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Towards Sub-cellular Modeling with Delaunay Triangulation

G. Grise, M. Meyer-Hermann (2010)

Mathematical Modelling of Natural Phenomena

In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –,...

Translative packing of a square with sequences of squares

Janusz Januszewski (2010)

Colloquium Mathematicae

Let S be a square and let S' be a square of unit area with a diagonal parallel to a side of S. Any (finite or infinite) sequence of homothetic copies of S whose total area does not exceed 4/9 can be packed translatively into S'.

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