Skip to main content

Nichtlineare Dynamik in der Physik: Forschungsbeispiele und Forschungstrends

  • Conference paper
Komplexe Systeme und Nichtlineare Dynamik in Natur und Gesellschaft

Zusammenfassung

Nichtlineare Prozesse sind in Natur, Technik und Gesellschaft weit verbreitet. Bei der Untersuchung dieser Phänomene gibt es heute schon große Fortschritte, die sich aber hauptsächlich auf Systeme mit wenigen Freiheitsgraden (niedrig-dimensionale Systeme) beziehen. Reale komplexe Systeme sind allerdings im allgemeinen hochdimensional; typische Beispiele dafür finden sich in den Erd-und Umweltwissenschaften oder der Astrophysik. Schwerpunkt sind dabei Fragestellungen zu kritischen Phänomenen, z.B. Klima-relevante Variationen der Sonnenaktivität oder die Vorhersagbarkeit starker Erdbeben. Diese natürlichen Systeme, die meist fernab vom thermodynamischen Gleichgewicht sind, zeichnen sich durch vielfältige komplexe Rückkopplungen und reichhaltige Dynamik in einem breitbandigen Spektrum raumzeitlichen Verhaltens aus; sie sind eine besondere Herausforderung für die Nichtlineare Dynamik.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 149.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. Arnold, V. I. (1984) On the evolution of a magnetic field under the influence of advection and diffusion (in Russian). In: Tikhomirov, V. M. (ed.) Some Problems of Modern Analysis. Moscow State University, Moscow, pp. 8–21

    Google Scholar 

  2. Bak, P., Tang, C., Wiesenfeld, K. (1987) Self-organized criticality: An explanation of 1/f noise, prl 59, 381–384

    Google Scholar 

  3. Brandenburg, A., Klapper, I., Kurths, J. (1995) Generalized entropies in a turbulent dynamo simulation. Phys. Rev. E 52, R4602-R4605

    Article  ADS  Google Scholar 

  4. Braun, R., Feudel, F., Seehafer, N. (1997) Bifurcations and chaos in an array of forced vortices. Phys. Rev. E 55, 6979–6984

    Article  MathSciNet  ADS  Google Scholar 

  5. Bridges, F.G., Hatzes, A.P., Lin, D.N.C. (1984) Structure, stability and evolution of Saturn’s rings. Nature 309, 333–338

    Article  ADS  Google Scholar 

  6. Brilliantov, N., Pöschel, T., Spahn, F., Hertzsch, J.-M. (1996) Model for collisions in granular gases. Phys. Rev. E 53, 5382–5392

    Article  ADS  Google Scholar 

  7. Cardoso, O., Marteau, D., Tabeling, P. (1994) Quantitative experimental study of free decay of quasi-two-dimensional turbulence. Phys. Rev. E 49, 454–461

    Article  ADS  Google Scholar 

  8. Colwell, J. E. (1994) The disruption of planetary satellites and the creation of planetary rings. Planetary and Space Science 42, 1139–114

    Article  ADS  Google Scholar 

  9. Colwell, Joshua E., Esposito, Larry W. (1992) Origins of the rings of Uranus and Neptune. I — Statistics of satellite disruptions. Journal of Geophys. Research 97, 110227 h

    Google Scholar 

  10. Eddy, J. A. (1977) The case of missing sunspots. Sci. American 236, 80–92

    Article  ADS  Google Scholar 

  11. Esposito, Larry W. (1993) Understanding planetary rings. Annual Review of Earth and Planetary Sciences 21, 487–523

    Article  ADS  Google Scholar 

  12. Feudel, F, Seehafer, N. (1995) Bifurcations and pattern formation in a two- dimensional Navier-Stokes fluid. Phys. Rev. E 52, 3506–3511

    Article  MathSciNet  ADS  Google Scholar 

  13. Feudel, F., Seehafer, N. (1995) On the bifurcation phenomena in truncations of the 2D Navier-Stokes equations. Chaos, Solitons & Fractals 5, 1805–1816

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Feudel, F., Seehafer, N., Galanti, B., Rüdiger, S. (1996) Symmetry-breaking bifurcations for the magnetohydrodynamic equations with helical forcing. Phys. Rev. E. 54(3), 2589–2596

    Article  ADS  Google Scholar 

  15. Feudel, F., Seehafer, N., Schmidtmann, O. (1995) Fluid helicity and dynamo bifurcations. Phys. Lett. A. 202, 73–78

    Article  ADS  Google Scholar 

  16. Feudel, F., Seehafer, N., Schmidtmann, O. (1996) Bifurcation phenomena of the magnetofluid equations. Math. Comput. Simula. 40(3), 235–246

    Article  Google Scholar 

  17. Feudel, F., Jansen, W. (1992) CANDYS/QA — a software system for the qualitative analysis of nonlinear dynamical systems. Int. J. Bifurcation and Chaos 2, 773–794

    Article  MathSciNet  MATH  Google Scholar 

  18. Feudel, U., Jansen, W., Kurths, J. (1993) Tori and chaos in a nonlinear dynamo model for solar activity. Int. J. Bifurcation and Chaos 3, 131–138

    Article  MATH  Google Scholar 

  19. Galloway, D., Frisch, U. (1986) Dynamo action in a family of flows with chaotic streamlines. Geophys. Astrophys. Fluid Dyn. 36, 53–83

    Article  MathSciNet  ADS  Google Scholar 

  20. Geller, R. J., Jackson, D. D., Kagan, Y. Y., Mulargia, F. (1997) Earthquake cannot be predicted. Science 275, 1616–1617

    Article  Google Scholar 

  21. Glatzmaier, G. A., Roberts, P. H. (1995) A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle. Phys. Earth. Planet. Int. 91, 63–75

    Article  Google Scholar 

  22. Glatzmaier, G. A., Roberts, P. H. (1995) A three-dimensional self-consistent computer simulation of a geomagnetic field reversal. Nature 377, 203–209

    Article  ADS  Google Scholar 

  23. Goldreich, P., Tremaine, S. (1978) Velocity dispersion in Saturn’s rings. Icarus 34, 227–239

    Article  ADS  Google Scholar 

  24. Gutenberg, B., Richter, C. F. (1954) Earthquake magnitude, intensity, energy and acceleration. Bull. Seismol. Soc. Am. 46, 105–145

    Google Scholar 

  25. Hertzsch, J. M., Scholl, H., Spahn, F., Katzorke, I. (1997) Simulation of collisions in planetary rings. Astronomy and Astrophysics 320, 319–324

    ADS  Google Scholar 

  26. Krause, F., Rädler, K.-H. (1980) Mean-Field Magnetohydrodynamics and Dynamo Theory. Akademie-Verlag, Berlin

    MATH  Google Scholar 

  27. Krause, F., Schmidt, H.-J. (1988) A low-dimensional attractor for modelling the reversals of the Earth’s magnetic field. Phys. Earth. Planet. Int. 52, 23–29

    Article  ADS  Google Scholar 

  28. Krivcky, L. (1984) Long-term fluctuations of solar activity during the last thousand years. Solar Phys. 93, 189–194

    ADS  Google Scholar 

  29. Kurths, J., Schwarz, U., Sonett, C.P., Parlitz, U. (1994) Testing for nonlinearity in radiocarbon data. Nonlin. Processes Geophys. 1, 72–75

    Article  ADS  Google Scholar 

  30. Marion, M., Temam, R. (1989) Nonlinear Galerkin methods. SIAM. J. Num. Anal. 26, 1139–1157

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. Meshalkin, L. D. Sinai, Y. G. (1961) Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous liquid. J. Appl. Math. Mech. 25, 1700–1705

    Article  MathSciNet  MATH  Google Scholar 

  32. Olami, Z., Feder, H. S., Christensen, K. (1992) Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes. Phys. Rev. Lett. 68, 1244–1247

    Article  ADS  Google Scholar 

  33. Rand, D.A., Wilson, H.B. (1995) Using spatio-temporal chaos and intermediate- scale determinism to quantify spatially extended ecosystems. Proc. R. Soc. Lond. B259, 111–117

    Article  ADS  Google Scholar 

  34. Rüdiger, S., Feudel, F., Seehafer, N. (1998) Dynamo bifurcations in an array of driven convectionlike rolls. Phys. Rev. E 57, 5533–5538

    Article  ADS  Google Scholar 

  35. Schmidt, J., Spahn, F., Petzschmann, O. (1998) Vertical distribution of temperature and density in a planetary ring. Icarus (submitted)

    Google Scholar 

  36. Schmidt mann, O., Feudel, F., Seehafer, N. (1997) Nonlinear Galerkin methods for the 3D magnetohydrodynamic equations. Int. J. Bifurcation and Chaos 7, 1497–1507

    Article  MathSciNet  MATH  Google Scholar 

  37. Seehafer, N., Feudel, F., Schmidtmann, O. (1996) Nonlinear dynamo with ABC forcing. Astron. Astrophys. 314, 693–699

    ADS  Google Scholar 

  38. Showalter, Mark R. (1991) Visual detection of 1981S13, Saturn’s eighteenth satellite, and its role in the Encke gap. Nature 351, 709–713

    Article  ADS  Google Scholar 

  39. Sommeria, J. (1986) Experimental study of the two-dimensional inverse energy cascade in a square box. J. Fluid Mech. 170, 139–168

    Article  ADS  Google Scholar 

  40. Sonett, C. P. (1984) Very long solar periods and the radiocarbon record. Rev. Geophys. Space Phys. 22, 239–254

    Article  ADS  Google Scholar 

  41. Spahn, F., Hertzsch, J.-M., Brilliantov, N.V. (1995) The role of particle collisions for the dynamics in planetary rings. Chaos, Solitons and Fractals 5, 1945

    Article  ADS  Google Scholar 

  42. Spahn, F., Schwarz, U., Kurths, J. (1997) Clustering of granular assemblies with temperatur dependent restitution and under differential rotation. Phys. Rev. Lett. 78, 1596–1601

    Article  ADS  Google Scholar 

  43. Spahn, F., Greiner, J., Schwarz, U. (1992) Moonlets in Saturn’s rings. Advances in Space Research 12, 141–147

    Article  ADS  Google Scholar 

  44. Stieglitz, R., Müller, U. (1996) GEODYNAMO Eine Versuchsanlage zum Nachweis des homogenen Dynamoeffektes. Research Report FZKA-5716, Forschungszentrum Karlsruhe

    Google Scholar 

  45. Stuiver, M., Braziunas, T. F. (1989) Atmospheric 14C and century-scale solar oscillations. Nature 338, 405–408

    Article  ADS  Google Scholar 

  46. Thess, A. (1992) Instabilities in two-dimensional spatially periodic flows. Part I: Kolmogorov flow. Phys. Fluids A 4, 1385–1395

    Article  MathSciNet  ADS  MATH  Google Scholar 

  47. Turcotte, D. L. (1997) Fractals and Chaos in Geology and Geophysics. Cambridge University Press, Cambridge

    Google Scholar 

  48. Voss, H., Kurths, J., Schwarz, U. (1996) Reconstruction of grand minima of solar activity from A14C data: Linear and nonlinear signal analysis. J. Geophys. Res. A (Space Physics) 101, 15637–15643

    Article  ADS  Google Scholar 

  49. Witt, A., Kurths, J., Krause, F., Fischer, K. (1994) On the validity of a model for the reversals of the Earth’s magnetic field. Geophys. Astrophys. Fluid. Dyn. 77, 79–91

    Article  ADS  Google Scholar 

  50. Wittmann, A. (1978) The sunspot cycle before the Maunder minimum. Astron. Astrophys. 66, 93–97

    ADS  Google Scholar 

  51. Zöller, G., Engbert, R., Hainzl, S., Kurths, J. (1998) Testing for unstable periodic orbits to characterize spatiotemporal dynamics. Chaos, Solitons & Fractals 9(8), 1–20

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kurths, J., Seehafer, N., Spahn, F. (1999). Nichtlineare Dynamik in der Physik: Forschungsbeispiele und Forschungstrends. In: Mainzer, K. (eds) Komplexe Systeme und Nichtlineare Dynamik in Natur und Gesellschaft. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60063-0_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-60063-0_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64240-1

  • Online ISBN: 978-3-642-60063-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics