Abstract
In order to find expressions or to find numerical values for sorne physical or physicochemical properties in systems in which particles are distributed totally at random (or that can be considered, in good approximation, as ifthey were) sometimes it is necessary to have distribution functions for the nth-nearest-neighbour particle around sorne generic one. To our knowledge, a general formula <loes not exist which allows obtain them. There are specific expressions reported for only the four first functions, a couple of which with sorne mistakes. In this paper such a general formula is derived, it is indicated how to use it, and the particular first five functions are listed, including their plots.
References
Chandrasekhar, S. 1943. Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15: 86-87.
Tonooka, K. Yamada, K., Kato, Y., Hayakawa, T. & Kamata, N. 1997. Theory ofdonor fluorescence govemed by discrete energy transfers between rare-earth ions in glasses J. Opt. Soc. Am. B. 14, 713-721.
Tewari, A. & Gokhale, A. M. 2006. Nearest-neighbor distributions in thin films. sheets, and plates. Acta Mater. 54: 1957-1963.
lnokuti M. & Hirayama, F. 1965. lnfluence of energy transfer by the exchange mechanism on donor luminescence. J. Chem. Phys. 43: 1978-1989.
Hadad, C. Z. & Vásquez, S. O. 2003. Statistical approach to the transient up-converted population in monodoped amorphous solids. Chem. Phys. 5: 3027-3033.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright (c) 2023 Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales