Communications by Vector Manifolds

  • Guennadi Kouzaev
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 27)


The topological structure of the electromagnetic fields of signals is studied. It is shown that the topology of field-force line maps is a natural carrier of digital information. In this paper, a new type of topologically modulated signals is proposed. They are impulses the vectorial content of which varies with the time and spatial coordinates. Impulses can have topologically different spatiotemporal shapes of fields described by a combination of 3-D vector manifolds, and they carry logical information by this spatiotemporal content. The noise immunity of these signals is estimated, and hardware design principles are proposed based on the geometrical interpretation of the energy conservation law. The derived results are interesting for communications through dispersive and noisy media and for advanced computing.


Phase Space Noise Immunity Ricci Flow Topological Description Topological Modulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Milnor J (2003) Towards the Poincaré conjecture and the classification of 3-manifolds. Not Am Math Soc 50:126–1233MathSciNetGoogle Scholar
  2. 2.
    Perelman G (2002) The entropy formula for the Ricci flow and its geometric applications.
  3. 3.
    Hamilton RS (1982) Three-manifolds with positive Ricci curvature. J Differ Geom 17:255–306MATHMathSciNetGoogle Scholar
  4. 4.
    Thurston WP (1982) Three-dimensional manifolds. Kleinian groups and hyperbolic geometry. Bull Am Math Soc 6:357–381CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Gvozdev VI, Kouzaev GA (1988) A field approach to the CAD of microwave three-dimensional integrated circuits. In: Proceedings of the microwave 3-D integrated circuits. Tbilisy, Georgia, pp 67–73Google Scholar
  6. 6.
    Gvozdev VI, Kouzaev GA (1991) Physics and the field topology of 3-D microwave circuits. Russ Microelectron 21:1–17Google Scholar
  7. 7.
    Kouzaev GA (1991) Mathematical fundamentals for topological electrodynamics of 3-D microwave IC. In: Electrodynamics and techniques of micro- and millimeter waves. MSIEM, Moscow, pp 37–48Google Scholar
  8. 8.
    Bykov DV, Gvozdev VI, Kouzaev GA (1993) Contribution to the theory of topological modulation of the electromagnetic field. Russ Phys Doklady 38:512–514Google Scholar
  9. 9.
    Kouzaev GA (1996) Theoretical aspects of measurements of the topology of the electromagnetic field. Meas Tech 39:186–191CrossRefGoogle Scholar
  10. 10.
    Kouzaev GA (2006) Topological computing. WSEAS Trans Comput 6:1247–1250Google Scholar
  11. 11.
    Fabrizio M, Morro A (2003) Electromagnetism of continuous media. Oxford University Press, OxfordCrossRefMATHGoogle Scholar
  12. 12.
    Andronov AA, Leontovich EA (1973) Qualitative theory of second-order dynamical systems. Transl. from Russian. Halsted Press, New YorkGoogle Scholar
  13. 13.
    Peikert R, Sadlo F (2005) Topology guided visualization of constrained vector fields. In: Proceedings of the TopolnVis 2005, Bumerize, SlovakiaGoogle Scholar
  14. 14.
    Shi K, Theisel H, Weinkauf T, Hauser H, Hege H-C, Seidel H-P (2006) Path line oriented topology for periodic 2D time-dependent vector fields. In: Proceedings of the Eurographics/IEEE-VGTC Symp. Visualization.Google Scholar
  15. 15.
    Gvozdev VI, KouzaevGA (1992) Microwave flip-flop. Russian Federation Patent, No 2054794, dated 26 Feb 1992Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Guennadi Kouzaev
    • 1
  1. 1.Department of Electronics and TelecommunicationsNorwegian University of Science and TechnologyTrondheimNorway

Personalised recommendations