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Riemann Algorithms

These are algorithms that I have stored under the directory, …/numRecipes/EllipticIntegrals/Riemann


Whitworth's (1981) Isothermal Free-Energy Surface
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Riemann02 (12 June 2020)

Basically the same as "Riemann01," but with the output formatted more clearly. The example output file shown immediately below refers to …

Example Output File


Riemann S-type Ellipsoid having: (b/a,c/a) = (9.000000000000D-01,6.410000000000D-01)

*************
TEST (part 1):

 Elliptic Integrals of the 1st and 2nd kinds:

          phi(deg)             (rad)           asin(k) (deg)          (rad)                 F(phi,k)            E(phi,k)
     5.013357254094D+01  8.749959066267D-01  3.253852919374D+01  5.679044681871D-01  9.090259485521D-01  8.431180475729D-01

            A1                  A2                  A3      
     5.214502732782D-01  5.951310119083D-01  8.834187148135D-01

*************
TEST (part 2):

           a2A12                B12                alpha               beta 
     3.877933612108D-01  2.073376506975D-01  2.472452000855D-01  3.797483470425D+00

             f                 omega                 f_Ad              omega_Ad
    -2.680088866444D-01  1.131374738327D+00 -1.509117086331D+01 -1.507716218767D-01

*************
Table 2:


  Direct (omega,lambda,zeta,f):        1.131374738327      0.150771621841     -0.303218483925     -0.268008886644

  Adjoint (omega,lambda,zeta,f):      -0.150771621877     -1.131374730590      2.275320291519    -15.091170863305

*************

Riemann01 (21 August 2019)

Evaluate terms associated with construction of various Riemann S-type Ellipsoids, especially for comparison with work by Ou (2006). Enter two axis-ratio values: bovera covera (separated by space).

See Also

Whitworth's (1981) Isothermal Free-Energy Surface

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