Stereological estimation of the size distribution for systems of random convex polyhedrons

1996 ◽  
Vol 28 (2) ◽  
pp. 340-341
Author(s):  
Joachim Ohser ◽  
Werner Nagel
Keyword(s):  
Size Distribution ◽  
Particle Systems ◽  
Parameter Distribution ◽  
Two Dimensional ◽  
Size Parameter ◽  
Typical Particle ◽  
Dimensional Section ◽  
Random Convex

Consider homogeneous spatial particle systems consisting of homothetic particles. Important examples are systems of balls or systems of homothetic convex polyhedrons. For such models the distribution of the typical particle can be expressed by the distribution of one size parameter. We are interested in the stereological estimation of this size parameter distribution from observations on two-dimensional section planes.

Stereological estimation of the size distribution for systems of random convex polyhedrons

1996 ◽  
Vol 28 (02) ◽  
pp. 340-341
Author(s):  
Joachim Ohser ◽  
Werner Nagel
Keyword(s):  
Size Distribution ◽  
Particle Systems ◽  
Parameter Distribution ◽  
Two Dimensional ◽  
Size Parameter ◽  
Typical Particle ◽  
Dimensional Section ◽  
Random Convex

Consider homogeneous spatial particle systems consisting of homothetic particles. Important examples are systems of balls or systems of homothetic convex polyhedrons. For such models the distribution of the typical particle can be expressed by the distribution of one size parameter. We are interested in the stereological estimation of this size parameter distribution from observations on two-dimensional section planes.

scholarly journals Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

2021 ◽  
Vol 5 (4) ◽  
pp. 53-60
Author(s):  
Daniel Gurgul ◽  
Andriy Burbelko ◽  
Tomasz Wiktor
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Size Distribution ◽  
Density Function ◽  
Cross Section ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Two Dimensional ◽  
Mathematical Formulas ◽  
Transparent Materials

This paper presents a new proposition on how to derive mathematical formulas that describe an unknown Probability Density Function (PDF3) of the spherical radii (r3) of particles randomly placed in non-transparent materials. We have presented two attempts here, both of which are based on data collected from a random planar cross-section passed through space containing three-dimensional nodules. The first attempt uses a Probability Density Function (PDF2) the form of which is experimentally obtained on the basis of a set containing two-dimensional radii (r2). These radii are produced by an intersection of the space by a random plane. In turn, the second solution also uses an experimentally obtained Probability Density Function (PDF1). But the form of PDF1 has been created on the basis of a set containing chord lengths collected from a cross-section.The most important finding presented in this paper is the conclusion that if the PDF1 has proportional scopes, the PDF3 must have a constant value in these scopes. This fact allows stating that there are no nodules in the sample space that have particular radii belonging to the proportional ranges the PDF1.

The Estimation of mean shape and mean particle number in overlapping particle systems in the plane

1995 ◽  
Vol 27 (01) ◽  
pp. 102-119 ◽  
Author(s):  
Wolfgang Weil
Keyword(s):  
Particle Number ◽  
Convex Set ◽  
Boolean Model ◽  
Particle Systems ◽  
Typical Particle ◽  
The Mean ◽  
Convexity Assumptions ◽  
Particle Process ◽  
Simply Connected ◽  
Number Of Particles

A stationary (but not necessarily isotropic) Boolean model Y in the plane is considered as a model for overlapping particle systems. The primary grain (i.e. the typical particle) is assumed to be simply connected, but no convexity assumptions are made. A new method is presented to estimate the intensity y of the underlying Poisson process (i.e. the mean number of particles per unit area) from measurements on the union set Y. The method is based mainly on the concept of convexification of a non-convex set, it also produces an unbiased estimator for a (suitably defined) mean body of Y, which in turn makes it possible to estimate the mean grain of the particle process.

Transition of the flutter mode of a two-dimensional section with an external store

1992 ◽  
Vol 29 (3) ◽  
pp. 511-512 ◽  
Author(s):  
Zhi-chun Yang ◽  
Ling-cheng Zhao
Keyword(s):  
Two Dimensional ◽  
Dimensional Section
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