18 publications

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“…For the calculation of electrostatic potentials in the gas space and oil space in the tank, the Laplace equation and the Poisson equation are considered , respectively:

({, \begin{array}{l} \nabla^{2} U_{g} = 0 \\ \nabla^{2} U_{l} = - \frac{ρ_{boldc}}{ε_{0} ε_{l}} \end{array})

where U g and U l are the electrostatic potentials in the gas space and oil space (V), respectively; ρ c is the electrostatic charge density (C/m 3 ); ε 0 is the permittivity of vacuum (F/m); ε l is the relative permittivity of the oil.…”

Section: Theoretical Modelmentioning

confidence: 99%

“…The local electrostatic potentials in the gas space and oil space in tanks are related to the local electrostatic charge density by the Laplace and the Poisson equations . In most researches the solving of Poisson equation was based on the assumptions that the electrostatic charges were uniform distribution throughout the oil and the charge density kept constant during the filling process. However, these assumptions may not be accurate.…”

Section: Introductionmentioning

confidence: 99%

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Law of Distribution and Variation of Electrostatic Potential in Oil Tanks during Filling Process

Wang

Chen

Yan

et al. 2018

Process Safety Progress

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Electrostatic potential is a critical factor to evaluate the severity of electrostatic hazard during filling oil tanks. A novel model is proposed for calculating electrostatic potential in tanks during filling process. In the model, the nonuniform electrostatic charge distribution is solved by considering the diffusion, convection, conduction, and dissipation forces acting on the electrostatic charge. Additionally, an experiment was carried out for measuring electrostatic potential, and the maximum surface potential from the experiment coincided with that of calculation well. By applying the model, the distribution of electrostatic potential is explored, and the influences of relaxation time and some other factors on the electrostatic potential are analyzed. The results show that the peak value of the maximum surface potential calculated by the proposed model occurs much later in the filling than the existed model with the assumption of uniform electrostatic charge distribution. The relaxation time is a key factor to influence the electrostatic potential, and it also affects the filling fraction at which surface potential reaches the peak value. The maximum surface potential increases with the increase of the diffusion coefficient of the ion, the dynamic viscosity of the oil and the filling rate, respectively.

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“…For the calculation of electrostatic potentials in the gas space and oil space in the tank, the Laplace equation and the Poisson equation are considered , respectively:

({, \begin{array}{l} \nabla^{2} U_{g} = 0 \\ \nabla^{2} U_{l} = - \frac{ρ_{boldc}}{ε_{0} ε_{l}} \end{array})

Section: Theoretical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Law of Distribution and Variation of Electrostatic Potential in Oil Tanks during Filling Process

Wang

Chen

Yan

et al. 2018

Process Safety Progress

View full text Add to dashboard Cite

show abstract

“…To address this gap, Markov Chains for whole-field computations was proposed by Andrey Markov [29] [30]. The applications of MCMC to rectangular and axisymmetric problems are presented in [29] [31].…”

Section: Introductionmentioning

confidence: 99%

Markov Chain Monte Carlo Solution of Laplace’s Equation in Axisymmetric Homogeneous Domain

Shadare¹,

Sadiku²,

Musa³

2019

OJMSi

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With increasing complexity of today's electromagnetic problems, the need and opportunity to reduce domain sizes, memory requirement, computational time and possibility of errors abound for symmetric domains. With several competing computational methods in recent times, methods with little or no iterations are generally preferred as they tend to consume less computer memory resources and time. This paper presents the application of simple and efficient Markov Chain Monte Carlo (MCMC) method to the Laplace's equation in axisymmetric homogeneous domains. Two cases of axisymmetric homogeneous problems are considered. Simulation results for analytical, finite difference and MCMC solutions are reported. The results obtained from the MCMC method agree with analytical and finite difference solutions. However, the MCMC method has the advantage that its implementation is simple and fast.

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“…Poisson's equation is an elliptic partial differential equation that frequently appears in many scientific problems such as electrostatics, surface reconstruction, gravitational problems, and semiconductors [1]- [2]. Due to its convenience, Poisson's equation in rectangular coordinate has been extensively studied using different numerical methods [3]- [5].…”

Section: Introductionmentioning

confidence: 99%

Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions

Shadare

Sadiku

Musa

2019

AEM

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The advent of the Monte Carlo methods to the field of EM have seen floating random walk, fixed random walk and Exodus methods deployed to solve Poisson’s equation in rectangular coordinate and axisymmetric solution regions. However, when considering large EM domains, classical Monte Carlo methods could be time-consuming because they calculate potential one point at a time. Thus, Markov Chain Monte Carlo (MCMC) is generally preferred to other Monte Carlo methods when considering whole-field computation. In this paper, MCMC has been applied to solve Poisson’s equation in homogeneous and inhomogeneous axisymmetric regions. The MCMC results are compared with the analytical and finite difference solutions.

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Neuro-monte carlo solution of electrostatic problems

Cited by 8 publications

References 18 publications

Law of Distribution and Variation of Electrostatic Potential in Oil Tanks during Filling Process

Law of Distribution and Variation of Electrostatic Potential in Oil Tanks during Filling Process

Markov Chain Monte Carlo Solution of Laplace’s Equation in Axisymmetric Homogeneous Domain

Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions

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