Efficient calculation of the lightning generated underground electric field

2011 ◽  
Author(s):  
Konstantinos Rallis ◽  
Theodoros Theodoulidis
Keyword(s):  
Electric Field ◽  
Efficient Calculation

scholarly journals Compact representation of generalized molecular polarizabilities and efficient calculation of polarization energy in an arbitrary electric field

2021 ◽  
Author(s):  
Krzysztof Wolinski ◽  
Peter Pulay
Keyword(s):  
Electric Field ◽  
Compact Representation ◽  
Efficient Calculation ◽  
Density Response Function ◽  
Molecular Charge ◽  
Order Of Magnitude ◽  
Speed Up ◽  
Molecular Polarizabilities ◽  
Polarizability Matrix ◽  
Natural Polarization

Generalized polarizabilities and the molecular charge distribution can describe the response of a molecule in an arbitrary static electric field up to second order. Depending on the expansion functions used to describe the perturbing potential, the generalized polarizability matrix can have rather large dimension (~1000). This matrix is the discretized version of the density response function or electronic susceptibility. Diagonalizing and truncating it can lead to significant (over an order of magnitude) speed-up in simulations. We have analyzed the convergence behavior of the generalized polarizability using a plane wave basis for the potential. The eigenfunctions of the generalized polarizability matrix are the natural polarization potentials. They are potentially useful to construct efficient polarizability models for molecules.

scholarly journals Highly Efficient Calculation Schemes of Finite-Element Filter Approach for the Eigenvalue Problem of Electric Field

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Yu Zhang ◽  
Yidu Yang ◽  
Jie Liu
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Electric Field ◽  
High Efficiency ◽  
Numerical Results ◽  
Linear Algebraic System ◽  
Highly Efficient ◽  
Efficient Calculation ◽  
Interpolation Postprocessing ◽  
Filter Approach

This paper discusses finite-element highly efficient calculation schemes for solving eigenvalue problem of electric field. Multigrid discretization is extended to the filter approach for eigenvalue problem of electric field. With this scheme one solves an eigenvalue problem on a coarse grid just at the first step, and then always solves a linear algebraic system on finer and finer grids. Theoretical analysis and numerical results show that the scheme has high efficiency. Besides, we use interpolation postprocessing technique to improve the accuracy of solutions, and numerical results show that the scheme is an efficient and significant method for eigenvalue problem of electric field.

Resolution in photoelectron microscopy

1991 ◽  
Vol 49 ◽  
pp. 458-459
Author(s):  
G. F. Rempfer
Keyword(s):  
Electron Microscopy ◽  
Electric Field ◽  
Ultraviolet Light ◽  
Uniform Field ◽  
Virtual Image ◽  
Lens System ◽  
Photoemission Electron Microscopy ◽  
Planar Electrode ◽  
Electron Lens ◽  
Photoemission Electron

In photoelectron microscopy (PEM), also called photoemission electron microscopy (PEEM), the image is formed by electrons which have been liberated from the specimen by ultraviolet light. The electrons are accelerated by an electric field before being imaged by an electron lens system. The specimen is supported on a planar electrode (or the electrode itself may be the specimen), and the accelerating field is applied between the specimen, which serves as the cathode, and an anode. The accelerating field is essentially uniform except for microfields near the surface of the specimen and a diverging field near the anode aperture. The uniform field forms a virtual image of the specimen (virtual specimen) at unit lateral magnification, approximately twice as far from the anode as is the specimen. The diverging field at the anode aperture in turn forms a virtual image of the virtual specimen at magnification 2/3, at a distance from the anode of 4/3 the specimen distance. This demagnified virtual image is the object for the objective stage of the lens system.

Field-assisted ionization theory for microscopists

1994 ◽  
Vol 52 ◽  
pp. 820-821
Author(s):  
Patrick P. Camus
Keyword(s):  
Electric Field ◽  
Electron Tunneling ◽  
Ionization Probability ◽  
Critical Distance ◽  
Tunneling Probability ◽  
Field Ionization ◽  
Radius Of Curvature ◽  
Field Evaporation ◽  
A Value ◽  
Ion Emission

The theory of field ion emission is the study of electron tunneling probability enhanced by the application of a high electric field. At subnanometer distances and kilovolt potentials, the probability of tunneling of electrons increases markedly. Field ionization of gas atoms produce atomic resolution images of the surface of the specimen, while field evaporation of surface atoms sections the specimen. Details of emission theory may be found in monographs.Field ionization (FI) is the phenomena whereby an electric field assists in the ionization of gas atoms via tunneling. The tunneling probability is a maximum at a critical distance above the surface,xc, Fig. 1. Energy is required to ionize the gas atom at xc, I, but at a value reduced by the appliedelectric field, xcFe, while energy is recovered by placing the electron in the specimen, φ. The highest ionization probability occurs for those regions on the specimen that have the highest local electric field. Those atoms which protrude from the average surfacehave the smallest radius of curvature, the highest field and therefore produce the highest ionizationprobability and brightest spots on the imaging screen, Fig. 2. This technique is called field ion microscopy (FIM).

Linear growth of instabilities on a liquid metal under normal electric field

1993 ◽  
Vol 3 (8) ◽  
pp. 1201-1225 ◽  
Author(s):  
G. N�ron de Surgy ◽  
J.-P. Chabrerie ◽  
O. Denoux ◽  
J.-E. Wesfreid
Keyword(s):  
Liquid Metal ◽  
Electric Field ◽  
Linear Growth ◽  
Normal Electric Field
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