28 Sep 2016
Adapting the range of validity for the Carleman linearization
Harry Weber
CORRESPONDING AUTHOR
Institute for Theoretical Electrical Engineering, Leibniz Universität Hannover, Hannover, Germany
Wolfgang Mathis
Institute for Theoretical Electrical Engineering, Leibniz Universität Hannover, Hannover, Germany
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Harry Weber and Wolfgang Mathis
Adv. Radio Sci., 15, 223–230, https://doi.org/10.5194/ars-15-223-2017, https://doi.org/10.5194/ars-15-223-2017, 2017
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In diesem Beitrag wird eine selbstkonsistente Carleman Linearisierung zur Untersuchung von Oszillatoren vorgestellt. Anstelle einer linearen Näherung um einen Arbeitspunkt, erfolgt mit Hilfe der selbstkonsistenten Carleman Linearisierung eine Approximation auf einem vorgegebenen Gebiet. Um in Anschluss das stationäre Verhalten von Oszillatoren zu beschreiben, wird die Berechnung einer Poincaré-Abbildung durchgeführt. Mit dieser ist eine anschließende Analyse des Oszillators möglich.
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Based on new archive sources, it is shown that Egbert von Lepel is one of the pioneers of early radio technology, which has not been adequately dealt with in the history of radio science. In particular, the significance of his 1907 patent of the spark-gap transmitter ("Löschfunkensender") is unknown, although it was granted as a key patent by the Imperial Patent Office in 1911. Therefore, Telefunken paid licenses to von Lepel, but this was the subject of a secret treaty of 1919.
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In this article, we examined the emergence of the new broadcast medium
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The simulation of large scale nonlinear dynamical interconnected systems is a usual task. Due to the high complexity of the considered systems, the principle of thinking in hierarchical structures is common among engineers. This contribution proposes an approach for the numerical simulation of large systems, which keeps the hierarchical system structure alive during the entire simulation and order reduction process, which results in several benefits compared with the state of the art.
Hoang Duc Pham, Soeren Ploennigs, and Wolfgang Mathis
Adv. Radio Sci., 16, 35–41, https://doi.org/10.5194/ars-16-35-2018, https://doi.org/10.5194/ars-16-35-2018, 2018
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This paper deals with the propagation of electromagnetic waves in cylindrical waveguides with irregularly deformed cross-sections. Waveguides are of high interest because of its practical use as a transmission medium. Schelkunoff's method, is a semi-analytical method for computing electromagnetic waves in hollow and cylindrical waveguides bounded by PEC walls. The aim of this paper is to derive the so-called GTE's for irregular deformed waveguides.
Harry Weber and Wolfgang Mathis
Adv. Radio Sci., 15, 223–230, https://doi.org/10.5194/ars-15-223-2017, https://doi.org/10.5194/ars-15-223-2017, 2017
Short summary
Short summary
In diesem Beitrag wird eine selbstkonsistente Carleman Linearisierung zur Untersuchung von Oszillatoren vorgestellt. Anstelle einer linearen Näherung um einen Arbeitspunkt, erfolgt mit Hilfe der selbstkonsistenten Carleman Linearisierung eine Approximation auf einem vorgegebenen Gebiet. Um in Anschluss das stationäre Verhalten von Oszillatoren zu beschreiben, wird die Berechnung einer Poincaré-Abbildung durchgeführt. Mit dieser ist eine anschließende Analyse des Oszillators möglich.
Michał Mika, Mirjam Dannert, Felix Mett, Harry Weber, Wolfgang Mathis, and Udo Nackenhorst
Adv. Radio Sci., 15, 55–60, https://doi.org/10.5194/ars-15-55-2017, https://doi.org/10.5194/ars-15-55-2017, 2017
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Adv. Radio Sci., 15, 43–47, https://doi.org/10.5194/ars-15-43-2017, https://doi.org/10.5194/ars-15-43-2017, 2017
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Recently, for modeling biological amplification processes, nonlinear amplifiers based on the Andronov–Hopf bifurcation have become a focus of attention.
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Seyed Mohammadamin Moosavi, Christian Widemann, and Wolfgang Mathis
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Adv. Radio Sci., 14, 47–50, https://doi.org/10.5194/ars-14-47-2016, https://doi.org/10.5194/ars-14-47-2016, 2016
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Recently, nonlinear amplifiers based on the Andronov–Hopf bifurcation have become a focus of attention in modeling of the mammalian hearing organ. We present a flexible framework implemented on a DSP to analyze various bifurcation based amplifiers to get deeper insights in their nonlinear input-output behavior. A comparison shows the Neimark–Sacker amplifier remarkably outperforms the Andronov–Hopf amplifier regarding the CPU usage.
T. Vennemann, T. Frye, Z. Liu, M. Kahmann, and W. Mathis
Adv. Radio Sci., 13, 1–8, https://doi.org/10.5194/ars-13-1-2015, https://doi.org/10.5194/ars-13-1-2015, 2015
E. Hintzen, T. Vennemann, and W. Mathis
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M. Weber, T. Vennemann, and W. Mathis
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Cited articles
Carleman, T.: Application de la théorie des équations intégrales linéaires aux systèmes d'équations différentielles non linéaires, Acta Mathematica, 1932.
Chua, L. O., Desoer, C. A., and Kuh, E. S.: Linear and Nonlinear Circuits, McGraw-Hill Book Company, 1987.
Kerner, E. H.: Universal formats for nonlinear ordinary differential systems, J. Math. Phys., 22, 1366–1371, 1981.
Kowalski, K.: Nonlinear dynamical systems and classical orthogonal polynomials, J. Math. Phys., 38, 2483–2505, 1997.
Kowalski, K. and Steeb, W.-H.: Nonlinear Dynamical Systems and Carleman Linearization, World Scientific, 1991.
Lesky, P.: Die charakterisierung der klassischen orthogonalen polynome durch Sturm-Liouvillesche Differentialgleichungen, Archive for Rational Mechanics and Analysis, 10, 341–351, 1962.
Rugh, W. J.: Nonlinear System Theory, The Johns Hopkins University Press, 1981.
Tsividis, Y. and Andrew, C. M.: Operation and Modeling of the MOS Transistor, OXFORD University Press, 2011.
Short summary
In this contribution, the limitations of the Carleman linearization approach are presented and discussed. The Carleman linearization transforms an ordinary nonlinear differential equation into an infinite system of linear differential equations which cannot be solved in general. Therefore, the infinite dimensional system has to be approximated by a finite one. The idea of this contribution is to use a Taylor series for the approximation of the infinite system.
In this contribution, the limitations of the Carleman linearization approach are presented and...
