Programs in Physics & Physical Chemistry
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|Manuscript Title: A program package for the Landau distribution.|
|Authors: K.S. Kolbig, B. Schorr|
|Program title: LANDAU|
|Catalogue identifier: ABAD_v1_0|
Distribution format: tar.gz
|Journal reference: Comput. Phys. Commun. 31(1984)97|
|Programming language: Fortran.|
|Computer: CDC 7600.|
|Operating system: CDC SCOPE.|
|RAM: 3K words|
|Word size: 60|
|Keywords: Nuclear physics, Landau density, Landau distribution, Landau random numbers, Ionization losses, Energy loss simulation, Energy loss data fitting.|
Nature of problem:
The density phi(lambda) of the Landau distribution, as well as the corresponding distribution function Phi(lambda) and its inverse Psi(x), are used to describe the energy loss of charged particles traversing a thin layer of material. The first two moments Phi1(x), Phi2(x) of the densityfunction truncated on the right-hand tail, as well as the derivative phi'(lambda) = dphi(lambda)/dlambda, are also needed in this field. For Monte Carlo simulations it is of particular interest to have a random number generator for the full and the truncated Landau distribution. The function psi(x) for 0 < x < 1 can be used for this purpose. The other functions are important for fitting a truncated Landau distribution to measured or simulated energy-loss data.
The functions phi(lambda) : DESLAN(X) phi(lambda) : DISLAN(X) phi'(lambda) : DIFLAN(X) phi1(x) : XM1LAN(X) phi2(x) : XM2LAN(X)are calculated from rational approximations and asymptotic expressions for any real argument lambda or x. In view of the high speed required, the program for the Landau random numbers
psi(x) : RANLAN(Xconsists essentially of a table from which psi(x) is computed by linear or quadratic interpolation. In this case, x is restricted to 0 < x < 1.
The following table gives an indication of the running time on the CDC 7600 computer for the different subprograms. The figures were obtained by computing 40000 function values for arguments distributed at random in the given intervals.
Function Interval Time DELAN phi(lambda) -5 < lambda < 200 15.2 DISLAN phi(lambda) -5 < lambda < 200 14.3 DIFLAN phi'(lambda) -5 < lambda < 200 16.7 XM1LAN phi1(x) -5 < x < 200 17.3 XM2LAN phi2(x) -5 < x < 200 13.4 RANLAN psi(x) 0 < x < 1 8.1
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