Prabhu Lal Bhatnagar (8 August 1912 – 5 October 1976), commonly addressed as P. L. Bhatnagar, was an Indian mathematician known for his contribution to the
Bhatnagar–Gross–Krook operator
The Bhatnagar–Gross–Krook operator (abbreviated BGK operator) term refers to a collision operator used in the Boltzmann equation and in the lattice Boltzmann method, a computational fluid dynamics technique. It is given by the formula
: \O ...
used in
Lattice Boltzmann methods
The lattice Boltzmann methods (LBM), originated from the lattice gas automata (LGA) method (Hardy- Pomeau-Pazzis and Frisch- Hasslacher- Pomeau models), is a class of computational fluid dynamics (CFD) methods for fluid simulation. Instead of s ...
(LBM).
Early years and career
He was born in
Kota in Rajasthan and was the second of five sons. He did his schooling in
Rampura and later at Herberter College in Kota. After schooling he went to Maharajah's College in
Jaipur
Jaipur (; , ) is the List of state and union territory capitals in India, capital and the List of cities and towns in Rajasthan, largest city of the north-western States and union territories of India, Indian state of Rajasthan. , the city had ...
where in 1935 he completed BSc with first rank, followed by MSc.
His research career started at the
Allahabad University
The University of Allahabad is a Central University located in Prayagraj, Uttar Pradesh. It was established on 23 September 1887 by an act of Parliament and is recognised as an Institute of National Importance (INI). It is the 4th oldest mode ...
under the supervision of Prof. B. N. Prasad on summability theory but soon he joined Prof. Amiya Charan Banerjee to work in differential equations. The results of his work (with Prof. Banerji, published in Proceeding of National Academy of Sciences, 1938) are included in the book of
Erich Kamke. He became interested in the area of
astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the ...
after coming in contact with
Meghnad Saha
Meghnad Saha (6 October 1893 – 16 February 1956) was an Indian astrophysicist and politician who helped devise the theory of Thermal ionization, thermal ionisation. His Saha ionization equation, Saha ionisation equation allowed astronomers to ...
. In 1939 he obtained DPhil degree in mathematics for his thesis titled ''On the Origin of the Solar System''.
In 1939 he joined
St. Stephen's College, Delhi on the invitation of
S. N. Mukherjee and spent the next 16 years there. There he worked on the theory of
white dwarf
A white dwarf is a Compact star, stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very density, dense: in an Earth sized volume, it packs a mass that is comparable to the Sun. No nuclear fusion takes place i ...
s, independently and together with
Daulat Singh Kothari.
In 1952 he was invited to
Harvard University
Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
as a
Fulbright scholar
The Fulbright Program, including the Fulbright–Hays Program, is one of several United States cultural exchange programs with the goal of improving intercultural relations, cultural diplomacy, and intercultural competence between the peopl ...
. There he worked together with
Donald Howard Menzel and
Hari Kesab Singh in the field of non-linear gases. His work with the
Boltzmann equation
The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium; it was devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G ...
led to his well-known BGK collision model in 1954 together with
Eugene P. Gross and
Max Krook. It was at first extensively developed for ionized gases with many applications. These days, the BGK collision operator is essential for the recent development of lattice Boltzmann automata methods.
In 1950 he was elected fellow of
Indian National Science Academy
The Indian National Science Academy (INSA) is a national academy in New Delhi
New Delhi (; ) is the Capital city, capital of India and a part of the Delhi, National Capital Territory of Delhi (NCT). New Delhi is the seat of all three b ...
and in 1955 the fellow of
Indian Academy of Sciences. In 1956 he was invited to join
Indian Institute of Science
The Indian Institute of Science (IISc) is a Public university, public, Deemed university, deemed, research university for higher education and research in science, engineering, design, and management. It is located in Bengaluru, Karnataka. The ...
as the founding Professor of the Department of Applied Mathematics. There he expanded his research area into the field of non-Newtonian fluid mechanics. Alongside to his research work he also laid down the foundation stone of the
Indian National Mathematics Olympiad. For his contributions to the nation, on 26 January 1968 he was awarded the
Padma Bhushan
The Padma Bhushan (IAST: ''Padma Bhūṣaṇa'', lit. 'Lotus Decoration') is the third-highest civilian award in the Republic of India, preceded by the Bharat Ratna and the Padma Vibhushan and followed by the Padma Shri. Instituted on 2 Januar ...
.
During the early 1960s he developed complications in the lower spinal region and was operated on in the United States. In 1969 he moved to
Rajasthan University in
Jaipur
Jaipur (; , ) is the List of state and union territory capitals in India, capital and the List of cities and towns in Rajasthan, largest city of the north-western States and union territories of India, Indian state of Rajasthan. , the city had ...
as Vice-Chancellor and in 1971 joined
Himachal Pradesh University
Himachal Pradesh University (HPU) is a Public university, public State university (India), state university at Summer Hill, Shimla, Summer Hill, Shimla, Himachal Pradesh. It was established on 22 July 1970 by ''The Himachal Pradesh University A ...
in
Shimla
Shimla, also known as Simla ( the official name until 1972), is the capital and the largest city of the northern Indian state of Himachal Pradesh. In 1864, Shimla was declared the summer capital of British India. After independence, the city ...
as Head of the Mathematics Department. He was also member of the Union Public
Service Commission and the first Director of the Mehta Research Institute (now renamed as the
Harish-Chandra Research Institute).
Honors and awards
He was awarded the
Padma Bhushan
The Padma Bhushan (IAST: ''Padma Bhūṣaṇa'', lit. 'Lotus Decoration') is the third-highest civilian award in the Republic of India, preceded by the Bharat Ratna and the Padma Vibhushan and followed by the Padma Shri. Instituted on 2 Januar ...
by the President of India on 26 January 1968.
After he died on 5 October 1976 at Allahabad, the
Illustrated Weekly of India paid a tribute to him through an article on him by the well-known science writer Jagajit Singh.
Later years
His wife died in January 1973. He moved to Delhi in October as member of the
Union Public Service Commission
The Union Public Service Commission (UPSC) is a constitutional body tasked with recruiting officers for All India Services and the Central Civil Services (Group A and B) through various standardized examinations. In 2023, 1.3 million applica ...
. In 1975 he accepted the post of Director of the newly created
Mehta Research Institute in
Allahabad
Prayagraj (, ; ISO 15919, ISO: ), formerly and colloquially known as Allahabad, is a metropolis in the Indian state of Uttar Pradesh.The other five cities were: Agra, Kanpur, Kanpur (Cawnpore), Lucknow, Meerut, and Varanasi, Varanasi (Benar ...
. He died of a heart attack on 5 October 1976.
References
External links
Biography on Springer website
{{DEFAULTSORT:Bhatnagar, Prabhu Lal
1912 births
1976 deaths
20th-century Indian mathematicians
Recipients of the Padma Bhushan in science & engineering
Rajasthani people
University of Allahabad alumni
Harvard University alumni
Academic staff of the University of Rajasthan
Academic staff of the Indian Institute of Science
People from Kota, Rajasthan
Presidents of the Indian Mathematical Society
Scientists from Rajasthan