Abstract
This paper discusses aspects of topology as relevant for loop dynamics as they occur in physical modeling synthesis algorithms. Boundary and interaction point behavior is treated purely from a topological perspective for some dynamical systems in one and two dimensions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Smith, J.O.: Acoustic modeling using digital waveguides. In: Roads, C., Pope, S.T., Piccialli, A., De Poli, G. (eds.) Musical Signal Processing. Swets, Lisse, Netherlands, pp. 221–263 (1997)
Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)
Jänich, K.: Topologie, 7th edn. Springer, Berlin (2001)
Tabachnikov, S.: Billiards. Soc. Math. de France, Paris (1995)
Brack, M., Bhaduri, R.K.: Semiclassical Physics, vol. 96. Addison-Wesley Publishing, Reading (1997)
Keller, J.B., Rubinow, S.I.: Asymptotic Solution of Eigenvalue Problems. Annals of Physics 9, 24–75 (1960)
Essl, G., Serafin, S., Cook, P.R., Smith, J.O.: Theory of Banded Waveguides. Computer Music Journal 28, 37–50 (2004)
Bar-Natan, D.: On the Vassiliev Knot Invariants. Topology 34, 423–472 (1995)
Essl, G.: Velocity Excitations and Impulse Responses of Strings – Aspects of Continuous and Discrete Models. ArXiv preprint physics/0401065 (2004), http://arxiv.org/abs/physics/0401065
Rayleigh, J.W.S.: The Theory of Sound, vol. II. Dover, New York (1945)
Essl, G.: Trapping and Steering on Lattice Strings: Virtual SlowWaves, Directional and Non-propagating Excitations. Physical Review E 69 (066601–1–6) (2004)
Essl, G.: Physical Wave Propagation Modeling for Real-Time Synthesis of Natural Sounds. PhD thesis, Princeton University, Princeton, NJ (2002) Available also as Princeton University Computer Science Technical Report TR-659-02 at, http://ncstrl.cs.princeton.edu/expand.php?id=TR-659-02
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Essl, G. (2005). Aspects of the Topology of Interactions on Loop Dynamics in One and Two Dimensions. In: Wiil, U.K. (eds) Computer Music Modeling and Retrieval. CMMR 2004. Lecture Notes in Computer Science, vol 3310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31807-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-31807-1_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24458-5
Online ISBN: 978-3-540-31807-1
eBook Packages: Computer ScienceComputer Science (R0)