scholarly journals Analytic solutions of the nonlinear radiation diffusion equation with an instantaneous point source in non-homogeneous media

2021 ◽  
Vol 33 (5) ◽  
pp. 057105
Author(s):  
Menahem Krief
Keyword(s):  
Diffusion Equation ◽  
Point Source ◽  
Analytic Solutions ◽  
Radiation Diffusion ◽  
Nonlinear Radiation ◽  
Instantaneous Point ◽  
Homogeneous Media

Self-similar solutions for a nonlinear radiation diffusion equation

2006 ◽  
Vol 13 (9) ◽  
pp. 092703 ◽  
Author(s):  
Josselin Garnier ◽  
Guy Malinié ◽  
Yves Saillard ◽  
Catherine Cherfils-Clérouin
Keyword(s):  
Diffusion Equation ◽  
Radiation Diffusion ◽  
Nonlinear Radiation ◽  
Self Similar ◽  
Similar Solutions

scholarly journals A consistent approach to solving the radiation diffusion equation

2003 ◽  
Vol 10 (5) ◽  
pp. 1829-1845 ◽  
Author(s):  
James H. Hammer ◽  
Mordecai D. Rosen
Keyword(s):  
Diffusion Equation ◽  
Radiation Diffusion ◽  
Consistent Approach

Filtering for the Inverse Problem of Convection–Diffusion Equation with a Point Source

2012 ◽  
Vol 81 (11) ◽  
pp. 114401 ◽  
Author(s):  
Fujihiro Hamba ◽  
Satoshi Abe ◽  
Daisuke Kitazawa ◽  
Shinsuke Kato
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Point Source ◽  
Convection Diffusion ◽  
Convection Diffusion Equation

scholarly journals The heat radiation diffusion equation: Explicit analytical solutions by improved integral-balance method

2018 ◽  
Vol 22 (2) ◽  
pp. 777-788 ◽  
Author(s):  
Jordan Hristov
Keyword(s):  
Diffusion Equation ◽  
Analytical Solutions ◽  
Approximate Solutions ◽  
Step Change ◽  
Balance Method ◽  
Heat Radiation ◽  
Integration Technique ◽  
Residual Function ◽  
Radiation Diffusion ◽  
Closed Form Solutions

Approximate explicit analytical solutions of the heat radiation diffusion equation by applying the double integration technique of the integral-balance method have been developed. The method allows approximate closed form solutions to be developed. A problem with a step change of the surface temperature and two problems with time dependent boundary conditions have been solved. The error minimization of the approximate solutions has been developed straightforwardly by minimization of the residual function of the governing equation.

Radiation patterns: Possibility for monitoring seismic sources

Geophysics ◽  
1996 ◽  
Vol 61 (1) ◽  
pp. 282-287
Author(s):  
Philip Carrion ◽  
José Carcione ◽  
Edson E. S. Sampaio
Keyword(s):  
Point Source ◽  
Field Measurements ◽  
Seismic Sources ◽  
Seismic Events ◽  
Elastic Media ◽  
Radiation Patterns ◽  
Source Radiation ◽  
Earth Environment ◽  
Source Excitation ◽  
Homogeneous Media

Recent field measurements of the radiation in boreholes indicate that the radiation patterns of real seismic sources are not always in agreement with those corresponding to the point‐source excitation in unbounded homogeneous and isotropic acoustic or elastic media [we refer the reader to Aki and Richards (1980) for the basic discussion on the radiation patterns in homogeneous media]. This mismatch results from the fact that the point‐source radiation patterns corresponding to homogeneous media are too simplistic to satisfy any experiment in the more realistic Earth environment. A study of radiation patterns is certainly important not only to predict possible seismic events but also to analyze the source performance itself by recording seismic arrivals.

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