Herr Bauer, I got the referee report
on your article, although the referee did not used the form we provided, the
recommendation is to accept the paper provided you incorporate the
recommendations listed below.
I ask you to please modify your
paper and send me a revised version.
I thank you ahead of time for your
prompt answer.
Best wishes . . .
Jorge
Jorge A.
López
Chair and Shumaker
professor
Physics Dept.,
UTEP
915-747-7528
http://jorgelopez.utep.edu/JorgeNYT/jorge.html
Report on manuscript "Zipf's Law and the Universality
Class of the Fragmentation Phase Transition" by W. Bauer, S. Pratt and B.
Alleman,
submitted for publication to Acta Phys.
Hung.
The goal of this work is to study the link between a
Zipf's law on the ranking of the clusters and a power law average yield of
cluster sizes. This (or closely related problems) has been addressed previously
in refs. (a) and (b) cited below and in ref. [15], among others. Following a
more complicated reasoning (in particular assuming that the probabilities to
have k (small) clusters in a given event are Poissonian, which is not
necessary), the authors calculate the probability that a cluster of given size
is the largest one (eq. (9)) and the same for the second biggest (eq. (11)).
This part of the paper is very detailed and easy to follow (notice some
misprints quoted below). In contrast, a big jump is made when claiming on top of
page 5 that "If one uses an expansion for our analytical results, one finds that
the average cluster size as a function of rank r follows a more general
Zipf-Mandelbrot distribution...". It is not clear how one goes from r=2 to a
general formula. In addition, because this result is in disagreement with
the above mentioned works (in which a "generalized Zipf's law, with lambda given
by the same eq. (13) is found):
i) The derivation of equ. (12) and (13)
should be presented.
ii) The reasons of the discrepancies with
previous works should be explained.
iii) The values of lambda reported on
bottom of page 4 show large deviations with respect to the predictions of eq.
(13). Why ?
Because Zipf's law is becoming a popular tool for some
experimental groups working in nuclear fragmentation, I believe it is important
to clearly explain why this method of analysis is not bringing any new
information. This message should appear more strongly in the
paper.
- On top of page 3 one should read "...of size A is
<N(A)>=..."
- In equation (8), the exponential should be
exp(-<N(i)> and n! should be k!
- In equation (9), the last exponential should be
exp(-[....])
- In figure. 3 (left), one should replace t=2 by
tau=2
- In the caption of figure 3, the last sentence is:
"Dashed line: asymptotic
expansion of equation 13". I do not understand
what means an asymptotic
expansion of this equation.
- Ref. [15] has been published in Phys. Rev. C72,
057602(2005).
(a) J. Bouchaud and M. Potters, in Theory of Financial
Risk and Derivative Pricing, page 19, Cambridge University Press, 2nd edition,
(2003).
(b) M. Newman, Contemporary Physics, 46, 323
(2005).
(c) L. A. Adamic,
www.hpl.hp.com/research/idl/papers/ranking/ranking.html.