longitudinal dispersion in nonuniform isotropic porous media

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to a known distribution function. The values may be compared to
tabulated values of K+ (or K-) which give the probability of the
+ ( -
computed K or K). Table A.I shows 30 independent samples of N
1000 using the random number generator given by equations (A.2) and
(A.3). The values of K+ (or K-) which correspond to the given place in
the cumulative distribution when N = 1000 are shown at the bottom of
Table A.I. By comparing the sample with the theoretical values, we see
that no extraordinary behavior is detected. Table A.2 shows a similar
calculation for a single linear congruential random number generator
(equation (A.I». Again, acceptable random behavior is found. The
Kolmogorov-Smirnov test may be applied to the sets of K+ and K- values
displayed in Tables A.I and A.2. This is useful in detecting global
nonrandom behavior in the original sequences. Global nonrandom
behavior refers to deviation from expected random behavior over the
entire sequence of random numbers (which is 30000 random numbers in
this case). The theoretical cumulative distribution for the
Kolmogorov-Smirnov coefficients (K+ and K-) is approximated by
F(x) = 1 - exp(-2x 2 ).
Table A.3 shows the global test as applied to the values in Tables A.I
and A.2. We find that both generators display acceptable bahavior at
the global scale (30000 random numbers). Table A.4 presents a summary
of the constants and seed numbers used in the random number generators
tested.