Abstract
We report investigations regarding the possibility for improving ultrasonic imaging by an analysis of pulse deformations. Starting with a stochastic solution of the lossy wave equation, we present a general approach for perturbing stochastic processes on Lie groups by a Poisson process. Applications to radiation transport are indicated.
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
G. Bayer, H. Kuttruff, and T. Niedertränk. Zur Mehrfachstreuung von Ultraschall. Bestimmung der mittleren freien Weglänge in stark streuenden Medien. Acustica, 80:170–17, 1994.
E. B. Dynkin. Markov processes. Vols. I, IL Academic Press Inc., Publishers, New York, 1965. Translated with the authorization and assistance of the author by J. Fabius, V. Greenberg, A. Maitra, G. Majone. Die Grundlehren der Mathematischen Wissenschaften, Bände 121, 122.
POAN Research Group (Ed.). New Aspects of Electromagnetic and Acoustic Wave Diffusion. Number 144 in Springer Tracts in Modern Physics. Springer, Berlin Heidelberg, 1998.
Mark Kac. A stochastic model related to the telegrapher’s equation. Rocky Mountain J. Math., 4:497–509, 1974. Reprinting of an article published in 1956, Papers arising from a Conference on Stochastic Differential Equations (Univ. Alberta, Edmonton, Alta., 1972).
Stanley Kaplan. Differential equations in which the Poisson process plays a role. Bull. Amer. Math. Soc, 70:264–268, 1964.
J. Kisyński. On M. Kac’s probabilistic formula for the solution of the telegraphist’s equation. Ann. Polon. Math., 29:259–272, 1974. Collection of articles dedicated to the memory of Tadeusz Wazewski, III.
Enzo Orsingher. A planar random motion governed by the two-dimensional telegraph equation. J. Appl. Probab., 23(2):385–397, 1986.
R.-D. Reiss. A course on point processes. Springer-Verlag, New York, 1993.
Ping Sheng. Wave Scattering, Localization and mesoscopic phenomena. Academic Press, San Diego, 1995.
A. Z. Veselovskaya. Solution of a mixed problem for a telegraph equation by the Monte Carlo method. Vestnik Leningrad. Univ. Mat. Mekh. Astronom., 1986(vyp. 3):96–98, 125.
E. Weiland, K. Giese, and C. Hundertmark. Ultraschall-Transmissionsmessungen zur Charakterisierung von Gewebe-Einschlüssen in der Mamma. Z. Med. Phys., pages 75–82, 1997.
R. Willenbrock. Streuung von Picosekundenlaserimpulsen in turbiden Medien: Abbildung mittels Photonendichtewellen. Master’s thesis, Physikalisch-Technische Bundesanstalt, Berlin, 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mathé, P., Hinrich Zacharias-Langhans, J. (2003). On Scattering of Ultrasonic Waves. In: Jäger, W., Krebs, HJ. (eds) Mathematics — Key Technology for the Future. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55753-8_40
Download citation
DOI: https://doi.org/10.1007/978-3-642-55753-8_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62914-3
Online ISBN: 978-3-642-55753-8
eBook Packages: Springer Book Archive