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 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. .

The structure of the impulse corona in a rod/plane gap I. The positive corona

1970 ◽  
Vol 315 (1520) ◽  
pp. 1-25 ◽  
Keyword(s):  
Spatial Distribution ◽  
Electric Field ◽  
Space Charge ◽  
Negative Ions ◽  
Corona Discharges ◽  
Theoretical Derivation ◽  
Plane Electrode ◽  
Positive Space Charge ◽  
Positive Ion ◽  
Positive Space

The dissipation of space charge following the growth of impulse corona discharges in positive rod/earthed plane gaps has been measured with an electrostatic fluxmeter. A method is described to determine the spatial distribution and magnitude of the space charge together with the associated electric field. Initial positive ion densities of up to 100 μC m -3 have been found. The total positive space charge deposited in a 40 cm gap at 160 kV is 500 nC. Electrons emitted from the plane electrode as a result of corona channels crossing the gap are shown to be trapped in the discharge space as negative ions. The recovery of the gap over several seconds is largely due to ionic drift to the electrodes. A theoretical derivation of the rate of deionization agrees with observed values.

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.

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

Optimum Configuration of an Expanding-Contracting-Nozzle for Thrust Enhancement by Bubble Injection

2010 ◽  
Author(s):  
Sowmitra Singh ◽  
Jin-Keun Choi ◽  
Georges Chahine
Keyword(s):  
Bubble Dynamics ◽  
Bubbly Flow ◽  
Outlet Section ◽  
Inlet Section ◽  
Concept Design ◽  
Two Phase ◽  
Approximate Analytical Expression ◽  
Analytical Expression ◽  
Bubble Number ◽  
Analytical Approaches

This paper addresses the concept of thrust augmentation through bubble injection into an expanding-contracting nozzle. Two-phase models for bubbly flow in an expanding-contracting nozzle are developed, in parallel with laboratory experiments, and used to ascertain the geometry configuration for the nozzle that would lead to maximum thrust enhancement upon bubble injection. For preliminary optimization of experimental setup’s design, a quasi 1-D approach is used. Averaged flow quantities (such as velocities, pressures, and void fractions) in a cross-section are used for the analysis. The mixture continuity and momentum equations are numerically solved simultaneously, along with equations for bubble dynamics, bubble motion, and an equation for conservation of bubble number. Various geometric parameters such as the exit and inlet areas, the area of the bubble injection section, the presence of a throat and its location, the length of the diffuser section and the length of the contraction section are varied, and their effects on thrust enhancement are studied. Investigation on the effect of the injected void fraction is also carried out. The key objective function of the optimization is the normalized thrust parameter, which is the difference between the thrust with the bubble injection and the thrust before the bubble injection, normalized by the inlet momentum. An approximate analytical expression for the normalized thrust parameter was also derived starting from the mixture continuity and momentum equations. This analytical expression involved flow variables only at three locations; inlet section, injection section, and outlet section, and the expression is simple enough to produce a quick concept design of the diffuser-nozzle thruster. The numerical and analytical approaches are verified against each other and the limitations of the analytical approach are discussed.

The Approximate Calculation of Eigenvalues for Certain Second-Order Linear Differential Equations

1961 ◽  
Vol 65 (605) ◽  
pp. 360-360 ◽  
Author(s):  
W. J. Goodey
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Simple Formula ◽  
Approximate Calculation ◽  
Technical Note ◽  
Second Order ◽  
Numerical Results ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential

In a recent technical note, Squire discussed the approximate solution of certain second-order linear differential equations by the method attributed variously to Riccati, Madelung, Wentzel, Kramers and Brillouin (the W.K.B. method), and others. The problem of eigenvalues, frequently met with in this type of equation, does not, however, appear to have received much attention by this method, and in this note a simple formula is developed which appears to give excellent numerical results in many cases.

The motion of a charged black hole in an electromagnetic field

1980 ◽  
Vol 371 (1746) ◽  
pp. 429-438 ◽  
Keyword(s):  
Exact Solution ◽  
Black Hole ◽  
Electromagnetic Field ◽  
Approximate Solution ◽  
Electric Field ◽  
Hamiltonian Formalism ◽  
Charged Black Hole ◽  
Uniform Electric Field ◽  
Inertial Observer ◽  
Gravitational Perturbations

The motion of a charged black hole in a weak, asymptotically uniform electric field is analysed by using the Hamiltonian formalism for coupled electromagnetic and gravitational perturbations of the Reissner-Nordstrom space-time. The hole is shown to accelerate with respect to a distant inertial observer according to Newton’s law. The relation of the approximate solution obtained to the exact solution of Ernst, representing the charged C-metric without nodal singularity, is then clarified.

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