Prabhu Lal Bhatnagar
|Prabhu Lal Bhatnagar|
18 August 1912|
|Died||5 October 1976
|Institutions||University of Delhi
Indian Institute of Science
Smithsonian Astrophysical Observatory
|Alma mater||Agra University|
|Doctoral advisor||Amiya Charan Banerjee|
|Doctoral students||Purushottam Lal Sachdev
|Notable awards||Padma Bhushan in 1968|
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 (BGK) collision model used in Lattice Boltzmann methods (LBM).
Early years 
P. L. Bhatnagar 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 where in 1935 he completed BSc with first rank, followed by MSc.
Middle years 
His research career started at the Allahabad University, where he worked from 1937 till 1939 on Fourier series and Allied series. The result of his work are included in the book of Erich Kamke. and also resulted in journal publications together with his supervisor Amiya Charan Banerjee. He became interested in the area of astrophysics after coming in contact with Megh Nad Saha, who was a well-known figure in the field. 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 dwarfs, independently and together with Daulat Singh Kothari.
In 1952 he was invited to Harvard University as a Fulbright scholar. 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 led to his well known BGK collision model in 1954 together with E. 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 and in 1955 the fellow of Indian Academy of Sciences. In 1956 he was invited to join Indian Institute of Science as professor of the newly created department of 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.
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 as Vice-Chancellor and in 1971 joined Himachal Pradesh University in Shimla as senior professor.
Research carrier of PLB started in 1936 as a research student at the university of Allahabad under the supervision of Prof. B.N. Prasad on summability theory but soon he joined Prof. A.C. Banerjee to work in diﬀerential equations. Two of his results (with Prof. Banerji, published in Proceeding of National Academy of Sciences, 1938) have been incorporated in the famous book of Kamke: Diﬀerential Gleichungen, Vol I. Under the inspiration of Prof. M.N. Saha (Saha, FNA, FRS, was already famous) PLB’s, interest slowly shifted to astrophysics and he started working on the spiral nebula and tidal theory of planetary formation. For the best research work in the Faculty of Science, Allahabad University, during 1937-39 he won EG Hill Memorial Prize. He obtained his D.Phil degree for his thesis entitled On the origin of the solar system. Soon after he completed his doctoral degree, he was invited to join the St. Stephen’s Collage, Delhi, where he spent 16 years ﬁrst as a lecturer and later as Head of the Department of Mathematics and concurrently as a Reader in Mathematics at Delhi University. These years could be termed as the blossoming years when Bhatnagar was in full bloom. He worked in astrophysics both independently and in collaboration with D.S. Kothari. Pulsation phenomenon had been observed only in ”Supergiant Stars”. Bhatnagar worked on the theory of anharmonic pulsations of Cepheids and white dwarf stars and found the pulsations lasting for 10 3 years. This work brought important international recognition - reported in Britain as ”discovery of a young Indian astrophysicist”. This work was quoted in S. Rosseland’s book ”Pulsation Theory of Variable Stars” published in 1949. A busy schedule of over 20 hours of teaching per week at St. Stephen did not dampen Bhatnagar’s enthusiasm for research. In 1947, he was awarded the D.Sc. degree from the Allahabad University. His interest in stellar structures and interiors led him to study of rareﬁed gases and ionized media. This was a harbinger of the monumental work he was to do a few years later - what is now known as the BGK Model. In 1951, Bhatnagar went to Harvard University, Cambridge as a Fullbright scholar for two years. This handsome tall scholar from India was often mistaken in the University corridors for a student. Once he took his place at the lecture rostrum, the students realized that he was indeed a senior faculty. He lectured on mathematical theory of gases based on the mathematically formidable book by S. Chapman and T.G. Cowling. At Harvard, he produced two very important publications (1) a book ”Stellar Interiors” jointly with D.H. Menzel and H.K. Sen, published in the International Astrophysical Series and (2) a research paper in Physical Review in 1954 which contained the famous BGK (Bhatnagar, Gross, Krook) model. The Bolzmann equation, governing the evolution of a state of molecules in gases, contains an extremely complicated integral term containing integration with respect to a vector v∗ over R3 and with respect to n over a unit hemisphere. Faced with the reality that the Boltzmann equation was too diﬃcult to handle due to 3this collision integral term, Bhatnagar, Gross and Krook used their deep understanding of relaxation process of a swarm of molecules towards an equilibrium state to replace this term by a much simpler term free from the integration over a domain in the 5-dimensional half space. This gives a simple, yet a very realistic Boltzmann like equation, which has since been used as alternative to the Boltzmann equation in solving problems in rareﬁed gas dynamics, plasma physics and the kinetic theory itself. So far, I have copied in this article many points from the article of Tikekar, Prasad and Ravindran and I could present here more from this article, which contains a good description of the life and work of Bhatnagar, which led to many academic and public honours to him after he returned to Delhi University, and there after joined in 1956 the Indian Institute of Science, Bangalore as the founding Professor of the Department of Applied Mathematics. After this, he was invited as vice-chancellor of the Jaipur University, Head of the Mathematics Department of the newly formed Himachal Pradesh University, Member of the Union Public Service Commission and ﬁnally as the ﬁrst Director of the Mehta Research Institute (now renamed as the Harischandra Research Institute). After his wife, Anand Kumari, died in 1973, his personal life was far from comfortable. I would suggest the readers of this article to read for details the two references which are available on my web page. Let me mention here a beautiful book, which PLB wrote in just six months from the reprints of recent articles on the Korteweg-de-Vries equation, which I had carried with me from IISc, Bangalore to the Mehta Research Institute during my stay at MRI in 1975-76. This book is ”Nonlinear Waves in One-dimensional Dispersive Systems”, published in the series ”Oxford Mathematical Monograph” edited by I.G. MacDonald and R. Penrose. The importance of the book was realized by M.J. Lighthill, who had written a foreword for the book before PLB died and added in it later ”I had written the above words before the deeply regretted and untimely death of Professor Bhatnagar on 5 October 1976, when the world of applied mathematics suddenly lost one of its most respected ﬁgures. After the shock of this great loss had subsided, I felt anxious to ensure that Professor Bhatnagar’s last book would receive the wide circulation that it richly merits. I am deeply grateful to Dr. Phoolan Prasad for his excellent work as editor. Applied mathematicians owe him a great debt for helping to make this important text generally available”. I would like to make a clarification in these words of Lighthill. In the editorial work of this book, three more students of PLB contributed as enthusiastically as me. They are V.G. Tikekar, Renuka Ravindran and Swarnalata Prabhu. The book received good reviews, was immediately translated into Russian and it was used as a text book in USSR. No less than V.E. Zakharov, who has contributed significantly to the development of the theory of solitons, told me ”I was surprised to see the ﬁrst book (a good book) on the subject from a country where no contribution to the theory of solitary wave was made.
Honors and Awards 
PLB received many academic honors, which are described in the reference 3 but let me mention here two public honours. For his service to nation, he was ﬁttingly awarded the Padma Bhushan by the President of India on January 26, 1968. After he died on October, 5, 1976 at Allahabad, the most important weekly magazine of India at that time, The Illustrated Weekly of India paid a tribute to his multi-colour personality through a two 4page (central pages) 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. In 1975 he accepted the post of Director of the newly created Mehta Research Institute in Allahabad. He died of a heart attack on 5 October 1976.
See also 
- Kamke, Erich (1971). Differentialgleichungen-Lösungsmethoden und Lösungen. Chelsea Publishing Company. ISBN 978-0-8284-0044-2.
- Bhatnagar, P. L.; A. C. Banerji (1938). "On the solution of certain types of differential equations". Proceedings of National Academy of Science India 8: 85–91.
- Bhatnagar, P. L.; D. H. Menzel, H. K. Sen (1963). Stellar Interiors. International Astrophysics. Chapman and Hall.
- Bhatnagar, P.; Gross, E.; Krook, M. (1954). "A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems". Physical Review 94 (3): 511. Bibcode:1954PhRv...94..511B. doi:10.1103/PhysRev.94.511.
- Bhatnagar, P. L.; M. K. Singal (1974). "Mathematical Olympiads". Bulletin of Mathematical Association of India 6.
- Singal, M. K. (1972). "P. L. Bhatnagar, Man and Mathematician". The Mathematics Student 40: 1–12.
- Prasad, Phoolan (1978). "A few glimpses of Professor P. L. Bhatnagar". Mathematics Teacher (India) 14: 82–85.