Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Milnor J (2003) Towards the Poincaré conjecture and the classification of 3-manifolds. Not Am Math Soc 50:126–1233
Perelman G (2002) The entropy formula for the Ricci flow and its geometric applications. http://arxiv.org/abs/math.DG/0211159
Hamilton RS (1982) Three-manifolds with positive Ricci curvature. J Differ Geom 17:255–306
Thurston WP (1982) Three-dimensional manifolds. Kleinian groups and hyperbolic geometry. Bull Am Math Soc 6:357–381
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 67–73
Gvozdev VI, Kouzaev GA (1991) Physics and the field topology of 3-D microwave circuits. Russ Microelectron 21:1–17
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 37–48
Bykov DV, Gvozdev VI, Kouzaev GA (1993) Contribution to the theory of topological modulation of the electromagnetic field. Russ Phys Doklady 38:512–514
Kouzaev GA (1996) Theoretical aspects of measurements of the topology of the electromagnetic field. Meas Tech 39:186–191
Kouzaev GA (2006) Topological computing. WSEAS Trans Comput 6:1247–1250
Fabrizio M, Morro A (2003) Electromagnetism of continuous media. Oxford University Press, Oxford
Andronov AA, Leontovich EA (1973) Qualitative theory of second-order dynamical systems. Transl. from Russian. Halsted Press, New York
Peikert R, Sadlo F (2005) Topology guided visualization of constrained vector fields. In: Proceedings of the TopolnVis 2005, Bumerize, Slovakia
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.
Gvozdev VI, KouzaevGA (1992) Microwave flip-flop. Russian Federation Patent, No 2054794, dated 26 Feb 1992
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this paper
Cite this paper
Kouzaev, G. (2009). Communications by Vector Manifolds. In: Mastorakis, N., Mladenov, V., Kontargyri, V. (eds) Proceedings of the European Computing Conference. Lecture Notes in Electrical Engineering, vol 27. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-84814-3_57
Download citation
DOI: https://doi.org/10.1007/978-0-387-84814-3_57
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-84813-6
Online ISBN: 978-0-387-84814-3
eBook Packages: EngineeringEngineering (R0)