Inverse solution for one-dimensional infiltration, and the ratio a/K1

1990 ◽  
Vol 26 (9) ◽  
pp. 2023-2027 ◽  
Author(s):  
J. R. Philip
Keyword(s):  
Inverse Solution ◽  
One Dimensional

Reply by author to Dr. Naidu’s discussion

Geophysics ◽  
1971 ◽  
Vol 36 (3) ◽  
pp. 618-618
Author(s):  
D. J. Gendzwill
Keyword(s):  
Density Distribution ◽  
Gravity Model ◽  
Fourier Transformation ◽  
Exact Expression ◽  
Inverse Solution ◽  
Density Contrast ◽  
Closed Expression ◽  
One Dimensional ◽  
Particular Solution ◽  
Density Pattern

I appreciate Dr. Naidu’s interest in my paper. He has omitted some detail in the equations (such as the factor G) but the sense of his argument is perfectly clear, and I agree that the method of Fourier transformation is more general than my particular solution. In fact, Novosolitskii (1965) has presented the inverse solution for any horizontal density distribution in a slab. Nevertheless, it seems to me that the existence of a closed exact expression for the model I discussed is of some interest in that it presents a unique formula for an elementary gravity model. The closed expression may be manipulated to derive characteristic interpretation curves such as those presented. The gradational density contrast models may be superimposed to produce almost any arbitrary one‐dimensional density pattern in a slab.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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