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A collision probability problem

Published online by Cambridge University Press:  14 July 2016

Irini Papaderou-Vogiatzaki  and
Rolf Schneider
Irini Papaderou-Vogiatzaki*
Affiliation:
Universität Freiburg i. Br.
Rolf Schneider*
Affiliation:
Universität Freiburg i. Br.
*
∗ Postal address: Friedrichstr. 3a, D-1000 Berlin 45, W. Germany.
∗∗ Postal address: Mathematisches Institut, Albert-Ludwigs-Universität, Albertstr. 23b, D-7800 Freiburg i. Br., W. Germany.
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Abstract

A random stream of convex particles in , all moving uniformly in the same direction, is given. A convex test body is brought into the stream by means of a random rigid motion, independent of the stream. The number of particles that hit the test body at a preassigned boundary set within unit time is a random variable. Its expected value is determined under different model assumptions.

Keywords

RANDOM COLLISIONSPOINT PROCESSES IN SPACES OF CONVEX BODIESCURVATURE MEASURES

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 3 , September 1988 , pp. 617 - 623
Copyright
Copyright © Applied Probability Trust 1988 

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References

[1] Bonnesen, T. and Fenchel, W. (1934) Theorie der konvexen Körper. Springer-Verlag, Berlin.Google Scholar
[2] Cohn, D. L. (1980) Measure Theory. Birkhäuser, Boston.Google Scholar
[3] Enns, E. G., Smith, B. R. and Ehlers, P. F. (1984) Hitting spheres with straight-line motion or Brownian motion. J. Appl. Prob. 21, 70–79.Google Scholar
[4] Federer, H. (1969) Geometric Measure Theory. Springer-Verlag, Berlin.Google Scholar
[5] Leichtweiss, K. (1980) Konvexe Mengen. VEB Deutsch. Verl. d. Wiss., Berlin.Google Scholar
[6] Papaderou-Vogiatzaki, I. (1983) Kollisionswahrscheinlichkeiten bei konvexen Körpern. Thesis, Freiburg i. Br.Google Scholar
[7] Schneider, R. (1975) Kinematische Berührmaße für konvexe Körper und Integralrelationen für Oberflächenmaße. Math. Ann. 218, 253–267.Google Scholar
[8] Schneider, R. (1978) Curvature measures of convex bodies. Ann. Mat. Pura Appl. 116, 101–134.Google Scholar
[9] Schneider, R. (1979) Bestimmung konvexer Körper durch Krümmungsmaße. Comment. Math. Helvet. 54, 42–60.Google Scholar
[10] Schneider, R. (1979) Boundary structure and curvature of convex bodies. In Contributions to Geometry, ed. Tölke, J. and Wills, J. M., Birkhäuser, Basel, 13–59.Google Scholar
[11] Schneider, R. (1986) Curvature measures and integral geometry of convex bodies, II. Rend. Sem. Mat. Univers. Politecn. Torino 44, 263–275.Google Scholar
[12] Schneider, R. and Wieacker, J. A. (1984) Random touching of convex bodies. In Stochastic Geometry, Geometric Statistics, Stereology, ed. Ambartzumian, R. and Weil, W.; Teubner, Leipzig, 154–169.Google Scholar