Application of bradford's law of scattering to the literature of stellar

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PEARL - A Journal of Library and Information Science
Vol. 9, No. 3, July-September 2015: 133-140
DOI : 10.5958/0975-6922.2015.00018.2
Indianjournals.com 133
1
Library Trainee, Indian Institute of Astrophysics, 2nd
Block, Koramangala, Bangalore-560034, India
2
Scientist, Information and Documentation Synthite Industries Ltd., Synthite Valley, Kolenchery-682311, Kerala, India
3
Scientist/Engineer, SC, Library and Documentation, ISRO Headquarters, Antariksh Bhavan, New BEL Road, Bangalore-560 094, India
*Corresponding author email id: iqbal786@isro.gov.in
Application of Bradford’s Law of Scattering to the
Literature of Stellar Physics
Shweta B. Joshi1
Ghouse Modin N. Mamdapur2
Iqbalahmad U. Rajgoli3
*
ABSTRACT
The present paper tests one of the important bibliometric laws of Bradford’s Law of scattering for the literature
related to ‘stellar physics’ for the period 1988-2013 as available in the Web of Science Core Collection database.
A total of 2738 articles related to Stellar Physics published in journals in English language during the study
period are retrieved. Data are analysed with respect to year-wise growth of articles, relative growth rate and
doubling time of literature. The 2738 articles are scattered in 188 journals. A list of ranked journals was
prepared and it was found that the Astrophysical Journal with 895 articles is the most productive journal
publishing Stellar Physics literature followed by Monthly Notices of the Royal Astronomical Society with 507
articles and Astronomy and Astrophysics with 380 articles. In this study, theoretical aspects of Bradford’s Law
of Scattering are tested and found that the data do not fit to the present sample. The Leimkuhler model is tested
and found to fit the data for the Bradford Multiplier (k) at 11.65. The Bradford law is also tested through
graphical formulation by drawing the Bradford bibliograph and is found to confirm all the three characteristics.
Keywords: Bibliometrics, Bradford’s Law of Scattering, Relative Growth Rate, Doubling Time, Stellar
Physics, Ranking of Journals, Bradford Bibliograph
INTRODUCTION
Stellar Physics is a term coined for the research
concerning the formation, evolution, interior and
the atmosphere of stars. The understanding of the
birth and death of stars requires the application
of almost all branches of modern physics. These
areas include: gravitation, hydrodynamics, atomic
physics, liquid-solid state theory, super
conductivity and super fluidity. This distinguishes
it from stellar dynamics, which concerns mainly
gravitational interactions between stars
(Bisnovatyi-Kogan, 2002). Stellar Physics as a
subject is expanding due to the enormous research
undergoing in various facets throughout the
world. Consequent upon this, there is a drastic
growth of literature in the form of research output
through various formats such as journal articles,
conference papers, books, research reports and so
on. Every field of research has few journals (core
journals) where researchers prefer to publish their
research work. Bibliometric techniques are very
useful in determination of various scientific
indicators, evaluation of scientific output, selection
of journals to the libraries and forecasting the
potential of a particular field. Bibliometric analysis
reveals the pattern of growth of literature, inter-
relationship among different branches of
knowledge, productivity, authorship pattern,
degree of collaboration, etc. (Kattimani, 2012). In
this paper, an attempt is made to reveal the
research trends in Stellar Physics and to identify
the core journals in the subject by analyzing the
literature using Bradford’s Law of Scattering by
tapping Web of Science Core Collection database.

134 Vol. 9, No. 3, July - September 2015
Shweta B. Joshi, Ghouse Modin N. Mamdapur and Iqbalahmad U. Rajgoli
OBJECTIVES OF THE STUDY
The present study has been designed with the
following objectives:
 To present growth of Stellar Physics literature.
 To study relative growth rate and doubling
time of Stellar Physics articles.
 To identify the core journals in Stellar Physics.
 To test Bradford’s Law of Scattering.
 To verify Bradford’s Law of Scattering
through the Leimkuhler model and Graphical
formulation.
METHODOLOGY
The research output covered in the Web of Science
Core Collection database has been searched with
the keyword as ‘Stellar Physics’ in the ‘Title’ for
the period 1988-2013 and 2738 articles published
in 188 journals in English language were
downloaded with full bibliographic details for
further analysis.
ANALYSIS AND DISCUSSION
A total of 2738 articles were identified in the field
of ‘Stellar Physics’ for the period from 1988 to
2013. The analysis of the data has been made on
the following aspects to meet the stated objectives.
Growth of Articles
Table 1 presents the year-wise distribution of
articles. It is observed from Table 1 that the highest
number of 298 (8.814%) articles are published in
the year 2011, followed by 287 (8.489%) in 2009
and 273 (8.075%) in 2010. Though the number of
papers published each year is not consistent but
except for the few years the research output in
Stellar Physics is consistently increasing.
Relative Growth Rate and Doubling Time
The relative growth rate (RGR) is the increase in
number of articles per unit of time. The mean
relative growth rate (R) over the specific period
of interval can be calculated from the following
equation:
Loge
W2
– Loge
W1
1 – 2R
=
T2
– T1
where,
1 – 2R
= Mean relative growth rate over the specific
period of interval
Loge
W1
= log of initial number of articles
Loge
W2
= log of final number of articles after a
specific period of interval
T2
– T1
= Unit difference between the initial time
and the final time
aa –1
= average number of articles
The year of publication is taken here as the unit
of time. The RGR for articles is hereby calculated
as below.
Table 1: Year-wise distribution of articles
Publication years No. of papers Percent of 2738
1988 4 0.146
1991 26 0.950
1992 45 1.644
1993 40 1.461
1994 48 1.753
1995 63 2.301
1996 64 2.337
1997 64 2.337
1998 72 2.630
1999 83 3.031
2000 73 2.666
2001 95 3.470
2002 95 3.470
2003 119 4.346
2004 152 5.551
2005 147 5.369
2006 148 5.405
2007 132 4.821
2008 156 5.698
2009 197 7.195
2010 190 6.939
2011 236 8.619
2012 235 8.583
2013 254 9.277
2738 100.00

PEARL - A Journal of Library and Information Science 135
Application of Bradford’s Law of Scattering to the Literature of Stellar Physics
1 – 2R
(aa–1
year–1
) can represent the mean RGR
per unit of articles per unit of year over a specific
period of interval.
Loge
(30) – Loge
(4)
1991 =
1991 – 1988
= 3.40 – 1.39 = 2.01
3 3
1991 = 0.67
Loge
(75) – Loge
(30)
1992 =
1992 – 1991
= 4.32 – 3.40 = 0.92
1 1
1992 = 0.92
In the same way, the relative growth rate for other
years is also calculated (Table 2). The mean relative
growth rate is 0.23.
Table 2: Relative growth rate (RGR) and doubling
time (DT) of publications
Year No. of Cumu- Loge
W1
Loge
W2
RGR DT
publi- lative
cations total
1988 4 4 1.38
1991 26 30 1.38 3.40 0.67 1.03
1992 45 75 3.40 4.32 0.92 0.75
1993 40 115 4.32 4.74 0.42 1.65
1994 48 163 4.74 5.10 0.36 1.92
1995 63 226 5.10 5.42 0.32 2.16
1996 64 290 5.42 5.67 0.25 2.77
1997 64 354 5.67 5.87 0.20 3.46
1998 72 426 5.87 6.05 0.18 3.85
1999 83 509 6.05 6.23 0.18 3.85
2000 73 582 6.23 6.37 0.14 4.95
2001 95 677 6.37 6.52 0.15 4.62
2002 95 772 6.52 6.65 0.13 5.33
2003 119 891 6.65 6.80 0.15 4.62
2004 152 1043 6.80 6.95 0.15 4.62
2005 147 1190 6.95 7.08 0.13 5.33
2006 148 1338 7.08 7.20 0.20 3.46
2007 132 1470 7.20 7.30 0.10 6.93
2008 156 1626 7.30 7.40 0.10 6.93
2009 197 1823 7.40 7.51 0.11 6.30
2010 190 2013 7.51 7.61 0.10 6.93
2011 236 2249 7.61 7.72 0.11 6.30
2012 235 2484 7.72 7.82 0.10 6.93
2013 254 2738 7.82 7.91 0.09 7.70
0
0.2
0.4
0.6
0.8
1
1988
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
Doubling Time (DT)
There exists a direct equivalence between the
relative growth rate and the doubling time. If the
number of articles of a subject doubles during a
given period, then the difference between the
logarithms of numbers at the beginning and end
of this period must be logarithm of the number 2.
If natural logarithm is used, this difference has a
value of 0.693. Thus, the corresponding doubling
time for each specific period of interval and for
articles can be calculated by using the formula:
0.693
Doubling time (DT) =
R
Therefore,
Doubling time for articles:
0.693
Dt (a) =
1 - 2R
(aa-1
year-1
)
0.693 = 1.03
1991 =
0.67
0.693 = 0.75
1992 =
0.92
In the same way, doubling time for other years is
also calculated. The mean doubling time is 4.45.

Table 3: Ranked list of journals
S. Name of the journal No. of Rank
No. articles
1. Astrophysical Journal 895 1
2. Monthly Notices of the Royal 507 2
Astronomical Society
3. Astronomy & Astrophysics 380 3
4. Astrophysical Journal Letters 87 4
5. Astrophysics and Space Science 59 5
6. Physics of Plasmas 50 6
7. Astrophysical Journal Supplement 37 7
Series
8. Nuclear Physics A 28 8
9. Physical Review D 28 8
10. Astronomische Nachrichten 27 9
11. IAU Symposia 27 9
12. Astronomical Journal 26 10
13. Physical Review C 22 11
14. New Astronomy 18 12
15. Publications of the Astronomical 17 13
Society of Japan
16. Physica Scripta 16 14
17. New Astronomy Reviews 14 15
18. Journal of Cosmology and 13 16
Astroparticle Physics
19. Physical Review Letters 13 16
20. Advances in Space Research 12 17
21. American Journal of Physics 12 17
22. Astronomy Astrophysics Supplement 12 17
Series
23. Journal of Mathematical Physics 11 18
24. Physics Letters B 11 18
25. Journal of Chemical Physics 10 19
26. Journal of Physics G: Nuclear and 9 20
Particle Physics
Table 3 contd............
S. Name of the journal No. of Rank
No. articles
27. Nuclear Physics B Proceedings 9 20
Supplements
Society of the Pacific
29. Acta Physica Polonica B 8 21
30. Nature 8 21
31. Science 8 21
32. Acta Astronomica 7 22
33. Chinese Journal of Astronomy and 7 22
Astrophysics
34. Physical Review E 7 22
35. Solar Physics 7 22
36. Comptes Rendus Physique 6 23
37. Journal of High Energy Physics 6 23
38. Physics Essays 6 23
39. Review of Scientific Instruments 6 23
40. Reviews of Modern Physics 6 23
41. Annales Geophysicae 5 24
42. Annual Review of Astronomy and 5 24
Astrophysics
43. Astroparticle Physics 5 24
44. Chaos 5 24
45. Classical and Quantum Gravity 5 24
46. European Physical Journal A 5 24
47. International Journal of Modern 5 24
Physics D
48. International Journal of Modern 5 24
Physics E: Nuclear Physics
49. Journal of the Korean Physical Society 5 24
50. Philosophical Transactions of the 5 24
Royal Society A: Mathematical Physical
and Engineering Sciences
51. Progress in Particle and Nuclear Physics 5 24
52. Progress of Theoretical Physics 5 24
Supplement
Society of Australia
11 Journals with 4 Articles 44
77 Journals with 1 Article 77
188 Journals 2738
Ranked List of Journals
Table 3 provides the rank list of journals preferred
by the authors during the period 1988-2013. The
0
1
2
3
4
5
6
7
8
1988
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012

2738 articles in journals are scattered over 188
journals. The top three journals accounted for
almost 65.08% of total 2738 articles. Astrophysical
Journal has emerged as the most preferred journal
among the researchers of Stellar Physics with 895
(32.70%) articles followed by Monthly Notices of
the Royal Astronomical Society with 507 (18.52%)
articles and Astronomy and Astrophysics with 380
(13.80%) articles.
Bradford’s Law of Scattering
Bradford’s Law of Scattering is a bibliometric law
formulated by Samuel Clement Bradford and
Table 4: Distribution of cited journals by decreasing
frequencies of citations
No. of Cumulative Log of No. of Cumulative
journals No. of cumulative citations citations
journals journals
1 1 0 895 895
1 2 0.30 507 1402
1 3 0.48 380 1782
1 4 0.60 87 1869
1 5 0.70 59 1928
1 6 0.78 50 1978
1 7 0.85 37 2014
2 9 0.95 56 2071
2 11 1.04 54 2125
1 12 1.08 26 2151
1 13 1.11 22 2173
1 14 1.15 18 2191
1 15 1.18 17 2208
1 16 1.20 16 2224
1 17 1.23 14 2238
2 19 1.28 26 2264
3 22 1.34 36 2300
2 24 1.38 22 2322
1 25 1.40 10 2332
3 28 1.45 27 2359
3 31 1.50 24 2383
4 35 1.54 28 2411
5 40 1.60 30 2441
13 53 1.72 65 2506
11 64 1.81 44 2550
17 81 1.91 51 2601
30 111 2.04 60 2661
77 188 2.30 77 2738
188 2738
coined by BC Vickery. Bradford’s Law of
Scattering states that one could assume . . . . ‘that
the bulk of the papers on a specific subject would
be published in a few journals specially devoted
to that subject or to the major subject of which it
forms a part, together with certain border-line
journals and some more general periodicals
(Bradford, 1985).’ Bradford’s Law of Scattering
indicates three productive zones where the
number of journals published increases from one
zone to the next according to the expression
1:n:n2
:n3
. . . . . Accordingly, considering this
expression into the present study, the total 2738
articles are divided into three groups as presented
in Table 5.
Table 5: Zone-wise distribution of journals
Zone No. of No. of Percent of K
journals articles articles
1 1 895 32.70
2 3 974 35.60 3
3 184 869 31.70 61.33
Mean ~ 32.165
It is clear from Table 5 that the first zone (core
journals) contained only 1 journal with 895
(32.70%) articles. The second zone (allied journals)
contained 3 journals with 974 (35.60%) articles.
The third zone (alien journals) contained 184
journals with 869 (31.70%) articles. The summary
of division of zones is as below.
According to Bradford’s Law of Scattering, the
zones, thus identified will form an approximately
geometric series in the form 1:n:n2
. The relationship
of each zone in the present study is 1:3:184. Here,
1 denotes the number of journals in the nucleus
and the mean Bradford multiplier is 32.165.
Hence, 1 : 32.165 × : 1 × (32.165)2
1 : 32.165 : 1034.60 > 1067.765
1067.765 - 188 × 100 = 468%
The Percentage of error =
188
It is clear that the percentage of error is very high
and hence the present data of Stellar Physics
literature does not fit Bradford’s Law of Scattering.

Verification of Bradford Law through the
Leimkuhler Model
The Leimkuhler model is applied to verify
Bradford’s Law of Scattering. In this study both
Bradford’s as well as Leimkuhler’s models are
tested to verify the scattering of literature on Stellar
Physics (Leimkuhler, 1967). The Leimkuhler
model expressed in the form of verbal formulation
of Bradford’s Law of Scattering as:
R(r) = a log(1 + br)
Where, R(r) = cumulative number of articles
contributed by journals of rank 1, 2, 3. …… r
Egghe explained the Leimkuhler model as (Egghe,
1990):
a = Y0
b = k - 1
Log(k) r0
r0
= number of journals in Bradford’s first group
k = Bradford’s multiplier
a and b are the constants appearing in the
Leimkuhler model.
For calculating the Bradford Multiplier, Egghe has
given a mathematical expression as:
k = (e
×ym
)1/p
 = 0.5772 (Euler’s number)
e = 2.718 (constant)
e
= 1.781
p = 3
ym
= number of articles in the most productive
journal (197 in this study)
k = (1.781 × 895) 1/3
k = 11.65
r0
= T(k - 1) r0
= number of journals in
Bradford’s first zone
(kp
- 1) T = Total number of
journals in Bradford zone
r0
= 188(11.65 - 1)
(11.653
- 1)
r0
= 1.27
r1
= r0
× k = 1.27 × 11.65 = 14.80
r2
= r0
× k2
= 1.27 × (11.65)2
= 172.37
y0
= A y0
= number of articles in every Bradford zone
p
y0
= 2738 = 912.67
3
a = y0
= 912.67 = 912.67 = 852.96
Log(k) Log(11.65) 1.07
b = (k - 1) =
(11.65 - 1) = 10.65 = 8.38
r0
1.27 1.27
Therefore, Bradford’s distribution is written as
below:
Table 6: Scattering of journals and articles over
Bradford’s zones
Zone No. of No. of Percent of
journals articles articles
1 1.27 895 32.70
2 14.80 1329 48.53
3 172.37 514 18.77
188.44 2738 100.00
Hence, 1.27 : 1.27 × 11.65 : 1.27 × (11.65)2
1.27 : 14.7955 : 172.37 >> 188.44
188.44 - 188 * 100 = 0.23%
Percentage error =
188
Hence, it can be noted from the above calculations
that the percentage of error is very negligible and
Bradford’s Law of Scattering fits very well in the
present data set for Bradford multiplier k = 11.65.
It can also be noted from Table 6 that the three
zones are not exactly the 1/3rd
of total citations.
Graphical Formulation of Bradford’s Law
(Bradford Bibliograph)
The graphical (formulation) approach was
developed by Brookes which tries to verify the
Verbal formulation of Bradford’s Law (Brookes,
1969). The graph should display three distinct
characteristics:

Table 7: Bradford bibliograph
No. of Cumulative Log of No. of Cumulative
journals No. of cumulative citations citations
journals journals
1 1 0 895 895
1 2 0.30 507 1402
1 3 0.48 380 1782
1 4 0.60 87 1869
1 5 0.70 59 1928
1 6 0.78 50 1978
1 7 0.85 37 2014
2 9 0.95 56 2071
2 11 1.04 54 2125
1 12 1.08 26 2151
1 13 1.11 22 2173
1 14 1.15 18 2191
1 15 1.18 17 2208
1 16 1.20 16 2224
1 17 1.23 14 2238
2 19 1.28 26 2264
3 22 1.34 36 2300
2 24 1.38 22 2322
1 25 1.40 10 2332
3 28 1.45 27 2359
3 31 1.50 24 2383
4 35 1.54 28 2411
5 40 1.60 30 2441
13 53 1.72 65 2506
11 64 1.81 44 2550
17 81 1.91 51 2601
30 111 2.04 60 2661
77 188 2.30 77 2738
188 2738
 initially a rapid rise, indicating core journals
whose points lay on the initial curved part of
the graph until tangentially becomes a straight
line
 then a big portion of linear rise and
 a ‘droop’ towards the tail, Brookes argued that
droop was an indication of the incomplete
nature of the bibliography examined
The graph is plotted for the cumulative number
of citations with respect to the log of cumulative
number of journals. It can be seen clearly from
Figure 3 that very less number of journals are cited
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000
0
0.3
0.48
0.6
0.7
0.78
0.85
0.95
1.04
1.08
1.11
1.15
1.18
1.2
1.23
1.28
1.34
1.38
1.4
1.45
1.5
1.54
1.6
1.72
1.81
1.91
2.04
2.3
Log of Cumulative Number of Journals
CumulativeNumberofCitations
highly and the maximum number of journals cited
are very less.
CONCLUSION
Bibliometric studies have been very useful in
determining various scientific indicators,
evaluation of scientific/research output, selection
of journals for libraries and in understanding
growth and development of a research field.
Libraries have the responsibility of selecting and
procuring the best literature in the form of books
and journals in a given field of research. As cost
of books and subscription amount of journals is
increasing at a rapid pace, it is increasingly
important for libraries to carefully select the
resources. Bradford’s Law of Scattering is one such
bibliometric law which is helpful in selecting core
journals in a research field. In this study an
attempt is made to apply Bradford’s Law of
Scattering to the journal articles literature of Stellar
Physics for the period 1988-2013. Search in Web
of Science Core Collection database retrieved 2738
articles published in 188 journals. According to
Bradford’s Law of Scattering, the articles in each
zone should be equal, which does not hold good
in the present study. The percentage of deviation
in three zones and the percentage of error are also
too high. Therefore, Bradford’s Law is verified
through the Leimkuhler model. It can be
concluded that the theoretical aspects of
Bradford’s Law are successfully verified through
verbal formulation given by Leimkuhler. Bradford
Bibliograph is drawn and confirms all the three

characteristics. This study will be very useful to
the researchers in the field of astronomy and
astrophysics for publishing their research work
and to the libraries for subscribing to the core
journals in the field of Stellar Physics.
REFERENCES
Bisnovatyi-Kogan GS, 2002. Stellar Physics, Vol. 2: Stellar
Evolution and Stability, Springer-Verlag; Berlin, pp. 1–4.
Bradford SC, 1985. Sources of information on specific subjects.
Journal of Information Science, Vol. 10, No. 4, pp. 173–180.
Brookes BC, 1969. Bradford’s law and the bibliography of
science. Nature, Vol. 224, pp. 953–956.
Egghe L, 1990. Note on different Bradford multipliers. Journal
of the American Society for Information Science and
Technology, Vol. 43, No. 3, pp. 204–209.
Kattimani PS, 2012. Indian contributions in the field of
emotional intelligence (1999-2003): a scientometric
study. International Journal of Information Dissemination and
Technology, Vol. 2, No. 3, pp. 196–200. Online [http://
www.ijidt.com/index.php/ijidt/article/view/200]
(Accessed on 15.02.2015).
Leimkuhler FF, 1967. The Bradford distribution. Journal of
Documentation, Vol. 23, No. 3, pp. 197–207.

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