Manley–Rowe relations

The Manley–Rowe relations are mathematical expressions developed originally for electrical engineers to predict the amount of energy in a wave that has multiple frequencies. They have since been found to describe systems in non-linear optics,[1] fluid mechanics and the theory of non-linear dynamical systems, as they provide a pair of invariants or conserved quantities for the three-wave equation. For example, in a resonant interaction in non-linear optics, the Manley–Rowe relations can be interpreted as saying one photon is created as two more are destroyed (or conversely, two are created when one is destroyed.) For the three-wave equation, the Manley–Rowe invariants can be related to the modular invariants and of the Weierstrass ℘-function.[2] This essentially follows because the three-wave interaction has exact solutions that are given by elliptic functions.

History

The original papers, written by two researchers at Bell Labs, J. M. Manley and H. E. Rowe between 1956 and 1960[3][4][5][6] was for an electrical circuit containing nonlinear capacitors and inductors. One or more oscillators, operating at specified frequencies, are connected to the input of this circuit. The Manley–Rowe relations predict the energy present in waves at various frequencies, including new frequencies (such as harmonics and sidebands) that arise in the circuit due to nonlinearity. The theory is based partly on the principle of conservation of energy. It requires that energy storage in the circuit is a stationary process that varies with time only due to the oscillations and not due to some steady increase or decrease with time. More precisely, the theory describes a resonant interaction between waves at various different frequencies; the resonant interaction describes which frequencies can mix and interact, and the strengths by which they couple.

Because the Manley–Rowe relations are based on general concepts like nonlinear waves and conservation of energy, their use is not limited to the original application in radio-frequency electrical circuits. They have also found use in other scientific fields, for example nonlinear optics. In the electrical circuit for the original derivation of Manley–Rowe relations, capacitors and inductors store energy from a wave and then release it. Other physical systems that involve energy storage for waves, and nonlinear generation of new waves, can make use of the same relations.

John Manley and Harrison Rowe were protégés of Ralph Hartley at Bell Laboratories. The work with nonlinear reactances (inductors and capacitors) was started back in 1917 by John Burton and Eugene Peterson.[7] When Hartley joined Bell Laboratories after being part of Western Electric, he started a research group on nonlinear oscillations. This group was later joined by Peterson, Manley, and Rowe.

Notes

  1. ^ Geoffrey New (2011). Introduction to Nonlinear Optics. Cambridge University Press. pp. 23–24. ISBN 978-0-521-87701-5.
  2. ^ Ruth Ann Martin and Harvey Segur (2016) Toward a General Solution of the Three-Wave Resonant Interaction Equations, Studies in Applied Mathematics, Volume 137, Issue 1.
  3. ^ Manley J. M and Rowe, H. E., "Some General Properties of Nonlinear Elements – Part I: General Energy Relations", Proceedings of the IRE, July 1956, p. 904 – 913.
  4. ^ Rowe H.E., “Some General Properties of Nonlinear Elements – Part II: Small Signal Theory”, Proceedings of the IRE, Volume 46, May 1958, pp 850 – 860
  5. ^ Manley J.M., Rowe H.E., “General Energy Relations in Nonlinear Reactances”, Proceedings of the IRE, Volume 47, December 1959, pp 2115–2116
  6. ^ Manley J.M., “Some Properties of Time Varying Networks”, IRE Transactions on Circuit Theory, CT-7, August 1960, pp 69–78
  7. ^ Peterson E., “Atomic Physics and Circuit Theory”; Bell Laboratories Record, Volume 7, February 1929, pp 231–233

Read other articles:

Krishna Nagar metro station (Lucknow)

Lucknow Metro's Red Line metro station Krishna Nagarकृष्णा नगर Lucknow Metro stationGeneral informationLocationBaldi Khera, Vijay Nagar Colony, Krishna Nagar, Alambagh, Lucknow, Uttar Pradesh 226023Coordinates26°47′40″N 80°53′30″E / 26.794386°N 80.891721°E / 26.794386; 80.891721Owned byLucknow MetroOperated byLucknow Metro Rail CorporationLine(s)Red LinePlatformsSide platform Platform-1 → Munshi PuliaPlatform-2 → CCS International Airp...

 

Basilika Bunda dari Lourdes, Poondi Madha

Basilika Poondi MadhaBasilika Bunda Maria dari LourdesBasilika Poondi MadhaLokasiAlamelupuram-Poondi, Tamil NaduNegaraIndiaDenominasiGereja Katolik RomaArsitekturStatusBasilika minorStatus fungsionalAktif Basilika Bunda Maria dari Lourdes, juga dikenal sebagai Basilika Poondi Madha, adalah sebuah gereja basilika minor Katolik yang terletak di Tamil Nadu, India Selatan. Terletak di Alamelupuram-Poondi, sebuah desa kecil yang terletak berdekatan dengan Thirukattupalli di Thiruvaiyaru taluk di d...

 

Korps Marinir Amerika Serikat

Korps Marinir Amerika SerikatUnited States Marine CorpsLambang Korps Marinir Amerika SerikatAktif1775 (1775)–1783 (1783), 1798 (1798)–sekarang[1]Negara Amerika SerikatTipe unitAngkatan Bersenjata MarinirPeranPerang Amfibi dan EkspedisiJumlah personel182,000 aktif (hingga 2017[update])[2] 38,500 cadangan (hingga 2017[update])[2] 1,304 pesawat berawak[3] (Total termasuk 11 VH-3D dan 8 VH-60N dari HMX-1[4] tidak terdaftar...

العلاقات الأسترالية الطاجيكستانية

العلاقات الأسترالية الطاجيكستانية أستراليا طاجيكستان   أستراليا   طاجيكستان تعديل مصدري - تعديل   العلاقات الأسترالية الطاجيكستانية هي العلاقات الثنائية التي تجمع بين أستراليا وطاجيكستان.[1][2][3][4][5] مقارنة بين البلدين هذه مقارنة عامة ومر...

 

Ejido

Communal farming unit in Mexico For other uses, see Ejido (disambiguation). Main articles: Land reform in Mexico and Agriculture in Mexico Ejido in Cuauhtémoc An ejido (Spanish pronunciation: [eˈxiðo], from Latin exitum) is an area of communal land used for agriculture in which community members have usufruct rights rather than ownership rights to land, which in Mexico is held by the Mexican state. People awarded ejidos in the modern era farm them individually in parcels and collec...

 

Syukuro Manabe

Japanese–American meteorologist and climatologist Syukuro ManabeBorn (1931-09-21) 21 September 1931 (age 92)Shinritsu, Uma, Ehime, JapanEducationUniversity of Tokyo (BA, MA, DSc)OccupationMeteorologist AwardsCarl-Gustaf Rossby Research Medal (1992)Blue Planet Prize (1992)Roger Revelle Medal (1993)Asahi Prize (1995)Volvo Environment Prize (1997)William Bowie Medal (2010)Franklin Institute Awards (2015)Crafoord Prize (2018)Nobel Prize in Physics (2021)Academic careerFieldsMeteorolog...

Department of Traditional Affairs

Department of Traditional AffairsDepartment overviewFormedDecember 1, 2009; 14 years ago (2009-12-01)Preceding departmentDepartment of Cooperative Governance and Traditional AffairsJurisdictionGovernment of South AfricaHeadquartersPencardia 1, 509 Pretorius Street, Arcadia, Pretoria25°44′49″S 28°12′18″E / 25.747°S 28.205°E / -25.747; 28.205Employees95 (2018/19)Annual budgetR173.4 million (2020/21)Minister responsibleNkosazana Dlamini-Zuma,...

 

Prva makedonska fudbalska liga 2002-2003

Questa voce o sezione sull'argomento edizioni di competizioni calcistiche non cita le fonti necessarie o quelle presenti sono insufficienti. Puoi migliorare questa voce aggiungendo citazioni da fonti attendibili secondo le linee guida sull'uso delle fonti. Segui i suggerimenti del progetto di riferimento. Prva makedonska fudbalska liga 2002-2003 Competizione Prva makedonska fudbalska liga Sport Calcio Edizione 11ª Organizzatore UEFA Luogo  Macedonia Partecipanti 12 Risultati Vinci...

 

Jaret Wright

Not to be confused with Jared Wright. American baseball player Baseball player Jaret WrightWright with the New York YankeesPitcherBorn: (1975-12-29) December 29, 1975 (age 48)Anaheim, California, U.S.Batted: RightThrew: RightMLB debutJune 24, 1997, for the Cleveland IndiansLast MLB appearanceApril 29, 2007, for the Baltimore OriolesMLB statisticsWin–loss record68–60Earned run average5.09Strikeouts694 Teams Cleveland Indians (1997–2002) San Diego Padre...

趙家驤

追晉陸軍二級上將趙家驤將軍个人资料出生1910年 大清河南省衛輝府汲縣逝世1958年8月23日(1958歲—08—23)（47—48歲） † 中華民國福建省金門縣国籍 中華民國政党 中國國民黨获奖 青天白日勳章（追贈）军事背景效忠 中華民國服役 國民革命軍 中華民國陸軍服役时间1924年－1958年军衔 二級上將 （追晉）部队四十七師指挥東北剿匪總司令部參謀長陸軍�...

 

格奥尔基·季米特洛夫

此條目之中立性有争议。其內容、語調可能帶有明顯的個人觀點或地方色彩。 (2011年6月)加上此模板的編輯者需在討論頁說明此文中立性有爭議的原因，以便讓各編輯者討論和改善。在編輯之前請務必察看讨论页。 格奥尔基·季米特洛夫保加利亚共产党中央委员会总书记任期1948年8月—1949年7月2日前任自己（第一书记）继任维尔科·契尔文科夫保加利亚共产党中央委员会第一�...

 

恩維爾·霍查

恩维尔·霍查Enver Hoxha霍查官方肖像照（摄于1980年代初）阿尔巴尼亚共产党中央委员会总书记任期1943年3月—1948年11月[1]前任無（首任）继任本人（劳动党中央委员会总书记）阿尔巴尼亚劳动党中央委员会总书记任期1948年11月—1954年7月[1]前任本人（共产党中央委员会总书记）继任本人（劳动党中央委员会第一书记）阿尔巴尼亚劳动党中央委员会第一书记任期1954�...

2015 Kansas City Chiefs season

NFL team season 2015 Kansas City Chiefs seasonOwnerThe Hunt familyGeneral managerJohn DorseyHead coachAndy ReidHome fieldArrowhead StadiumResultsRecord11–5Division place2nd AFC WestPlayoff finishWon Wild Card Playoffs(at Texans) 30–0Lost Divisional Playoffs(at Patriots) 20–27Pro Bowlers 6 S Eric BerryLB Tamba HaliLB Justin HoustonLB Derrick JohnsonTE Travis KelceCB Marcus Peters AP All-Pros 3 S Eric Berry (1st team)LB Derrick Johnson (2nd team)CB Marcus Peters (2nd team) Team MVPAl...

 

Darrin Jackson

American baseball player (born 1963) Baseball player Darrin JacksonJackson with the Cubs in 1987OutfielderBorn: (1963-08-22) August 22, 1963 (age 60)Los Angeles, California, U.S.Batted: RightThrew: RightProfessional debutMLB: June 17, 1985, for the Chicago CubsNPB: April 1, 1995, for the Seibu LionsLast appearanceNPB: October 5, 1996, for the Seibu LionsMLB: October 3, 1999, for the Chicago White SoxMLB statisticsBatting average...

 

2020年夏季奧林匹克運動會波蘭代表團

2020年夏季奥林匹克运动会波兰代表團波兰国旗IOC編碼POLNOC波蘭奧林匹克委員會網站olimpijski.pl（英文）（波兰文）2020年夏季奥林匹克运动会（東京）2021年7月23日至8月8日（受2019冠状病毒病疫情影响推迟，但仍保留原定名称）運動員206參賽項目24个大项旗手开幕式：帕维尔·科热尼奥夫斯基（游泳）和马娅·沃什乔夫斯卡（自行车）[1]闭幕式：卡罗利娜·纳亚（皮划艇）&#...

Chemung County Historical Society

42°5′19.5″N 76°48′2″W / 42.088750°N 76.80056°W / 42.088750; -76.80056 Chemung County Historical SocietyEstablished1923 (1923)Location415 East Water Street Elmira, New YorkAccreditationAmerican Alliance of MuseumsWebsiteOfficial website The Chemung County Historical Society is headquartered in the historic Chemung Canal Bank Building in Elmira, New York. It is dedicated to the collection, preservation, and presentation of the history of the Chemung Rive...

 

Slip of the Tongue

This article is about the Whitesnake album. For other uses, see Slip of the Tongue (disambiguation). 1989 studio album by WhitesnakeSlip of the TongueStudio album by WhitesnakeReleased7 November 1989 (US) 13 November 1989 (UK)[1]RecordedAugust 1988–1989StudioRecord Plant, Los AngelesGenreGlam metal[2][3]hard rockLength46:47LabelGeffenEMICBS/SonyProducer Mike Clink Keith Olsen Whitesnake chronology Whitesnake(1987) Slip of the Tongue(1989) Whitesnake's Greates...

 

Distinctive unit insignia

Badge or device worn by soldiers in the United States Army A soldier inventories all the DUIs at the Charles C. Carson Center for Mortuary Affairs A distinctive unit insignia (DUI) is a metallic heraldic badge or device worn by soldiers in the United States Army. The DUI design is derived from the coat of arms authorized for a unit. DUIs may also be called distinctive insignia (DI) or, imprecisely, a crest or a unit crest by soldiers or collectors. The U.S. Army Institute of Heraldry is respo...

Primera División de México 1979-80

Primera División de México 1979-80 Cruz Azul y Tigres protagonizaron una de las finales más memorables en la historia del fútbol mexicano en la cancha del Estadio Azteca.Datos generalesSede  MéxicoFecha 19 de septiembre de 197913 de julio de 1980PalmarésPrimero Cruz AzulSegundo Tigres UANLDatos estadísticosParticipantes 20Goles 1045Campeón de goleo individual Cabinho (30)Líder general Club América (57 pts.) Cronología Primera División 1978-79 Primera División de México 1979...

 

Rupture de la rate

Rupture de la rate Vue du thorax montrant les os dessinés au premier plan, les poumons (violet), la plèvre (bleue) et la rate (vert) Données clés Traitement Spécialité Médecine d'urgence Classification et ressources externes CISP-2 B76 CIM-10 S36.0 CIM-9 865 DiseasesDB 12369 eMedicine 432823 MeSH D013161 Mise en garde médicale modifier - modifier le code - voir Wikidata (aide) La rupture ou fracture de la rate est une urgence chirurgicale pouvant être causée par un traumatisme, com...