Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Random Laguerre tessellations
View through CrossRef
A systematic study of random Laguerre tessellations, weighted generalisations of the well-known Voronoi tessellations, is presented. We prove that every normal tessellation with convex cells in dimension three and higher is a Laguerre tessellation. Tessellations generated by stationary marked Poisson processes are then studied in detail. For these tessellations, we obtain integral formulae for geometric characteristics and densities of the typical
k
-faces. We present a formula for the linear contact distribution function and prove various limit results for convergence of Laguerre to Poisson-Voronoi tessellations. The obtained integral formulae are subsequently evaluated numerically for the planar case, demonstrating their applicability for practical purposes.
Cambridge University Press (CUP)
Title: Random Laguerre tessellations
Description:
A systematic study of random Laguerre tessellations, weighted generalisations of the well-known Voronoi tessellations, is presented.
We prove that every normal tessellation with convex cells in dimension three and higher is a Laguerre tessellation.
Tessellations generated by stationary marked Poisson processes are then studied in detail.
For these tessellations, we obtain integral formulae for geometric characteristics and densities of the typical
k
-faces.
We present a formula for the linear contact distribution function and prove various limit results for convergence of Laguerre to Poisson-Voronoi tessellations.
The obtained integral formulae are subsequently evaluated numerically for the planar case, demonstrating their applicability for practical purposes.
Related Results
Tessellations de Voronoï généralisées : modélisation CAO, propriétés statistiques et application à l'homogénéisation du comportement des agrégats polycristallins
Tessellations de Voronoï généralisées : modélisation CAO, propriétés statistiques et application à l'homogénéisation du comportement des agrégats polycristallins
De nombreux matériaux hétérogènes peuvent voir leur architecture représentée géométriquement au moyen de Diagrammes De Voronoi (DDV). Les agrégats polycristallins en particulier so...
On Non-Poissonian Voronoi Tessellations
On Non-Poissonian Voronoi Tessellations
<p>The Voronoi tessellation is the partition of space for a given seeds pattern and the result of the partition depends completely on the type of given pattern ”random”, Pois...
Seismological applications of Laguerre expansions
Seismological applications of Laguerre expansions
abstract
If we establish a set of orthogonal functions with resonant and decay characteristics quite similar to those of seismic signals, then a few, or at most a fe...
Solution of conformable Laguerre and associated Laguerre equations using Laplace transform†
Solution of conformable Laguerre and associated Laguerre equations using Laplace transform†
In this paper, the conformable Laguerre and associated Laguerre
differential equations are solved using the Laplace transform. The
solution is found to be in exact agreement with t...
An Efficient Laguerre Minimum Action Method for Computing Quasi-Potentials
An Efficient Laguerre Minimum Action Method for Computing Quasi-Potentials
Minimum action methods provide a powerful framework for analyzing rare transitions in small-noise-driven dynamical systems, but their practical performance is often limited by time...
The Perceived Beauty of Regular Polygon Tessellations
The Perceived Beauty of Regular Polygon Tessellations
Beauty judgments for regular polygon tessellations were examined in two experiments. In experiment 1 we tested the three regular and eight semi-regular tilings characterized by a s...
Projection estimation for inverses problems on Laguerre and Hermite spaces
Projection estimation for inverses problems on Laguerre and Hermite spaces
Estimation par projection pour des problèmes inverses sur des espaces de Laguerre et d'Hermite
Dans cette thèse, nous développons des procédures d'estimation non pa...
Effectiveness of Dynamic Matrix Control algorithm with Laguerre functions
Effectiveness of Dynamic Matrix Control algorithm with Laguerre functions
The paper is concerned with the presentation and analysis of the Dynamic Matrix Control (DMC) model predictive control algorithm with the representation of the process input trajec...