Prabhu Lal Bhatnagar
Encyclopedia
Prabhu Lal Bhatnagar commonly addressed as P. L. Bhatnagar, was an India
n mathematician
known for his contribution to the Bhatnagar-Gross-Krook
(BGK) collision model used in Lattice Boltzmann methods
(LBM).
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.
, 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 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 dwarf
s, 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 sixtees he developed complications in the lower spinal region and was opearated 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.
. 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.
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
known for his contribution to the Bhatnagar-Gross-Krook
Bhatnagar-Gross-Krook
The Bhatnagar–Gross–Krook operator term refers to a collision operator used in the Boltzmann Equation and in the Lattice Boltzmann method, a Computational fluid dynamics technique...
(BGK) collision model used in Lattice Boltzmann methods
Lattice Boltzmann methods
Lattice Boltzmann methods is a class of computational fluid dynamics methods for fluid simulation. Instead of solving the Navier–Stokes equations, the discrete Boltzmann equation is solved to simulate the flow of a Newtonian fluid with collision models such as Bhatnagar-Gross-Krook...
(LBM).
Early years
P. L. Bhatnagar was born in KotaKota, Rajasthan
Kota , formerly known as Kotah, is a city in the northern Indian state of Rajasthan. It is located south of state capital, Jaipur. Situated on the banks of Chambal River, the city is the trade centre for an area in which millet, wheat, rice, pulses, coriander and oilseeds are grown; industries...
in Rajasthan
Rajasthan
Rājasthān the land of Rajasthanis, , is the largest state of the Republic of India by area. It is located in the northwest of India. It encompasses most of the area of the large, inhospitable Great Indian Desert , which has an edge paralleling the Sutlej-Indus river valley along its border with...
and was the second of five sons. He did his schooling in Rampura
Rampura
Rampura can refer to the following locations in India:* Rampura, Neemuch - a town in Madhya Pradesh* Rampura, Jalaun - a town in Uttar Pradesh* Rampura Phul - a town in Bathinda district of Punjab...
and later at Herberter College in Kota. After schooling he went to Maharajah's College in Jaipur
Jaipur
Jaipur , also popularly known as the Pink City, is the capital and largest city of the Indian state of Rajasthan. Founded on 18 November 1727 by Maharaja Sawai Jai Singh II, the ruler of Amber, the city today has a population of more than 3.1 million....
where in 1935 he completed BSc with first rank, followed by MSc.
Middle years
His research career started at the Allahabad UniversityAllahabad University
Allahabad University , is a premier Central University located in Allahabad, Uttar Pradesh, India. Its origins lie in the Muir Central College, named after Lt...
, where he worked from 1937 till 1939 on Fourier series
Fourier series
In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...
and Allied series. The result of his work are included in the book of Erich Kamke
Erich Kamke
Erich Kamke was a German mathematician, who specialized in the theory of differential equations. Also, his book on set theory became a standard introduction to the field.-Biography:...
. and also resulted in journal publications together with his supervisor Amiya Charan Banerjee
Amiya Charan Banerjee
Amiya Charan Banerjee was a mathematician and educator popularly known as A.C.Banerjee or simply as Professor Banerjee.-Family background:...
. He became interested in the area of astrophysics
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
after coming in contact with Megh Nad Saha, who was 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
St. Stephen's College, Delhi
St. Stephen's College is a constituent college of the University of Delhi located in Delhi, India. The college admits both undergraduates and post-graduates, and awards degrees under the purview of the University. Famous for its rich history and many traditions, St...
on the invitation of S. N. Mukherjee and spent the next 16 years there. There he worked on the theory of white dwarf
White dwarf
A white dwarf, also called a degenerate dwarf, is a small star composed mostly of electron-degenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored...
s, independently and together with Daulat Singh Kothari
Daulat Singh Kothari
Daulat Singh Kothari was an eminent Indian scientist.He was born in Udaipur in Rajasthan state. He had his early education at Udaipur and Indore and did MSC in physics from Allahabad University inn 1928 under guidance of great physicist Megh Nad Saha...
.
In 1952 he was invited to Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
as a Fulbright scholar. There he worked together with Donald Howard Menzel
Donald Howard Menzel
Donald Howard Menzel was one of the first theoretical astronomers and astrophysicists in the US. He discovered the physical properties of the solar chromosphere, the chemistry of stars, the atmosphere of Mars, and the nature of gaseous neblulae.-Biography:Born in Florence, Colorado in 1901 and...
and Hari Kesab Singh in the field of non-linear gases. His work with the Boltzmann equation
Boltzmann equation
The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in rarefied gas...
led to his well known BGK collision model in 1954 together with E. P. Gross and Max Krook
Max Krook
Max Krook was an American mathematician and astrophysicst.He is remembered for his contribution to the Bhatnagar-Gross-Krook model.-Selected works:...
. 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
Indian National Science Academy
The Indian National Science Academy , New Delhi is the apex body of Indian scientists representing all branches of science & technology.-History:...
and in 1955 the fellow of Indian Academy of Sciences
Indian Academy of Sciences
The Indian Academy of Sciences, Bangalore was founded by Sir C. V. Raman, and was registered as a Society on 24 April 1934. Inaugurated on 31 July 1934, it began with 65 founding fellows. The first general meeting of Fellows, held on the same day, elected Professor Raman as President, and adopted...
. In 1956 he was invited to join Indian Institute of Science
Indian Institute of Science
Indian Institute of Science is a research institution of higher learning located in Bangalore, India. It was established in 1909.-History:After a chance meeting between Jamsetji N...
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
Indian National Mathematics Olympiad
The Indian National Mathematical Olympiad is an Olympiad in mathematics held in India.The INMO examination is conducted by the MO Cell in February of every year. School students of any class first need to write the Regional Mathematical Olympiad of their respective state or region, usually held...
. For his contributions to the nation, on 26 January 1968 he was awarded the Padma Bhushan
Padma Bhushan
The Padma Bhushan is the third highest civilian award in the Republic of India, after the Bharat Ratna and the Padma Vibhushan, but comes before the Padma Shri. It is awarded by the Government of India.-History:...
.
During the early sixtees he developed complications in the lower spinal region and was opearated in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
. In 1969 he moved to Rajasthan University in Jaipur
Jaipur
Jaipur , also popularly known as the Pink City, is the capital and largest city of the Indian state of Rajasthan. Founded on 18 November 1727 by Maharaja Sawai Jai Singh II, the ruler of Amber, the city today has a population of more than 3.1 million....
as Vice-Chancellor and in 1971 joined Himachal Pradesh University in Shimla
Shimla
Shimla , formerly known as Simla, is the capital city of Himachal Pradesh. In 1864, Shimla was declared the summer capital of the British Raj in India. A popular tourist destination, Shimla is often referred to as the "Queen of Hills," a term coined by the British...
as senior professor.
Later years
His wife died in January 1973. He moved to Delhi in October as member of the Union Public Service CommissionUnion Public Service Commission
The Union Public Service Commission is the central agency authorized to conduct the Civil Services Examination for entry-level appointments to the various Civil Services of India. The agency's charter is granted by the Constitution of India...
. In 1975 he accepted the post of Director of the newly created Mehta Research Institute in Allahabad
Allahabad
Allahabad , or Settled by God in Persian, is a major city of India and is one of the main holy cities of Hinduism. It was renamed by the Mughals from the ancient name of Prayaga , and is by some accounts the second-oldest city in India. It is located in the north Indian state of Uttar Pradesh,...
. He died of a heart attack on 5 October 1976.