Delaunay

Delaunay method - in this method the computational grid is essentially constructed by connecting a specified set of points in the problem domain. The connection of these points should, however, be based on specific rules to avoid unacceptable discreti2ations. To avoid breakthrough of the domain boundary it may be necessary to adjust (e.g. add) boundary points (Liseikin, 1999). 

Delaunay, D., D. Lakehal, C. Barre, and C. Sacre. 1997. Numerical and wind runnel siinula-rioiis of gas dispersion around a rectangular building. J. Wind Engineering and Industrial. Aerodynamics, vols. 67-68, pp. 721-732. 

Delaunay, J. Dhermy, D. (1993). Mutations involving the spectrin heterodimer contact site Clinical expression and alterations in specific function. Sem. Hematol. 30, 21-33. 

Pettersson K, Delaunay F, Gustafsson J-A (2000) Estrogen receptor beta acts as a dominant regulator of estrogen signaling. Oncogene 19 4970... 

Delaunay-El AUam, M., Marlier, L., and Schaal, B. (2006). Learning at the breast preference formation for an artificial scent and its attraction against the odor of maternal milk. Infant Behav. Dev. 29, 308-321. 

Voronoi-Delaunay Method for Description of Corpuscular and Sponge-Like Porous Solids... 

The way of the best choice to model PS s structure on both molecular and supramolecular levels begins with allocation of primary building units (PBUs), which without gaps and overlaps would fill a 3D space occupied by a PS. An universal method for allocation of such PBUs in both ordered and randomly arranged PSs, formed of packings of convex particles (or pores), is based on the construction of the assembles of Voronoi polyhedra (V-polyhedra) and Delaunay simplexes (or D-poly-hedra), which form Voronoi-Delaunay tessellation [100],... 

The terms Voronoi polyhedron and Delaunay simplex have English geometry school origin. The first was Rodgers [136], who started using them regarding a great fundamental impact to this field from Russian mathematicians G.F. Voronoi (1868 to 1908) and B.N. Delaunay (1890 to 1980). The term V-polyhedron was used by many mathematicians [131-134], This makes sense because similar... 

Figure 9.27 Example of Voronoi (V, dotted line) and Delaunay (D, solid line) tessellations for a 2D case.

The geometry of V-polyhedra and V-tessilations was elaborated by Voronoi and Delaunay [143,144], They have shown that all PBU/Ps have a convex shape, each facet is common for two neighboring PBU/Ps, each edge is formed by no less than d PBU/Ps (d is the dimension of V-tessellation), and no less than d + 1 PBU/Ps intersect at each vertex. We write no less but an exact coincidence usually takes place. 

To be on the safe side, we should note that this kind of partitioning of space was used by Descartes in 1644 [139], and its origin can possibly be found in ancient times [141]. The further development was proposed by Gauss [142], Dirichlet [139], and others, but the most detailed and thorough mathematical description was given by, namely, Voronoi and Delaunay [143,144]. 

Identify the Delaunay tetrahedra enclosing the cavities The union of the Delaunay tetrahedra corresponding to the aforementioned cluster of... 

Determine the actual cavity volume and surface area within the Delaunay tetrahedra The overlap of the exclusion spheres with the relevant Delaunay tetrahedra is subtracted analytically, leaving only the actual cavity volume and surface area. This nontrivial calculation is from the multiple overlap of exclusion spheres, but a systematic method for carrying it out is available.70 71... 

N. Delaunay, V. Pichon and M.C. Hennion, Experimental comparison of three monoclonal antibodies for the class-selective immunoextraction of triazines. Correlation with molecular modeling and principal component analysis studies. J. Chromatogr.A 999 (2003) 3-15. 

Maibeche-Coisne M, Sobrio F, Delaunay T, Lettere M, Dubroca J, Jacquin-Joly E, Nagnan-Le Meillour P (1997) Insect Biochem Mol Biol 27 213... 

C. Martineau, P. Blanchard, D. Rondeau, J. Delaunay, J. Roncali, Synthesis and electronic properties of adducts of oligothienylenevinylenes and fullerene C60, Advanced Materials, vol. 14, pp. 283-287, 2002. 

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