Polymers in Confined Geometry.pdf

4.4. SIMULATION OF UNCONFINED WORM-LIKE CHAINS 47
So the average and the error are easily calculated with minor storage overhead.
The only drawback is, when a blocking technique has to be used to free the
samples of the ‘omnipresent’ correlation in MC simulations, then all the averages
have to be stored anyway.
4.3.5 Random number generators
The quality of Monte-Carlo simulations depends crucially on the quality of the
pseudo-random numbers used. The quality of the linear congruential generators,
as for example implemented in most standard libraries, have poor statistical
quality and a very small period. Other generators have to be used. There is a
large list of different types but most of them fail to pass statistical tests rather
spectacularly. There is no exact measure for the quality of a generator but there
exists a list of structural mathematical and statistical tests which give a ‘feeling’
for the quality.
A good overview over the important details of random number generators and
examples is given in the review [28].
A fast generator with sufficient quality is based on the linear feedback shift
register or Tausworthe generator (see [27] and [29]). The implementation from
the GNU Scientific Library 5 has been used in our simulation. The advantage of
this generator, besides its structural mathematical qualities, is its speed. The
random number generation consumes up to one forth of the computational time
of our simulations. Test with different generator have been performed, but the
Tausworthe generator seems to be good enough.
If for some reason an even better generator is needed, the RANLUX generator
described in [30] should be used, which can provide, by choice of a numerical
constant, uncorrelated numbers down to the last digit of the used floating point
variable. This has been theoretically justified by chaos theory. The quality of
this generator goes on costs of computational speed which is up to 20 times lower
than in the aforementioned generator.
4.4 Simulation of unconfined worm-like chains
Simulation of semi-flexible polymers are based on the discrete worm-like chain
model as introduced in section 2.3.2. The basic Hamiltonian is given by eq. (2.13),
which can be directly used to perform simulations
N−1
e = βH ({ti}) = −k ˆti · ˆti+1 with k = βεl 2 , (4.25)
i=1
5 http://www.gnu.org/software/gsl/manual/gsl-ref 17.html#SEC262 (17.11.2004)