scholarly journals An approximate expression for the calculation of the electric field in vicinity of the cube electrode with rounded wedges

2008 ◽  
Vol 21 (1) ◽  
pp. 73-81
Author(s):  
Branko Kolundzija ◽  
Alenka Milovanovic
Keyword(s):  
Numerical Methods ◽  
Electric Field ◽  
Approximate Expression ◽  
Numerical Results ◽  
Approximate Analytical Expression ◽  
Analytical Expression

In this paper, an approximate analytical expression for calculation electric field in the centre of the rounded vertex of the metallic cube will be proposed. This expression is determined according to the numerical results obtained using different numerical methods. .

scholarly journals Approximate Calculation and Feature Analysis of Electric Field in Space by Thunderclouds

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lin Wang ◽  
Haojiang Wan ◽  
Yazhou Chen
Keyword(s):  
Approximate Solution ◽  
Electric Field ◽  
Approximate Calculation ◽  
Accurate Solution ◽  
Cylindrical Charge ◽  
Theoretical Derivation ◽  
Approximate Analytical Expression ◽  
Calculation Time ◽  
Analytical Expression ◽  
Pile Model

The calculation of electric field in space excited by thunderclouds is an important basis for lightning warning and protection. In numerical calculation of the electromagnetic field, it is often necessary to perform multiple loop nesting calculations on several triple integrals, which consume a lot of computing resources. In order to shorten the calculation time and improve the calculation efficiency, the electric field excited by the charged thunderclouds in space is theoretically derived with the analytical method by the thundercloud cylindrical charge pile model and based on the electrostatic field theory. The complex integrand function is approximated, so that the analytic expression of electric field in space is obtained in this paper. Through simulation and comparison, it is found that the approximate solution and the exact solution are similar in size, the change trend is the same, and the approximate analytical expression can be used for the approximate calculation of the electric field in a short range. Under certain conditions, the approximate solution can be converted into an accurate solution, which can be used for the accurate calculation of the electric field. Approximate calculation not only simplifies theoretical derivation but also improves calculation efficiency. The calculation time has been shortened from tens of hours to less than one second by using different calculation methods, which is a difference of 7 orders of magnitude. With approximate analytical expression, the electric field excited by charge pile with typical structures in thunderclouds in space is calculated and the characteristics of that are analyzed in this paper. For lightning protection of mobile targets, approximate calculation is of great significance in shortening the lightning warning time and enhancing the protection effect.

scholarly journals Numerical methods for solving the multi-term time-fractional wave-diffusion equation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Fawang Liu ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Pinghui Zhuang ◽  
Qingxia Liu
Keyword(s):  
Numerical Methods ◽  
Theoretical Analysis ◽  
Diffusion Equation ◽  
Fractional Derivatives ◽  
Fractional Laplacian ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Time Space ◽  
Methods And Techniques ◽  
Wave Diffusion

AbstractIn this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Observations Regarding Numerical Results Obtained by the Floquet-Method

2013 ◽  
Author(s):  
Till J. Kniffka ◽  
Horst Ecker
Keyword(s):  
Numerical Methods ◽  
Monodromy Matrix ◽  
Mathieu Equation ◽  
Numerical Results ◽  
The Other ◽  
Benchmark Problem ◽  
Stability Studies ◽  
Floquet Method ◽  
System Equations ◽  
Time Periodic

Stability studies of parametrically excited systems are frequently carried out by numerical methods. Especially for LTP-systems, several such methods are known and in practical use. This study investigates and compares two methods that are both based on Floquet’s theorem. As an introductary benchmark problem a 1-dof system is employed, which is basically a mechanical representation of the damped Mathieu-equation. The second problem to be studied in this contribution is a time-periodic 2-dof vibrational system. The system equations are transformed into a modal representation to facilitate the application and interpretation of the results obtained by different methods. Both numerical methods are similar in the sense that a monodromy matrix for the LTP-system is calculated numerically. However, one method uses the period of the parametric excitation as the interval for establishing that matrix. The other method is based on the period of the solution, which is not known exactly. Numerical results are computed by both methods and compared in order to work out how they can be applied efficiently.

Electric field distribution and voltage breakdown modeling for any PN junction

2016 ◽  
Vol 35 (1) ◽  
pp. 137-156 ◽  
Author(s):  
N. Rouger
Keyword(s):  
Numerical Methods ◽  
Electric Field ◽  
Field Distribution ◽  
Electric Field Distribution ◽  
Poisson’S Equation ◽  
Doping Profile ◽  
Distribution Analysis ◽  
Poisson's Equation ◽  
Content Type ◽  
Pn Junction

Purpose – Scientists and engineers have been solving Poisson’s equation in PN junctions following two approaches: analytical solving or numerical methods. Although several efforts have been accomplished to offer accurate and fast analyses of the electric field distribution as a function of voltage bias and doping profiles, so far none achieved an analytic or semi-analytic solution to describe neither a double diffused PN junction nor a general case for any doping profile. The paper aims to discuss these issues. Design/methodology/approach – In this work, a double Gaussian doping distribution is first considered. However, such a doping profile leads to an implicit problem where Poisson’s equation cannot be solved analytically. A method is introduced and successfully applied, and compared to a finite element analysis. The approach is then generalized, where any doping profile can be considered. 2D and 3D extensions are also presented, when symmetries occur for the doping profile. Findings – These results and the approach here presented offer an efficient and accurate alternative to numerical methods for the modeling and simulation of mathematical equations arising in physics of semiconductor devices. Research limitations/implications – A general 3D extension in the case where no symmetry exists can be considered for further developments. Practical implications – The paper strongly simplify and ease the optimization and design of any PN junction. Originality/value – This paper provides a novel method for electric field distribution analysis.

scholarly journals Degradation of multiphoton signal and resolution when focusing through a planar interface with index mismatch: Analytical approximation and numerical investigation

2018 ◽  
Vol 11 (04) ◽  
pp. 1850020
Author(s):  
Ping Qiu ◽  
Chen He
Keyword(s):  
Spherical Aberration ◽  
Numerical Aperture ◽  
Analytical Approximation ◽  
Planar Interface ◽  
Excitation Wavelength ◽  
Physical Parameters ◽  
Approximate Analytical Expression ◽  
Excitation Light ◽  
Analytical Expression ◽  
Imaging Depth

Multiphoton microscopy (MPM) is an invaluable tool for visualizing subcellular structures in biomedical and life sciences. High-numerical-aperture (NA) immersion objective lenses are used to deliver excitation light to focus inside the biological tissue. The refractive index of tissue is commonly different from that of the immersion medium, which introduces spherical aberration, leading to signal and resolution degradation as imaging depth increases. However, the explicit dependence of this index mismatch-induced aberration on the involved physical parameters is not clear, especially its dependence on index mismatch. Here, from the vectorial equations for focusing through a planar interface between materials of mismatched refractive indices, we derive an approximate analytical expression for the spherical aberration. The analytical expression explicitly reveals the dependence of spherical aberration on index mismatch, imaging depth and excitation wavelength, from which we can expect the following qualitative behaviors: (1) Multiphoton signal and resolution degradation is less for longer excitation wavelength, (2) a longer wavelength tolerates a higher index mismatch, (3) a longer wavelength tolerates a larger imaging depth and (4) both signal and resolution degradations show the same dependence on imaging depth, regardless of NA or immersion on the condition that the integration angle is the same. Detailed numerical simulation results agree quite well with the above expectations based on the analytical approximation. These theoretical results suggest the use of long excitation wavelength to better suppress index mismatch-induced signal and resolution degradation in deep-tissue MPM.

scholarly journals A PRACTICAL PERFORMANCE INDEX FOR COMPARING OF OPTIMIZATION SOFTWARE

2014 ◽  
pp. 7-12
Author(s):  
Andrea Attanasio ◽  
Patrizia Beraldi ◽  
Francesca Guerriero
Keyword(s):  
Numerical Methods ◽  
Performance Index ◽  
Relative Efficiency ◽  
Numerical Results ◽  
Optimization Software ◽  
Practical Performance

In this paper we propose a new practical performance index for ranking of numerical methods. This index may be very helpful especially when several methods are tested on a large number of instances, since it provides a concise and precise idea of the relative efficiency of a method with the respect to the others. In order to evaluate the efficiency of the proposed rule, we have applied it to the numerical results presented on previously published papers.

The Time Response of Exponential Doping NEA InGaAs Photocathode Applied to near Infrared Streak Cameras

2011 ◽  
Vol 415-417 ◽  
pp. 1403-1406
Author(s):  
Wei Dong Tang ◽  
Wen Zheng Yang ◽  
Zhi Peng Cai ◽  
Chuan Dong Sun
Keyword(s):  
Electric Field ◽  
Quantum Efficiency ◽  
Active Layer ◽  
Near Infrared ◽  
Streak Camera ◽  
Numerical Results ◽  
Time Response ◽  
Transport Time ◽  
Minority Carriers

An exponential doping NEA InGaAs photocathode is theoretically proposed to apply in the near infrared streak camera. The photocathode time response is calculated and analyzed by using a photoelectron non-steady method. The numerical results show that the excited electrons in the InGaAs active layer is accelerated due to the built-in electric field induced by the exponential doping structure, which shortens the transport time of minority carriers in the photocathode and thus, the time response is greatly improved. In addition, the exponential doping InGaAs photocathode possesses time response of less than 10 picoseconds and near-infrared quantum efficiency of 10%.

scholarly journals He's frequency–amplitude formulation for nonlinear oscillators using Jacobi elliptic functions

2020 ◽  
Vol 39 (4) ◽  
pp. 1216-1223 ◽  
Author(s):  
Alex Elías-Zúñiga ◽  
Luis Manuel Palacios-Pineda ◽  
Isaac H Jiménez-Cedeño ◽  
Oscar Martínez-Romero ◽  
Daniel Olvera Trejo
Keyword(s):  
Elliptic Functions ◽  
Nonlinear Oscillators ◽  
Numerical Results ◽  
Jacobi Elliptic Functions ◽  
Analytical Expression ◽  
Analytical Frequency

In this work, the Duffing’s type analytical frequency–amplitude relationship for nonlinear oscillators is derived by using Hés formulation and Jacobi elliptic functions. Comparison of the numerical results obtained from the derived analytical expression using Jacobi elliptic functions with respect to the exact ones is performed by considering weak and strong Duffing’s nonlinear oscillators.

An Analytical Expression for the Electric Field and Particle Tracing in Modelling of Be Erosion Experiments at the JET ITER-like Wall

2016 ◽  
Vol 56 (6-8) ◽  
pp. 640-645 ◽  
Author(s):  
I. Borodkina ◽  
D. Borodin ◽  
A. Kirschner ◽  
I.V. Tsvetkov ◽  
V.A. Kurnaev ◽  
...  
Keyword(s):  
Electric Field ◽  
Particle Tracing ◽  
Analytical Expression

A DNS Study of Falling Droplets Under Effects of Electric Field

2017 ◽  
Author(s):  
Esmaiil Ghasemisahebi ◽  
Hassan Bararnia ◽  
Soheil Soleimanikutanaei ◽  
Cheng-Xian Lin
Keyword(s):  
Electrical Conductivity ◽  
Electric Field ◽  
Open Source ◽  
External Electric Field ◽  
Three Dimensional ◽  
Numerical Results ◽  
Grid Refinement ◽  
Adaptive Grid Refinement ◽  
Side Walls ◽  
Density Ratios

In this study deformation and breakup of a falling drop which is surrounded by another liquid are modeled numerically. The drop is influenced by an external electric field which is applied uniformly on the side walls of the domain. An open-source volume-of-fluid solver, Gerris with dynamic adaptive grid refinement has been used for numerically modeling the three-dimensional deformation of a falling droplet. The numerical results are presented for various values of density ratios and electrical conductivity and permittivity. The current numerical results are compared with previous experimental and analytical works which shows a great agreement between them.

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