Harold Grad (January 23, 1923 in

New York City New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...

– November 17, 1986) was an American applied mathematician. His work specialized in the application of

statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...

plasma physics Plasma ()πλάσμα
, Henry George Liddell, R ...

and

magnetohydrodynamics Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals, ...

Work

In statistical mechanics he had developed in his thesis new methods for the solution of 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, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lerne ...

. He derived the

from

Liouville equation :''For Liouville's equation in dynamical systems, see Liouville's theorem (Hamiltonian).'' : ''For Liouville's equation in quantum mechanics, see Von Neumann equation.'' : ''For Liouville's equation in Euclidean space, see Liouville–Bratu–Gel ...

using

BBGKY hierarchy In statistical physics, the BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, sometimes called Bogoliubov hierarchy) is a set of equations describing the dynamics of a system of a large number of interacting particles. The equ ...

under certain limits, known as Boltzmann–Grad limit. Harold Grad was the founder of the Magneto-fluid Dynamics Division of the

Courant Institute The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research cente ...

and served as its head until shortly before his death From 1964 to 1967 and 1974 to 1977 he was a member of the Advisory Committee for Fusion Energy at

Oak Ridge National Laboratory Oak Ridge National Laboratory (ORNL) is a U.S. multiprogram science and technology national laboratory sponsored by the U.S. Department of Energy (DOE) and administered, managed, and operated by UT–Battelle as a federally funded research and ...

. Grad was a critic and supporter of many early fusion schemes including picket fences,

magnetic mirror A magnetic mirror, known as a magnetic trap (магнитный захват) in Russia and briefly as a pyrotron in the US, is a type of magnetic confinement device used in fusion power to trap high temperature plasma using magnetic fields. T ...

s and

Biconic cusp The biconic cusp was one of the earliest suggestions for plasma confinement in a fusion reactor. It consists of two parallel electromagnets with the current running in opposite directions, creating oppositely directed magnetic fields. The two f ...

Recognition

In 1970, Grad became a member of the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

. He was an

invited speaker at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

in Nice in 1970 and in Stockholm in 1962. In 1981, Grad was awarded a

Guggenheim Fellowship Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

. In 1982, he was awarded the

Eringen Medal The A. C. Eringen Medal or Eringen Medal is an award given annually bthe Society of Engineering Science(SES) to an individual "in recognition of sustained outstanding achievements in Engineering Science". This award was established in 1976. The ...

from the Society of Engineering Science, and in 1986, he received the

James Clerk Maxwell Prize for Plasma Physics The James Clerk Maxwell Prize for Plasma Physics is an annual American Physical Society (APS) award that is given in recognition of outstanding contributions to the field of the Plasma Physics. It was established in 1975 by Maxwell Technologies, ...

from the

American Physical Society The American Physical Society (APS) is a not-for-profit membership organization of professionals in physics and related disciplines, comprising nearly fifty divisions, sections, and other units. Its mission is the advancement and diffusion of k ...

. The Courant Institute offers the Harold Grad Memorial Prize to outstanding performance and promise as a graduate student.

Life

Dr. Grad received a bachelor's degree in

electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

from the

Cooper Union The Cooper Union for the Advancement of Science and Art (Cooper Union) is a private college at Cooper Square in New York City. Peter Cooper founded the institution in 1859 after learning about the government-supported École Polytechnique in ...

in 1943 and his masters at

New York University New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin. In 1832, the ...

in 1945. Grad did his doctoral work under

Richard Courant Richard Courant (January 8, 1888 – January 27, 1972) was a German American mathematician. He is best known by the general public for the book '' What is Mathematics?'', co-written with Herbert Robbins. His research focused on the areas of real ...

and graduated in 1948. His thesis was on the approximation of the Boltzmann Equation by torque. He was then at the

of Mathematical Sciences of

from 1948 as associate professor and from 1957 until his death. Dr. Grad conducted research in

, the mathematical formulation of plasma physics and applications of plasma physics to nuclear fusion. He led the

department from 1956 until 1980.

References

{{DEFAULTSORT:Grad, Harold 20th-century American mathematicians Scientists from New York City New York University alumni 1923 births 1986 deaths Courant Institute of Mathematical Sciences faculty Mathematicians from New York (state) Cooper Union alumni