Convergence of randomly oscillating point patterns to the Poisson point process

summary:Oscillating point patterns are point processes derived from a locally finite set in a finite dimensional space by i.i.d. random oscillation of individual points. An upper and lower bound for the variation distance of the oscillating point pattern from the limit stationary Poisson process is established. As a consequence, the true order of the convergence rate in variation norm for the special case of isotropic Gaussian oscillations applied to the regular cubic net is found. To illustrate these theoretical results, simulated planar structures are compared with the Poisson point process by the quadrat count and distance methods

Modelling spherulite growth by planar tessellations

Computer simulated models of planar Poisson-Voronoi and Johnson-Mehl tessellations are compared with a gradually growing thin spherulite layer of polypropylen. The growth kinetics is described and a non-homogeneous Johnson-Mehl tessellation is proposed as a suitable model

Problematika posuzování struktury nanomateriálů

Application of stereology in the quantitative description of nanomaterial grain structure

The selection of geometry

The laws of geometric sampling objects in 2D and 3D are presented and discussed

Classification of 3D tesellations

Classification of Voronoi tessellations generated by various point processes is proposed and discussed, the previously proposed models are reviewed and commented

History of mathematics around the turn of the XVII. and XVIII. centuries as reflected in the letters of Johann Bernoulli and Pierre Varignon

The origins and development of calculus in the correspondence of Johann Bernoulli and Pierre Varignon