Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-19T00:15:47.405Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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