Consistency of constructions for cell division processes

Nagel, Werner; Biehler, Eike

doi:10.1239/aap/1444308875

Cited by 3 publications

(1 citation statement)

References 8 publications

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“…They have been invented in [25] and since their introduction they have stimulated lots of research, cf. [4,11,13,14,15,16,20,23,26,34,35,36,37,38,40,41].…”

Section: Introductionmentioning

confidence: 99%

A Mecke-type formula and Markov properties for STIT tessellation processes

Nagel¹,

Nguyen²,

Thaele³

et al. 2017

ALEA

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“…They have been invented in [25] and since their introduction they have stimulated lots of research, cf. [4,11,13,14,15,16,20,23,26,34,35,36,37,38,40,41].…”

Section: Introductionmentioning

confidence: 99%

A Mecke-type formula and Markov properties for STIT tessellation processes

Nagel¹,

Nguyen²,

Thaele³

et al. 2017

ALEA

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Tessellation-valued processes that are generated by cell division

Martínez,

Nagel

2023

J. Appl. Probab.

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Processes of random tessellations of the Euclidean space $\mathbb{R}^d$ , $d\geq 1$ , are considered that are generated by subsequent division of their cells. Such processes are characterized by the laws of the life times of the cells until their division and by the laws for the random hyperplanes that divide the cells at the end of their life times. The STIT (STable with respect to ITerations) tessellation processes are a reference model. In the present paper a generalization concerning the life time distributions is introduced, a sufficient condition for the existence of such cell division tessellation processes is provided, and a construction is described. In particular, for the case that the random dividing hyperplanes have a Mondrian distribution—which means that all cells of the tessellations are cuboids—it is shown that the intrinsic volumes, except the Euler characteristic, can be used as the parameter for the exponential life time distribution of the cells.

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Parameter Optimization on a Tessellation Model for Crack Pattern Simulation

León,

Montero,

Nagel

2023

IEEE Access

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The capabilities of a parametric model for crack patterns simulation are presented. Planar tessellations are partitions of the plane into convex polygons (called cells) without overlapping. The Voronoi tessellations and Poisson line tessellations are the most prominent models; however, to model crack patterns, it is more appropriate to deal with tessellations that are generated by a cell division process. We describe the STIT tessellation as a reference model for crack patterns and introduce several modifications. Having described a variety of 40 parametric models and appropriate simulation algorithms, we delineate and specify tuning methods to optimize the adaption of the model to real crack pattern data. An example of a metalized polydimethylsiloxane demonstrates the capability of our approach. The results indicate that this approach yields a considerable improvement in modeling compared to previous studies.INDEX TERMS crack pattern, random tessellation, STIT tessellation, spatial statistics, metaheuristic tuning methods.

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Consistency of constructions for cell division processes

Cited by 3 publications

References 8 publications

A Mecke-type formula and Markov properties for STIT tessellation processes

A Mecke-type formula and Markov properties for STIT tessellation processes

Tessellation-valued processes that are generated by cell division

Parameter Optimization on a Tessellation Model for Crack Pattern Simulation

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