Evolution of Physics Sub-fields
Murali Krishna Enduri
1 a
, I. Vinod Reddy
2 b
and Shivakumar Jolad
3 c
1
SRM University-AP, Andhra Pradesh 522502, India
2
Indian Institute of Technology Bhilai, Chhattisgarh 492015, India
3
FLAME University, Pune, Maharashtra 412115, India
Keywords:
PACS Codes, Sub-fields, Physics.
Abstract:
We study the evolution and relationships between sub-fields of Physics using the large data set of articles
published in the various physical review journals from 1985-2010. Each article is assigned to some PACS
codes by their authors which represent specific sub-fields of Physics. We construct a weighted network with
nodes as PACS codes and there is a link between two PACS codes if there is an article assigned to both these
codes. The weight of a link represents the number of articles in which both PACS codes appears. We study the
time evolution of PACS network at various hierarchy levels of PACS codes. We observe that sub-fields Physics
of elementary particles and fields, Nuclear Physics and Condensed matter physics have stronger connections
inside the field compared to connections to other sub-fields. We also observe that both condensed matter
physics sub-fields are strongly related compared to any other pair of sub-fields.
1 INTRODUCTION
Scientific disciplines are becoming increasingly inter-
connected. New fields of research have emerged by
integrating concepts, ideas and tools different disci-
plines. Tracking the emergence of new areas can give
insights into working of scientific enterprise. Among
the natural sciences, Physics once considered most
rigid has become increasingly fluid. Not only differ-
ent sub fields of Physics are being merged/mixed to
create new ares of physics, but are being widely dif-
ferent areas such as study of system biology, social
dynamics, complex networks, etc.
With the emergence of Network Science to un-
derstand the study of complex networks using tools
from statistical physics, dynamical systems and com-
puter science, and availability of large data sets
we can approach the evolution from Network Dy-
namics perspective (Newman, 2001), (Palla et al.,
2007),(Palla et al., 2005), (Kumpula et al., 2008). Es-
pecially for physics there are many studies on Evolu-
tion of Physics Sub-Fields such as (Battiston et al.,
2019),(Liu et al., 2017), (Jia et al., 2017),(Sinatra
et al., 2015) (Dias et al., 2018) and (Pan et al., 2012).
Palla et al.(Palla et al., 2005) studied the evolution
a
https://orcid.org/0000-0002-9029-2187
b
https://orcid.org/0000-0002-0365-1138
c
https://orcid.org/0000-0001-9523-1693
of communities in weighted networks using Clique
Percolation Method (CPM) characterizing the com-
munity growth, merge split, and extinction.
The publications in American Physical Society
(APS) Journals covers all branches of physics from
1900’s. Articles published in APS journals from
1985 on wards carry subject classification codes
from Physics and Astronomy Classification System
(PACS). In past many authors have constructed PACS
network representing the interconnection between the
sub-fields and studied their dynamics.
Herrera et al. (Herrera et al., 2010) studied the
evolution of communities (physics fields) and found
that size of communities tend to increase with age of
communities and these communities will have higher
number of papers. Their analysis was restricted to
third level in PACS hierarchy. In Omodei et al.
(Omodei et al., 2013) analyzed the epistemic net-
works of PACS codes and socio-epistemic network of
authors and PACS codes influence the dynamics of
each other. Martin et al. (Martin et al., 2013), Red-
ner (REDNER, 2005) studied the co-authorship and
citations networks, observed that the tendency of au-
thors cite themselves or their collaborators is higher
than others. Pan et al. (Pan et al., 2012) studied
PACS networks evolution through k-shell decompo-
sition and observed that over the time there has been
an increase in the interdisciplinarity inside physics.
88
Enduri, M., Reddy, I. and Jolad, S.
Evolution of Physics Sub-fields.
DOI: 10.5220/0009424900880095
In Proceedings of the 5th International Conference on Complexity, Future Information Systems and Risk (COMPLEXIS 2020), pages 88-95
ISBN: 978-989-758-427-5
Copyright
c
2020 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
However, their work did not include the community
evolution.
In this work we study the evolution and rela-
tionships between the sub-fields of physics using the
physical review journals data. The rest of the paper
organized as follows. In Section 2, we give a short
description of our data set and PACS codes. In Sec-
tion 3, we describe the network construction by using
the PACS codes from prepared data set. In section 4,
we analyse the trend of single field papers in a field
for every five years with one and two level of PACS
hierarchy. In the results section, we study correla-
tion between the different sub-fields of physics using
PACS network at different hierarchy levels. Finally,
in the last section we conclude this paper and present
some future research direction.
2 DATA SET
The American Physical Society (APS) started pub-
lishing Physical Review journal from 1893. APS
added other journals like Reviews of Modern Physics
(1929), Physical Review Letters (1958), Physical Re-
view A,B,C and D (1970), Physical Review E (1993)
and most recently Physical Review X in 2011. In our
analysis we use all scientific papers published in APS
Physical Review (PR) journals from 1985 to 2010.
Metadata of each journal article contains an unique
digital object identifier (DOI), title, authors of paper,
date of publication, affiliations of each author, PACS
codes, references to other cited Physical review arti-
cles. We primarily use PACS codes, described below,
to identify the different sub-fields the articles belong
to. PACS is a hierarchical classification scheme devel-
oped by American Institute of Physics (AIP), repre-
senting different fields and sub-fields of Physics up to
five levels. The first level in the PACS hierarchy clas-
sifies the ten main fields of Physics such as general
Particle Physics, Nuclear Physics, Condensed Mat-
ter, Atomic and Molecular Physics etc, as shown in
the Figure 1. A journal article may contain PACS
codes one or many of these main fields. A PACS
code consists of two pairs of numbers followed by
a pair of non numeric characters, separated by dots.
For example in PACS code 04.25.dg, the first digit
0 represents General Physics, 4 - General relativity
and gravitation, 25 - Approximation methods; equa-
tions of motion and d represents Numerical relativ-
ity and g represents Numerical studies of black holes
and black-hole binaries. PACS codes are regularly
revised and updated overtime by American Institute
of Physics (AIP), new codes are introduced and some
codes are deleted. In our analysis we consider PACS
codes up to third level (first four digits) of hierarchy
as they are reasonably stable upto this level and rep-
resents all sub-fields of physics. We ignore the higher
level hierarchy to maintain consistency PACS codes
of all papers in our analysis. PACS codes were in-
troduced 1975 but large fraction of papers published
between 1975 and 1984 have not assigned any PACS
codes. Therefore we confined our analysis to the pa-
pers published between 1985 to 2010, as the usage to-
wards PACS code jumped to more than 90% and have
been consistently high since then. There is variation
in the PACS codes after 2010. So we consider only
data in between 1985 to 2010. Basic statistics of our
data set is given in Table 1.
Table 1: Basic statistics of the data set 1985-2012.
Number of authors 343055
Number of papers 399713
Average number of papers by an au-
thor
9.07
Average number of authors per paper 7.59
Average number of PACS codes per
author
10.04
Average number of PACS codes per
paper
2.92
3 NETWORK CONSTRUCTION
We construct a PACS network, where the nodes rep-
resents the PACS codes and there is an edge between
two PACS codes if they have appeared in the same
article (Herrera et al., 2010).
The weight of an edge between two nodes i and j
is defined as
s
i j
=
∑
p∈S
1
n
p
− 1
(1)
Where S is the set of papers which belongs to both
fields i and j and n
p
is the number of scientific fields
contained in PACS codes of paper p.
We construct two different PACS networks. The
first network contains 10 nodes representing the broad
research areas (shown in Figure 1) in physics. To con-
struct this network we treat all the PACS codes with
same first digit as a single node. The second network
contains 100 nodes representing sub-fields of physics
up to the second level of hierarchy. In this network
the PACS codes with same first two digits treated as a
single node. We use this PACS networks to study the
evolution of relationship between different sub-fields
of physics with time.
Evolution of Physics Sub-fields
89
90
Geophysics, Astronomy and Astrophysics
80
Interdisciplinary Physics and Related Areas
of Science and Technology
70
Condensed Matter: Electronic Structure, Electrical,
Magnetic, and Optical Properties
60
Condensed Matter: Structural, Mechanical and
Thermal Properties
50
Physics of Gases, Plasmas, and Electric Discharges
40
Electromagnetism,Optics, Acoustics, Heat Transfer,
Classical Mechanics, and Fluid Dynamics
30
Atomic and Molecular Physics
20
Nuclear Physics
10
Physics of Elementary Particles and Fields
00
General Physics
1
Figure 1: Sub-Fields of Physics based on PACS codes.
4 RESULTS
In the next subsections we present observation made
by analyzing the PACS network at different hierarchy
levels.
4.1 Descriptive Analysis of Single Field
Articles
We call an article as single field article if it is as-
signed only one PACS code. These articles are highly
specialized in one field and does not contribute to
the weights of the PACS network. However they are
helpful to define the extent to which a field is intra-
disciplinary as opposed to interdisciplinary. We ana-
lyze the single field articles at first and second levels
of hierarchy of PACS codes.
Example 1. The set of PACS codes S =
{71.10.Ca, 71.15.Dx, 72.15.Rn} represents sin-
gle field, two fields and three fields when restricted to
first, second and third level of hierarchy respectively.
The fraction of single field papers in a field is de-
fined as the ratio of number of single field papers to
total number of papers published in that field. For
both first and second level the fraction of single field
papers for each field are shown in Figure 2 for pa-
pers published between 1985-2010. In both the cases
we observe that high fraction of single field papers
are from the fields Physics of elementary particles
and fields, Nuclear Physics and Condensed matter
physics. In order to verify whether this trend is uni-
form over all the years we performed similar analysis
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0
0 . 1
0 . 2
0 . 3
0 . 4
0 . 5
0 . 6
F i r s t L e v e l
F r a c t i o n o f P a p e r s
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0
0 . 0
0 . 1
0 . 2
0 . 3
0 . 4
0 . 5
S u b f i e l d s o f P h y s i c s i n d i c a t e d b y t h e i r l e v e l o f P A C S h i e r a r c h y f r o m 1 9 8 5 - 2 0 1 0
F r a c t i o n o f P a p e r s
S e c o n d L e v e l
Figure 2: Fraction of single field articles at first and sec-
ond levels of PACS hierarchy respectively for the articles
published between 1985-2010.
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0
1
2
3
4
5
0
1 9 8 5 - 2 0 1 0
Figure 3: In and out ratio 1985-2010.
1 7 %
2 4 %
2 8 %
2 5 %
1 4 %
2 4 %
2 3 %
2 1 %
1 1 %
1 3 %
1 7 %
1 6 %
2 1 %
2 3 %
1 9 %
2 1 %
2 2 %
2 3 %
1 4 %
1 5 %
2 0 %
2 1 %
1 9 %
2 0 %
2 1 %
2 0 %
2 0 %
1 9 %
2 1 %
1 9 %
2 2 %
2 0 %
1 7 %
1 7 %
2 2 %
1 9 %
1 8 %
1 9 %
2 5 %
2 4 %
2 3 %
1 9 %
1 5 %
1 6 %
2 4 %
1 6 %
1 6 %
1 8 %
2 9 %
2 8 %
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0
0
2 5
5 0
7 5
1 0 0
P e r c e n t a g e
S u b f i e l d s o f p h y s i c s i n d i c a t e d b y t h e i r f i r s t l e v e l o f P A C S h i e r a r c h y
2 0 0 6 - 2 0 1 0 2 0 0 1 - 2 0 0 5 1 9 9 6 - 2 0 0 0
1 9 9 1 - 1 9 9 5 1 9 8 6 - 1 9 9 0
Figure 4: Evolution of fraction of single field articles over
the time at first level of PACS hierarchy over the time.
(see Figure 9) for every five years and observed the
similar trend. The reason for these fields to have high
fraction of single field papers might be they are well
established and researchers are able to write papers
without using the knowledge from other fields. For a
specific field, we call the ratio of the number of sin-
gle field articles in that field to the total number of
COMPLEXIS 2020 - 5th International Conference on Complexity, Future Information Systems and Risk
90
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0
0
2 5
5 0
7 5
1 0 0
P e r c e n t a g e
S u b f i e l d s o f p h y s i c s i n d i c a t e d b y t h e i r f i r s t l e v e l o f P A C S h i e r a r c h y
2 0 0 6 - 2 0 1 0 2 0 0 1 - 2 0 0 5 1 9 9 6 - 2 0 0 0
1 9 9 1 - 1 9 9 5 1 9 8 6 - 1 9 9 0
Second
Figure 5: Evolution of fraction of single field articles over
the time at second level of PACS hierarchy over the time.
Figure 6: First level PACS network.
articles published in that field as in/out ratio of that
field. The in/out ratio of top ten level sub-fields of
physics is shown in the Figure 3. The in/out ratio for
fields Physics of elementary particle and fields, Nu-
clear Physics and Condensed matter physics is greater
than one indicating that these fields have stronger
connections inside the fields compared to outside the
fields.
We analyzed the evolution of fraction of single
field articles over the time. Figure 4 and 5 shows frac-
tion of papers with single field over every five years
for first and second level of PACS hierarchy. We ob-
serve that over the time fraction of single fields are
decreasing. This might be due to increase in interdis-
ciplinary research.
5 EVOLUTION OF SUB-FIELDS
OF PHYSICS
In this section we study the evolution of relation be-
tween sub fields of physics from 1985-2010 at differ-
ent hierarchy levels.
Figure 7: Intensity plot showing the strength between sub-
fields of Physics at second level of PACS hierarchy.
5.1 First Level
We build a weighted PACS network by considering
PACS codes at first level of hierarchy. This network
contains ten nodes which represents the broad sub-
fields of physics. Figure 6 shows the weighted PACS
network for time period 1985-2010. We observe that
two condensed matter physics fields are strongly re-
lated. We can also see there are strong connections
from General physics to Condensed matter physics,
Interdisciplinary Physics (80), Electromagnetism (40)
and Nuclear Physics (20). To test whether this trend
is uniform over the period 1985-2010, we constructed
the same network for every five year interval (see ap-
pendix Figure 11). In all five-intervals we observe the
same trend showing the strong relationship between
the two condensed matter sub-fields.
5.2 Second Level
In this section, we study evolution of relation be-
tween the different sub-fields of physics using PACS
network by considering the PACS codes up to sec-
ond level of hierarchy. We have constructed a net-
work whose nodes are sub-fields of physics and there
is a edge between the two sub-fields if there is at
least one paper containing both sub-fields in its PACS
codes. Therefore we have at most 100 nodes denoted
as {00, 01, ··· , 99}. The edge weight w
i j
between the
two nodes i and j is defined as in equation (1).
Previously Pan et al.(Pan et al., 2012) have per-
formed k-shell analysis to understand the evolution of
PACS network. High and low k-shell indices indicates
the position of a node in core and periphery of the net-
work respectively. This does not captures the strength
of outside connection of a node, since a node may be
in core due to high internal connections. We define
Evolution of Physics Sub-fields
91
Figure 8: Evolution of communities in the PACS network for every five year intervals. The size of a block indicates the size
of a PACS community. The width of shaded flows corresponds to the fraction of PACS codes moving from one community to
another.
the in-strength and out-strength of node i (sub-field)
as follows.
i
in
=
∑
j∈V(G) : i and j have same first digit
w
i j
(2)
i
out
=
∑
j∈V(G) : i and j have different first digit
w
i j
(3)
Figure 3 shows that ratio of in and out strength for
each node for the time period 1985-2010. We observe
that for nodes {10, ··· 29, 70, ··· 79} which represent
the fields Physics of Elementary Particle and Fields,
Nuclear Physics and Condensed matter physics have
the in out ratio is more than one indicating that these
fields more interconnected and less interdisciplinary.
The intensity plot of strength between the sub-
fields of physics for second level of hierarchy are
shown in Figure 7. We observe that there is a
high cross-discipline interactions between Condensed
matter Physics (60,70) and Interdisciplinary Physics
(80). From the both the time periods we observe that
most of the papers published in Nuclear Physics (20),
Atomic and Molecular Physics (30), are either single
PAC papers or contains more than one PAC from same
disciplines.
5.3 Third Level
We use the CFinder algorithm to study the evolu-
tion of scientific fields which is based on the Palla et
al. (Palla et al., 2005),(Kumpula et al., 2008) clique
percolation method (CPM). A k-clique community
is defined as the union of all k-cliques that can be
reached from each other through a series of adjacent
k-cliques. Two k-cliques are said to be adjacent if
they share k-1 nodes.
Before applying the CPM method to PACS net-
work we preprocess the data by removing links
weaker than a fixed threshold W . We take the thresh-
old as the geometric mean of all its edge weights. We
remove all links whose weight is less than threshold
value.
The value of the k is chosen based on the follow-
ing properties (a) The number of communities is as
Table 2: Basic statistics of PACS network 1985-2010.
Number of nodes 914
Number of edges 51015
Average degree 111.63
Network diameter 4.0
Average Path Length 2.031
Modularity 0.515
Graph density 0.122
COMPLEXIS 2020 - 5th International Conference on Complexity, Future Information Systems and Risk
92
large as possible (b) Avoid the excessively large com-
munities. We consider value of k is 10 and shown
the evolution of communities over every 5 years span
(see Figure 8). We observe that from this Figure 8,
very few cross links in the 1985 to 1989 and very high
cross links in 2005 to 2009. This indicate the interdis-
ciplinary increase over the years.
6 DISCUSSION AND
CONCLUSION
We have studied the evolution of sub fields of physics
with the help of PACS codes used in all published ar-
ticles in Physical Review journal from 1985 to 2010.
We have constructed network using PACS codes.
First we have analyzed single field articles at differ-
ent hierarchy levels of PACS codes and observed that
high fraction of single field articles are from the fields
of Physics of elementary particles and fields, Nuclear
Physics and Condensed matter physics. We have ob-
served that this trend is uniform over all the years
by performing similar analysis for every five years.
We studied the inter and intra strength of PACS codes
and showed that Physics of elementary particle and
fields, Nuclear Physics and Condensed matter physics
is greater than one indicating that these fields have
stronger intra connections compared to inter connec-
tions.
Furthermore we studied the correlation between
the different fields of physics at different levels of
PACS hierarchy starting form first level to third level.
From the first level analysis we observed that both
structural and electronic condensed matter physics are
strongly related in the sense that many published ar-
ticles cite PACS codes from both these fields. In the
second level we analyzed strength of connections be-
tween the fields of physics using intensity plot. The
analysis shows that Nuclear Physics (20) and Molec-
ular Physics (30) have weak connections to the other
fields. Whereas there is a high cross-discipline in-
teractions between condensed matter physics (60, 70)
and interdisciplinary physics (80).
In future direction, we can quantify the interdisci-
plinary by using this PACS code network over years.
To do this we need to define a measure which mea-
sures the interdisciplinary. We constructed a PACS
network, where the nodes represents the PACS codes
and there is an edge between two PACS codes if they
have appeared in the same article. We can also create
network, there is an edge between two PACS codes
if both PACS codes used by single author. This also
gives us one more direction to measure the interdisci-
plinary.
ACKNOWLEDGEMENTS
The authors would like to thank American Physical
Society for providing us with the meta data of all
Physical Review journal articles with PACS codes.
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APPENDIX
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0
0 . 0
0 . 2
0 . 4
0 . 6 0 . 0
0 . 2
0 . 4
0 . 60 . 0
0 . 2
0 . 4
0 . 6 0 . 0
0 . 2
0 . 4
0 . 60 . 0
0 . 2
0 . 4
0 . 6
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0
S u b f i e l d s o f p h y s i c s i n d i c a t e d b y t h e i r
s e c o n d l e v e l o f P A C S h i e r a r c h y
1 9 8 6 - 1 9 9 0
0
0
1 9 9 1 - 1 9 9 5
F r a c t i o n o f p a p e r s
1 9 9 6 - 2 0 0 0
2 0 0 1 - 2 0 0 5
2 0 0 6 - 2 0 1 0
Figure 9: Fraction of single field papers for both first and second level for five year interval.
Figure 10: Intensity of two subfield for every 5 years span((a) 1986-1990 (b)1991-1995 (c) 1996-2000 (d) 2001-2005 (e)
2006-2010).
COMPLEXIS 2020 - 5th International Conference on Complexity, Future Information Systems and Risk
94
Figure 11: Strength of network for every 5 years span ((a) 1986-1990 (b)1991-1995 (c) 1996-2000 (d) 2001-2005 (e) 2006-
2010).
Evolution of Physics Sub-fields
95