Analytic approximation for the elastic radiation from a contained underground explosion

1990 ◽  
pp. 196-200
Author(s):  
N. A. Haskell
Keyword(s):  
Underground Explosion ◽  
Analytic Approximation

scholarly journals Accurate analytic approximation for the Chapman grazing incidence function

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Dmytro Vasylyev
Keyword(s):  
Asymptotic Expansion ◽  
Radiative Transfer ◽  
Bessel Functions ◽  
Grazing Incidence ◽  
Analytical Approximation ◽  
Analytic Approximation ◽  
Atmospheric Physics ◽  
Uniform Asymptotic Expansion ◽  
Grazing Angles ◽  
Physical And Chemical

AbstractA new analytical approximation for the Chapman mapping integral, $${\text {Ch}}$$ Ch , for exponential atmospheres is proposed. This formulation is based on the derived relation of the Chapman function to several classes of the incomplete Bessel functions. Application of the uniform asymptotic expansion to the incomplete Bessel functions allowed us to establish the precise analytical approximation to $${\text {Ch}}$$ Ch , which outperforms established analytical results. In this way the resource consuming numerical integration can be replaced by the derived approximation with higher accuracy. The obtained results are useful for various branches of atmospheric physics such as the calculations of optical depths in exponential atmospheres at large grazing angles, physical and chemical aeronomy, atmospheric optics, ionospheric modeling, and radiative transfer theory.

Improving the accuracy of the charge-sheet model for the long-channel metal-oxide semiconductor field-effect transistor

1987 ◽  
Vol 65 (8) ◽  
pp. 995-998
Author(s):  
N. G. Tarr
Keyword(s):  
Metal Oxide ◽  
Field Effect ◽  
Field Effect Transistor ◽  
Inversion Layer ◽  
Potential Drop ◽  
Metal Oxide Semiconductor ◽  
Oxide Semiconductor ◽  
Analytic Approximation ◽  
Effect Transistor ◽  
Long Channel

It is shown that the accuracy of the charge-sheet model for the long-channel metal-oxide-semiconductor field-effect transistor can be improved by allowing for the small potential drop across the inversion layer, and by using a more accurate analytic approximation for the charge stored in the depletion region.

scholarly journals Analytic approximation of the Tavis–Cummings ground state via projected states

2009 ◽  
Vol 80 (5) ◽  
pp. 055401 ◽  
Author(s):  
Octavio Castaños ◽  
Eduardo Nahmad-Achar ◽  
Ramón López-Peña ◽  
Jorge G Hirsch
Keyword(s):  
Ground State ◽  
Analytic Approximation
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