Bernd Ulmann Analog Computing Also of interest Analog and Hybrid Computer Programming Bernd Ulmann, 2020 ISBN 978-3-11-066207-8, e-ISBN 978-3-11-066220-7 Quantum Information Theory Concepts and Methods Joseph M. Renes, 2022 ISBN 978-3-11-057024-3, e-ISBN (PDF) 978-3-11-057025-0 Multi-level Mixed-Integer Optimization Parametric Programming Approach Styliani Avraamidou, Efstratios Pistikopoulos, 2022 ISBN 978-3-11-076030-9, e-ISBN (PDF) 978-3-11-076031-6 Automata Theory and Formal Languages Wladyslaw Homenda und Witold Pedrycz, 2022 ISBN 978-3-11-075227-4, e-ISBN (PDF) 978-3-11-075230-4 High Performance Parallel Runtimes Design and Implementation Michael Klemm, Jim Cownie, 2021 ISBN 978-3-11-063268-2, e-ISBN (PDF) 978-3-11-063272-9 Algorithms Design and Analysis Sushil C. Dimri, Preeti Malik, Mangey Ram, 2021 ISBN 978-3-11-069341-6, e-ISBN (PDF) 978-3-11-069360-7 Bernd Ulmann Analog Computing 2nd edition Mathematics Subject Classification 2010 Primary: 34-04, 35-04; Secondary: 92C45, 92D25, 34C28, 37D45 Author Prof. Dr. Bernd Ulmann Schwalbacher Str. 31 65307 Bad Schwalbach [email protected] ISBN 978-3-11-078761-0 e-ISBN (PDF) 978-3-11-078774-0 e-ISBN (EPUB) 978-3-11-078787-0 Library of Congress Control Number: 2022946448 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2023 Walter de Gruyter GmbH, Berlin/Boston Cover image: Bernd Ulmann Printing and binding: CPI books GmbH, Leck www.degruyter.com To my beloved wife Rikka Acknowledgments This book would not have been possible without the support and help of many people. First of all, I would like to thank my wife Rikka Mitsam, who not only did a lot of proofreading and a terrific job in preparing many of the pen-and-ink drawings, but also never complained about being neglected although I lived the last months more or less in seclusion writing this book. I am particularly grateful for the support and help of Jens Breitenbach, who did a magnificent job at proofreading and provided many suggestions and improvements enhancing the text significantly. He also spotted many LATEX-sins of mine, thus improving the overall appearance of this book considerably. In addition to that, I would like to thank Benjamin Barnickel, Arne Charlet,DanielaKoch,TheresaSzczepanski,Dr.ReinhardSteffensand Francis Massen for their invaluable help in proofreading. Additionally, I would like to thank Tore Sinding Bekkedal, who took the picture shown in figure 8.35, Tim Robinson, who built the incredible Meccano- Differential Analyser shown in figure 2.22, Tibor Florestan Pluto, who took thephotoshownonthetitlepage,Robert Limes,whotookthepictureshownin figure 9.3, and Bruce Baker, who donated the pictures shown in figures 13.60, 13.62, and 13.63, for their permissions to use the aforementioned pictures. Without the continuous encouragement of Dr. habil. Karl Schlagenhauf and his invaluable suggestions this book might very well not exist at all. Last but not least, I would like to thank Prof. Dr. Wolfgang Giloi, Prof. Dr. Rudolf Lauber, Dr. Adolf Kley, Prof. Dr. Günter Meyer-Brötz and Manfred Klittich for sharing their memories of the early days of analog com- puting at Telefunken, etc. Furthermore, Jeroen Brinkmann introduced me to the “Hammer Computer” and Bert Brouwer offered many the insights into solving partial differential equations in conjunction with heat transfer problems. This book was typeset with LATEX. Most schematics were drawn using EA- GLEandArnoJacob’swonderfulanalogcomputingsymbollibrary,othervector graphics were created with xfig. Registerednames,trademarks,designations,etc.,usedinthisbook,evenwhen not specifically marked as such, are not to be considered unprotected by law. https://doi.org/10.1515/9783110787740-202 Preface to the 2nd edition This second edition of “Analog Computing” would not exist if it wasn’t for Dr. Damiano Sacco, acquisition editor at DeGruyter, who asked me to prepare a new edition of “Analog Computing”, which has established itself as a standard textbook since it was first published in 2013. A lot has happened since then in the world of analog computing. First of all many“new”historicsources,papers,andphotographshavebecomeavailablesince 2013.Accordingly,thebibliographyofthis2nd editionhasbeenexpandedbymore then200additionalsources.Second,andevenmoreimportantly,interestinanalog computing has grown enormously. This computing paradigm is about to change theworldofcomputinginthenearfuturewithaplethoraofinterestingandcom- mercially important applications ranging from low power computing as required for medical implants to high performance computing, artificial intelligence, and many, many more. It seems even plausible that analog computers might be able to do things typically ascribed to quantum computers while being much simpler to implement, run, and program. Bringing back analog computers in much more advanced forms than their historicancestorswillchangetheworldofcomputingdrasticallyandforever.They will not replace the ubiquitous stored-program digital computers but they will complement them, thus making it possible to solve problems that are currently out of reach for standalone digital computers. The author is especially indebted to Dr. Chris Giles for many valuable dis- cussionsandhismeticulousproofreadingofthis2nd editionandtoNicoleMatje for her valuable corrections and suggestions. The author would also like to thank Achim Dassow for information about the QK-329 beam-deflection tube and ad- ditionalinformationonearlymultiplicationdevices.RainerGlaschickprovided muchbackgroundinformationonearlydifferentialanalysersandonthehyperbolic fieldtube.Oliver Bachalsoproofreadthebookandtookspecialcareofthebib- liography making sure that it is consistent and correct. Prof. Dr. Dirk Killat contributed figure 12.9. The new cover picture was taken by Tibor Florestan PlutoandshowstheauthorwithaGTE-22analogcomputerfromthelate1960s. https://doi.org/10.1515/9783110787740-203