Thomas Brooke Benjamin, FRS (15 April 1929 – 16 August 1995) was an

English English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national ide ...

mathematical physicist Mathematical physics refers to the development of mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developmen ...

and

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, best known for his work in

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

and

fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and bio ...

, especially in applications of

nonlinear differential equation In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many othe ...

Education and career

Benjamin was educated at

Wallasey Grammar School The Kingsway Academy (formerly Wallasey School) was a coeducational secondary school and sixth form located in Leasowe in the English county of Merseyside. Wallasey Grammar School in the Wirral area was first constructed on St George's Road. A ...

on the Wirral, the

University of Liverpool , mottoeng = These days of peace foster learning , established = 1881 – University College Liverpool1884 – affiliated to the federal Victoria Universityhttp://www.legislation.gov.uk/ukla/2004/4 University of Manchester Act 200 ...

(BEng. 1950) and

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

(MEng. 1952), before being awarded his doctorate at

King's College, Cambridge King's College is a constituent college of the University of Cambridge. Formally The King's College of Our Lady and Saint Nicholas in Cambridge, the college lies beside the River Cam and faces out onto King's Parade in the centre of the city ...

in 1955. He was a fellow of King's from 1955 to 1964. From 1979 until his death in 1995 he was

Sedleian Professor of Natural Philosophy The Sedleian Professor of Natural Philosophy is the name of a chair at the Mathematical Institute of the University of Oxford. Overview The Sedleian Chair was founded by Sir William Sedley who, by his will dated 20 October 1618, left the sum o ...

at the

Mathematical Institute The Mathematical Institute is the mathematics department at the University of Oxford in England. It is one of the nine departments of the university's Mathematical, Physical and Life Sciences Division. The institute includes both pure and appl ...

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

, and a

fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

The Queen's College, Oxford The Queen's College is a Colleges of the University of Oxford, constituent college of the University of Oxford, England. The college was founded in 1341 by Robert de Eglesfield in honour of Philippa of Hainault. It is distinguished by its pred ...

Contributions

The

Benjamin–Ono equation In mathematics, the Benjamin–Ono equation is a nonlinear partial integro-differential equation that describes one-dimensional internal waves in deep water. It was introduced by and . The Benjamin–Ono equation is :u_t+uu_x+Hu_=0 where ''H'' is ...

describes one-dimensional

internal wave Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface. To exist, the fluid must be stratified: the density must change (continuously or discontinuously) with depth/height due to changes, for example, in ...

s in deep water. It was introduced by Benjamin in 1967, and later studied also by Hiroaki Ono. Another equation named after Benjamin, the

Benjamin–Bona–Mahony equation The Benjamin–Bona–Mahony equation (BBM equation, also regularized long-wave equation; RLWE) is the partial differential equation :u_t+u_x+uu_x-u_=0.\, This equation was studied in as an improvement of the Korteweg–de Vries equation (KdV ...

, models long

surface gravity wave In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere ...

s of small amplitude. Benjamin studied it with Jerry L. Bona and J. J. Mahony in a 1972 paper.

References

External links

* {{DEFAULTSORT:Benjamin, T. Brooke Alumni of King's College, Cambridge English mathematicians Fellows of the Royal Society Fluid dynamicists Members of the French Academy of Sciences 1929 births 1995 deaths 20th-century French mathematicians Sedleian Professors of Natural Philosophy Fellows of The Queen's College, Oxford