Paul Irving Richards (1923–1978) was a physicist and applied mathematician. Richard's is best known to electrical engineers for the eponymous Richards' transformation. However, much of his career was concerned with

radiation transport Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission, and scattering processes. The equation of radiative trans ...

and

fluid flow In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

. Notably, he produced one of the earliest models of

traffic wave Traffic waves, also called stop waves, ghost jams, traffic snakes or traffic shocks, are traveling disturbances in the distribution of cars on a highway. Traffic waves travel backwards relative to the cars themselves. Relative to a fixed spot on t ...

s on busy highways.

Early life and education

Richards was born in

Orono, Maine Orono () is a town in Penobscot County, Maine, United States. Located on the Penobscot and Stillwater rivers, it was first settled by American colonists in 1774. They named it in honor of Chief Joseph Orono, a sachem of the indigenous Penobscot ...

in 1923. In 1943 he dropped out of his undergraduate course at Harvard after the first year to work at the

Radio Research Laboratory The Radio Research Laboratory (RRL), located on the campus of Harvard University, was an 800-person secret research laboratory during World War II. Under the U.S. Office of Scientific Research and Development (OSRD), it was a spinoff of the Radiati ...

(RRL) set up on the campus at Harvard during

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

to research

electronic countermeasures An electronic countermeasure (ECM) is an electrical or electronic device designed to trick or deceive radar, sonar, or other detection systems, like infrared (IR) or lasers. It may be used both offensively and defensively to deny targeting info ...

. At the end of the war, Richards was accepted back into Harvard as a Ph.D student without first completing his bachelor's degree. He received his Ph.D in physics in 1947 with a dissertation on

commensurate line theory Commensurate line circuits are electrical circuits composed of transmission lines that are all the same length; commonly one-eighth of a wavelength. Lumped element circuits can be directly converted to distributed-element circuits of this form by ...

that marked the beginning of this field.Levy & Cohn, pp. 1056–1057

Career

At RRL Richards worked on microwave filters, an important component of

radar Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...

and countermeasures against it. This work formed the background for his

, although that theory was apparently not well developed enough at the time to be put to use in wartime work. The culmination of this theory was in his 1948 paper "Resistor-transmission-line circuits", after which Richards left the field of microwave engineering. The theory formed the basis of most transmission-line type microwave filters for at least the next thirty-five years and the design technique is still in use today. Richards' transformation, introduced in this work, is still found in modern textbooks on

radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the upp ...

filter design. During this period Richards also discovered a theorem in

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

now known as Richards' theorem which has applications in network synthesis. Between 1947 and 1952 he was a physicist at the Brookhaven National Laboratory helping to develop the magnetic time-of-flight mass spectrometer with Earl E. Hays and Samuel Goudsmit. From 1952 to 1954 he was director of research at Transistor Products Inc. From 1954 to 1968 he was senior physicist with Technical Operations Inc.Woolf, p.86 In 1956, while at Technical Operations, Richards produced a paper "Shock waves on the highway", one of the earliest theoretical models of traffic waves (there was another paper on this the previous year by Lighthill and Whitham in the UK, but Richards was apparently not aware of it and his work is independent). The traffic flow model described in this paper is now known as the Lighthill-Whitham-Richards model.Kerner, pp. 67, 82 From 1968 until his death on 19 November 1978 he was a senior scientist with Arcon Corporation. At Arcon he was primarily concerned with

, particularly

neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...

Editorships

Richards was on the publications committee of the

Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific socie ...

and was an editor of '' SIAM Review''. Richards was interested in promoting clarity in scientific writing. He wrote a book and several articles on the subject.

Selected works

Books

* ''Manual of Mathematical Physics'', Pergamon Press, 1959 . * (with Irving T. Richards) ''Proper Words in Proper Places'', Christopher Publishing House, 1964 —A guide to technical writing.

Articles

"Applications of matrix algebra to filter theory"
''Proceedings of the IRE'', vol. 34, iss. 3, pp. 145–150, March 1946.
"Universal optimum-response curves for arbitrarily coupled resonators"
''Proceedings of the IRE'', vol. 34, iss. 9, pp. 624–629, September, 1946.
''General impedance-function theory and transmission-networks''
Ph.D thesis, Harvard, 1947.
"A special class of functions with positive real part in a half-plane"
''Duke Mathematical Journal'', vol. 14, no. 3, 777–786, 1947. * "General impedance-function theory", ''Quarterly of Applied Mathematics'', vol. 6, pp. 21–29, 1948.
"Resistor-transmission-line circuits"
''Proceedings of the IRE'', vol. 36, iss. 2, pp. 217–220, 1948.
"On the Hamiltonian for a particle in an electromagnetic field"
''Physical Review'', vol. 73, iss. 3, p. 254, February 1948.
"Probability of coincidence for two periodically recurring events"
''The Annals of Mathematical Statistics'', vol. 19, no. 1, pp. 16–29, March 1948. * (with Hartland S. Snyder
"Collision and saturation broadening in microwave spectra"
''Physical Review'', vol. 73, iss. 10, pp. 1178–1180, May 1948.
"Notes on Feenberg's series-rearrangements"
''Physical Review'', vol. 74, iss. 7, pp. 835–836, October 1948. * (with E. E. Hays and S. A. Goudsmit) "Magnetic time-of-flight mass spectrometer", ''Physical Review'', vol. 76, p. 180, 1949. * (with B. A. Rubins
"Irradiation of small volumes by contained radioisotopes"
''Nucleonics'', vol. 6, iss. 6, pp. 42–49, June 195
"Machines which can learn"
''American Scientist'', vol. 39, no. 4, pp. 711–716, October 1951. * (with E. E. Hays and S. A. Goudsmit
"Mass measurement with a magnetic time-of-flight mass spectrometer"
''Physical Review'', vol. 84, iss. 4, pp. 824–829, November 1951
"Multiple isotropic scattering"
''Physical Review'', vol. 100, iss. 2, pp. 517–522, October 1955. * (with S. S. Holland Jr.
"Neutron flux spectra in air"
''Journal of Applied Physics'', vol. 27, iss. 9, pp. 1024–1050, 1956.
"Scattering from a point source in plane clouds"
''Journal of the Optical Society of America'', vol. 46, iss. 11, pp. 927–934, 1956.
"Shock waves on the highway"
''Operations Research'', vol. 4, iss. 1, pp. 42–51, 1 February 1956.
"Transients in conducting media"
''IRE Transactions on Antennas and Propagation'', vol. 6, iss. 2, pp. 178–182, April 1958.
"Radiative transport from point sources in a stratified medium"
''Journal of the Optical Society of America'', vol. 49, iss. 3, pp. 245–249, 1959.
"The order of electron shells in ionized atoms"
''Proceedings of the National Academy of Sciences of the United States of America'', vol. 51, iss. 4, pp. 664–671, April 1964.
"Averages for polygons formed by random lines"
''Proceedings of the National Academy of Sciences of the United States of America'', vol. 52, no. 5, pp. 1160–1164, November 1964. * (with W. D. Lanning and M. D. Torrey
"Numerical integration of large, highly-damped, nonlinear systems"
''SIAM Review'', vol. 7, iss. 3, pp. 376–380, July 1965.
"Synthesizing transfer functions with two grounded pentodes"
''Proceedings of the IEEE'', vol. 55, iss. 4, pp. 552–553, April 1967.

References

Bibliography

* Kerner, Boris S., ''The Physics of Traffic'', Springer, 2012 . * Levy, Ralph; Cohn, Seymour B.
"A history of microwave filter research, design, and development"
''IEEE Transactions on Microwave Theory and Techniques'', vol. 32, iss. 9, pp. 1055–1067, September 1984. * Lighthill, M. J.; Whitham, G. B.
"On kinematic waves: II. A theory of traffic flow on long crowded roads"
''The Royal Society: Proceedings A'', vol. 229, iss. 1178, pp. 317–345, May 1955. * Needell, Allan A., ''Science, Cold War and the American State'', Routledge, 2013 . * Wen, Geyi, ''Foundations for Radio Frequency Engineering'', World Scientific, 2015 . * Woolf, Stanley
"Obituaries: Paul I. Richards"
''Physics Today'', vol. 32, iss. 5, pp. 86–87, May 1979. {{DEFAULTSORT:Richards, Paul I. 1923 births 1978 deaths People from Orono, Maine Harvard University alumni 20th-century American mathematicians 20th-century American physicists