Carl-Gustaf Rossby: National Severe Storms Laboratory, a Study in Mentorship Norman, Oklahoma
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The Brainstormers the Electromagnetic Field
COMMENT SPRING BOOKS weather forecasting, particularly in the United States. Between the birth of Bjerknes — the oldest — in 1862 and the death of Wexler, the youngest, in 1962, there passed a forma- Inventing tive and innovative Atmospheric century. As Fleming Science: reveals, their lives were Bjerknes, Rossby, linked, with Bjerknes Wexler, and the teaching Rossby and Foundations Rossby, Wexler. of Modern Meteorology In 1904, in ‘Weather JAMES RODGER forecasting as a prob- FLEMING lem in mechanics and MIT Press: 2016. physics’, Bjerknes set the agenda for applying the laws of physics to the atmosphere to predict the weather (V. Bjerknes Meteorol. Z. 21, 1–7; 1904). His vision was to use a sufficiently accurate knowledge of the state of the atmosphere and the laws that govern its evolution to forewarn people about weather to come. His motiva- METEOROLOGY tion was to make his mark in what was for him a new field of science — he began his career working with his father, a physicist at the University of Oslo, on fluid analogies for The brainstormers the electromagnetic field. He was eager, too, to provide practical advice on hazards that affected mariners, farmers and the public. Alan Thorpe enjoys a hymn to some of the founders of Fleming notes the absence of a book-length the science and institutions of weather forecasting. biography of Rossby, and I hope that this will be rectified soon. To me, he is a first among equals. As well as building institutions, he t is thanks to the efforts of an international impacts, mostly on US weather forecasting. -
European Mathematical Society
CONTENTS EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF MARTIN RAUSSEN Department of Mathematical Sciences, Aalborg University Fredrik Bajers Vej 7G DK-9220 Aalborg, Denmark e-mail: [email protected] ASSOCIATE EDITORS VASILE BERINDE Department of Mathematics, University of Baia Mare, Romania NEWSLETTER No. 52 e-mail: [email protected] KRZYSZTOF CIESIELSKI Mathematics Institute June 2004 Jagiellonian University Reymonta 4, 30-059 Kraków, Poland EMS Agenda ........................................................................................................... 2 e-mail: [email protected] STEEN MARKVORSEN Editorial by Ari Laptev ........................................................................................... 3 Department of Mathematics, Technical University of Denmark, Building 303 EMS Summer Schools.............................................................................................. 6 DK-2800 Kgs. Lyngby, Denmark EC Meeting in Helsinki ........................................................................................... 6 e-mail: [email protected] ROBIN WILSON On powers of 2 by Pawel Strzelecki ........................................................................ 7 Department of Pure Mathematics The Open University A forgotten mathematician by Robert Fokkink ..................................................... 9 Milton Keynes MK7 6AA, UK e-mail: [email protected] Quantum Cryptography by Nuno Crato ............................................................ 15 COPY EDITOR: KELLY -
History of Frontal Concepts Tn Meteorology
HISTORY OF FRONTAL CONCEPTS TN METEOROLOGY: THE ACCEPTANCE OF THE NORWEGIAN THEORY by Gardner Perry III Submitted in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June, 1961 Signature of'Author . ~ . ........ Department of Humangties, May 17, 1959 Certified by . v/ .-- '-- -T * ~ . ..... Thesis Supervisor Accepted by Chairman0 0 e 0 o mmite0 0 Chairman, Departmental Committee on Theses II ACKNOWLEDGMENTS The research for and the development of this thesis could not have been nearly as complete as it is without the assistance of innumerable persons; to any that I may have momentarily forgotten, my sincerest apologies. Conversations with Professors Giorgio de Santilw lana and Huston Smith provided many helpful and stimulat- ing thoughts. Professor Frederick Sanders injected thought pro- voking and clarifying comments at precisely the correct moments. This contribution has proven invaluable. The personnel of the following libraries were most cooperative with my many requests for assistance: Human- ities Library (M.I.T.), Science Library (M.I.T.), Engineer- ing Library (M.I.T.), Gordon MacKay Library (Harvard), and the Weather Bureau Library (Suitland, Md.). Also, the American Meteorological Society and Mr. David Ludlum were helpful in suggesting sources of material. In getting through the myriad of minor technical details Professor Roy Lamson and Mrs. Blender were indis-. pensable. And finally, whatever typing that I could not find time to do my wife, Mary, has willingly done. ABSTRACT The frontal concept, as developed by the Norwegian Meteorologists, is the foundation of modern synoptic mete- orology. The Norwegian theory, when presented, was rapidly accepted by the world's meteorologists, even though its several precursors had been rejected or Ignored. -
The History of Weather Prediction
Haley Cica 14 September 2009 Willard Clark Intro into Integrated Science Nicholas Scaturo Paper 1 The History of Weather Prediction The article “ The origins of computer weather prediction and climate modeling” by Peter Lynch is about all of the different people who made possible the current understanding of the world weather and the ability to predict it by making giant leaps in both mathematics, hydrodynamics, and computer technology. No one man could have made this possible; it took the life’s work of many different men to make weather prediction and understanding a reality. It all started with the development of thermodynamics and hydrodynamics. Then came three men who might be considered the founding fathers of weather prediction, these men were Cleveland Abbe, Vilhelm Bjerknes, and Lewis Fry Richardson. In 1901 Cleveland Abbe wrote a paper titled “ The physical basis of long-range weather forecasting” which proposed using mathematics to predict weather. Not long after, Vilhelm Bjerknes, a Norwegian scientist introduced a plan to predict weather which included two steps: To observe the atmosphere, then calculate movement using the laws of motion. In 1922, while working at the Meteorological Office in, Lewis Fry Richardson wrote a book titled “ Weather Prediction by Numerical Process” where he criticized the then current practice of using an “ Index of Weather Maps” to predict weather by finding a previous map that resembled your current map and deducing that the weather will act in a similar manner. This method was of course highly inaccurate as Richardson points out. He then laid out a forecasting scheme which was based on Bjerknes’ program and involved an unimaginable volume of numerical computation which he realized would be practically impossible without computers. -
Interview with Arild Stubhaug
Interview Interview with Arild Stubhaug Conducted by Ulf Persson (Göteborg, Sweden) Arild Stubhaug, who is known among mathematicians for his bio graphy of Abel, has also produced a noted biography of Sophus Lie and is now involved Arild Stubhaug with a statue of Gösta Mittag-Leffl er in the project of writing a bi- ography of the Swedish math- language turned out to be the most interesting subject of ematician Mittag-Leffl er and the work for me. After mathematics I studied Latin, history mathematical period in which he of literature and eastern religion purely out of personal was infl uential. Following up the curiosity and desire. At that time such a combination interview, we will also have the could never be part of a regular university degree, hence privilege of giving a sample of I have never been regularly employed. Arild Stubhaug the up-coming work in a forth- coming issue of the Newsletter. But why Mittag-Leffl er? Abel is one of the greatest mathematicians ever, this is an uncontroversial fact, You are an established literary writer in Norway, and if and his short life has all the ingredients of romantic I recall correctly you already had your fi rst work pub- tragedy. Lie may not be of the same exalted stature, lished by the age of twenty-two. You have written poetry but of course the notion of “Lie”, in group-theory and as well as novels, what made you start writing biogra- algebra, is a mathematical household word. But Mit- phies of Norwegian mathematicians in recent years? tag-Leffl er? I think that any mathematician would be In recent years…, that is not exactly correct. -
D6. 27Ri-7T Carleman's Result Was an Early Predecessor of the Beurling-Rudin Theorem [RUDI; HOF, Pp
transactions of the american mathematical society Volume 306, Number 2, April 1988 OUTER FUNCTIONS IN FUNCTION ALGEBRAS ON THE BIDISC HÂKAN HEDENMALM ABSTRACT. Let / be a function in the bidisc algebra A(D2) whose zero set Z(f) is contained in {1} x D. We show that the closure of the ideal generated by / coincides with the ideal of functions vanishing on Z(f) if and only if f(-,a) is an outer function for all a e D, and /(l, ■) either vanishes identically or is an outer function. Similar results are obtained for a few other function algebras on D2 as well. 0. Introduction. In 1926, Torsten Carleman [CAR; GRS, §45] proved the following theorem: A function f in the disc algebra A(D), vanishing at the point 1 only, generates an ideal that is dense in the maximal ideal {g £ A(D): g(l) = 0} if and only if lim (1-Í) log |/(0I=0. R3t->1- This condition, which Carleman refers to as / having no logarithmic residue, is equivalent to / being an outer function in the sense that log\f(0)\ = ± T log\f(e*e)\d6. 27ri-7T Carleman's result was an early predecessor of the Beurling-Rudin Theorem [RUDI; HOF, pp. 82-89], which completely describes the collection of all closed ideals in A(D). For a function / in the bidisc algebra A(D2), let Z(f) = {z £ D2 : f(z) = 0} be its zero set, and denote by 1(f) the closure of the principal ideal in A(D2) generated by /. For E C D , introduce the notation 1(E) = {/ G A(D2) : / = 0 on E}. -
Efficient Quantum Algorithm for Dissipative Nonlinear Differential
Efficient quantum algorithm for dissipative nonlinear differential equations Jin-Peng Liu1;2;3 Herman Øie Kolden4;5 Hari K. Krovi6 Nuno F. Loureiro5 Konstantina Trivisa3;7 Andrew M. Childs1;2;8 1 Joint Center for Quantum Information and Computer Science, University of Maryland, MD 20742, USA 2 Institute for Advanced Computer Studies, University of Maryland, MD 20742, USA 3 Department of Mathematics, University of Maryland, MD 20742, USA 4 Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway 5 Plasma Science and Fusion Center, Massachusetts Institute of Technology, MA 02139, USA 6 Raytheon BBN Technologies, MA 02138, USA 7 Institute for Physical Science and Technology, University of Maryland, MD 20742, USA 8 Department of Computer Science, University of Maryland, MD 20742, USA Abstract While there has been extensive previous work on efficient quantum algorithms for linear differential equations, analogous progress for nonlinear differential equations has been severely limited due to the linearity of quantum mechanics. Despite this obstacle, we develop a quantum algorithm for initial value problems described by dissipative quadratic n-dimensional ordinary differential equations. Assuming R < 1, where R is a parameter characterizing the ratio of the nonlinearity to the linear dissipation, this algorithm has complexity T 2 poly(log T; log n)/, where T is the evolution time and is the allowed error in the output quantum state. This is an exponential improvement over the best previous quantum algorithms, whose complexity is exponential in T . We achieve this improvement using the method of Carleman linearization, for which we give an improved convergence theorem. -
1999 Atmospheric Research Technical Highlights (PDF, 4.8
Laboratory for Atmospheres PHILOSOPHY, ORGANIZATION, MAJOR ACTIVITIES, AND 1999 HIGHLIGHTS JanuaryJanuary 20002000 National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, MD 20771 NASA GODDARD SPACE FLIGHT CENTER Laboratory for Atmospheres PHILOSOPHY, ORGANIZATION, MAJOR ACTIVITIES, AND 1999 HIGHLIGHTS January 2000 2 1 3 4 5 6 1 Hurricane Fran as rendered on NASA 5 An example of the very realistic patterns computers using data captured by NOAA’s of cyclones and fronts that appear in surface GOES-8 satellite on September 4, 1996. wind fields generated by the 1-degree latitude by 1-degree longitude ver- 2 The Cassini Mission to Saturn and its sion of the GEOS global atmospheric model. moon, Titan. 6 October average total column ozone as 3 The Leonardo-BRDF formation of measured by the Total Ozone Mapping microsatellites viewing the Himalayas and Spectrometer (TOMS). Red and yellow indi- the Indian subcontinent. cate high overhead column amounts. Blue 4 The Goddard Lidar Observatory for Winds and purple show low values. The Antarctic (GLOW), a mobile Doppler lidar system Ozone hole appears as the very low column designed for field measurement of wind pro- amounts in the two later years. files from the surface into the stratosphere. A profile of wind speed and direction appears in the foreground, along with wind data obtained from a balloon sonde. Cover designed by Bill Welsh National Aeronautics and Space Administration Goddard Space Flight Center Greenbelt, MD 20771 January 2000 Dear Reader: Welcome to the Laboratory for Atmospheres and to our review of the Laboratory’s accomplishments for 1999! The Laboratory for Atmospheres consists of four hundred scientists, technologists, and administrative per- sonnel working within the Earth Sciences Directorate of the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC). -
Generalized Fourier Transformations: the Work of Bochner and Carleman Viewed in the Light of the Theories of Schwartz and Sato
GENERALIZED FOURIER TRANSFORMATIONS: THE WORK OF BOCHNER AND CARLEMAN VIEWED IN THE LIGHT OF THE THEORIES OF SCHWARTZ AND SATO CHRISTER O. KISELMAN Uppsala University, P. O. Box 480, SE-751 06 Uppsala, Sweden E-mail: [email protected] Salomon Bochner (1899–1982) and Torsten Carleman (1892–1949) presented gen- eralizations of the Fourier transform of functions defined on the real axis. While Bochner’s idea was to define the Fourier transform as a (formal) derivative of high order of a function, Carleman, in his lectures in 1935, defined his Fourier trans- form as a pair of holomorphic functions and thus foreshadowed the definition of hyperfunctions. Jesper L¨utzen, in his book on the prehistory of the theory of dis- tributions, stated two problems in connection with Carleman’s generalization of the Fourier transform. In the article these problems are discussed and solved. Contents: 1. Introduction 2. Bochner 3. Streamlining Bochner’s definition 4. Carleman 5. Schwartz 6. Sato 7. On Carleman’s Fourier transformation 8. L¨utzen’s first question 9. L¨utzen’s second question 10. Conclusion References 1 Introduction In order to define in an elementary way the Fourier transform of a function we need to assume that it decays at infinity at a certain rate. Already long ago mathematicians felt a need to extend the definition to more general functions. In this paper I shall review some of the attempts in that direction: I shall explain the generalizations presented by Salomon Bochner (1899–1982) and Torsten Carleman (1892–1949) and try to put their ideas into the framework of the later theories developed by Laurent Schwartz and Mikio Sato. -
BJERKNES – LIKE FATHER – LIKE SON by Doria B. Grimes U.S. Dept
BJERKNES – LIKE FATHER – LIKE SON By Doria B. Grimes U.S. Dept. of Commerce National Oceanic and Atmospheric Administration Central Library [email protected] A comparison of the lives of the Bjerknes family of researchers – Carl Anton (1825- 1903), Vilhelm (1862-1951), and Jakob (1897-1975) reveal unique parallelisms that are significant to the history of meteorology and to this great family legacy of scholars. Some of these parallelisms were caused by international events, while others were by personal choice. In the following presentation, I will four notable occurrences: 1) personal decisions to postpone scholarship to support a father’s research 2) relocations due to international conflicts 3) establishment of world renowned schools of meteorology and 4) funding from the Carnegie Institute of Washington. 1. Personal Choice Both Vilhelm and Jakob willingly postponed their education and personal research interests in order to support their respective father’s scientific investigations. Vilhelm During the 1980’s and 1880’s Carl Anton Bjerknes worked in relative isolation on hydrodynamic analogies. In 1882, Carl represented Norway at the Paris International Electric Exhibition where he gained international recognition on his electromagnetic theory and analogies which was successfully demonstrated by his son, Vilhelm. Vilhelm continued to assist his father until 1889, when at the age of 27 he “had to get away … to develop his own skills and career opportunities.”1 Vilhelm earned a Norwegian Doctorate in 1892 at the age of 30. He preferred electromagnetic wave studies above his father’s interest in hydrodynamic theory. Through Carl Anton’s influence, a position was created at the Stockholm H»gskola. -
Circa 1900) Vilhelm Bjerknes (1862–1951
TCD 8th March, 2005 A Century of Numerical Weather Prediction: The Pre-history of Numerical The View from Limerick Weather Prediction Peter Lynch (circa 1900) [email protected] Meteorology & Climate Centre, University College Dublin Vilhelm Bjerknes, Max Margules and Lewis Fry Richardson Physics Society, Trinity College Dublin 2 Vilhelm Bjerknes (1862–1951) Vilhelm Bjerknes (1862–1951) • Born in March, 1862. • Matriculated in 1880. • Fritjøf Nansen was a fellow-student. • Paris, 1989–90. Studied under Poincar´e. • Bonn, 1890–92. Worked with Heinrich Hertz. Vilhelm Bjerknes • Worked in Stockholm, 1983–1907. • 1898: Circulation theorems published • 1904: Meteorological Manifesto • Christiania (Oslo), 1907–1912. • Leipzig, 1913–1917. • Bergen, 1917–1926. • 1919: Frontal Cyclone Model. • Oslo, 1926 — 1951. Retired 1937. Died, April 9,1951. Vilhelm Bjerknes on the quay at Bergen, painted by Rolf Groven, 1983 3 4 Bjerknes’ 1904 Manifesto Graphical v. Numerical Approach x To establish a science of meteorology, with the aim of pre- dicting future states of the atmosphere from the present Bjerknes ruled out analytical solution of the mathematical state. equations, due to their nonlinearity and complexity: “If it is true . that atmospheric states develop according to physi- cal law, then . the conditions for the rational solution of forecasting “For the solution of the problem in this problems are: form, graphical or mixed graphical and 1. An accurate knowledge of the state of the atmosphere numerical methods are appropriate, which at the initial time. methods must be derived either from the 2. An accurate knowledge of the physical laws according to partial differential equations or from the which one state . -
Hurricane Sandy (2012), the TRMM Satellite, and the Physics of the Hot Towers
Hurricane Sandy (2012), the TRMM Satellite, and the Physics of the Hot Towers Alan Stahler of KVMR interviews Owen Kelley of NASA Goddard — Broadcast on Tuesday, 27 November 2012, on the 15th Anniversary of the Launch of the TRMM Satellite Broadcast: 38.5 minutes duration starting at noon PST on KVMR-FM, Nevada City, California Contacts: [email protected], 530-265-9073, and [email protected], 301-614-5245 00:00 The TRMM Instruments Stahler: Owen, how does TRMM, the Tropical Rainfall Measuring Mission, see rain? Kelley: It is called the flying rain gauge1 because it has every instrument ever used from space to measure rain. It has an infrared camera that sees how high and cold the clouds are... Stahler: You can see those images from GOES. GOES is a geostationary satellite. That means it hovers over the equator and gives us our daily weather picture. Kelley: Since the 60s, we've had that view from space.2 Stahler: Because it's infrared, it is essentially giving you the temperature of the clouds, and the colder the cloud, the higher up it is in the atmosphere. This lets you see how high, how tall the clouds are... Kelley: And that matters because air doesn't get lifted from the earth's surface to high up unless there is energy being transformed into strong updrafts. So [cloud top temperature] tells you something about the physics that is going on inside the clouds. If you are out on a sunny day and a little puffy cloud comes along, you don't get worried, but if you suddenly see it get dark and a cloud shoots up and starts to cover a lot of territory, then you know it's a big storm cloud and you might not want to set out on a hike.