- Tytuł:
- Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials
- Autorzy:
-
Gurgul, Daniel
Burbelko, Andriy
Wiktor, Tomasz - Powiązania:
- https://bibliotekanauki.pl/articles/2056033.pdf
- Data publikacji:
- 2021
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
planimetric analysis
linear analysis
estimation of diameter sizes distribution
probability density function
analiza planimetryczna
analiza liniowa
szacowanie rozkładu wielkości średnic
funkcja gęstości prawdopodobieństwa - Opis:
- 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.
- Źródło:
-
Journal of Casting & Materials Engineering; 2021, 5, 4; 53--60
2543-9901 - Pojawia się w:
- Journal of Casting & Materials Engineering
- Dostawca treści:
- Biblioteka Nauki
Artykuł