Patterns covering the plane by fitting together replicas of the same basic shape have been created by Nature and Man either by accident or design. Examples range from the simple hexagonal pattern of the bees' honeycomb or a tiled floor to the intricate decorations used by the Moors in thirteent...
1.4 Examples: Poisson–, Cox– and Gibbs–Voronoi Tessellations It is easy to check that the assumptions listed in Sect. 1.2, are satisfied if the underlying point process is a stationary PPP. Indeed, for (3) note that by the Laplace transform, for any measurable B⊂R2 E[exp(β#(...
In all examples, the deformed configuration was validated by comparing all edge lengths and sector angles in the folded configuration with those in the unfolded configuration. Crease pattern optimization The optimizations were carried out using MATLAB’s implementation of the interior-point method. ...
design approaches have been proposed to create isotropic, stochastic cellular single-phase materials, with random point processes [48], Voronoi tessellations [49], inverse modeling [50], Gaussian random fields [51,52], and voxelization methods [10,53,54] to constitute representative examples. In...
{V}_3\), in the phase space of the three variables,\((m_{12}, m_{23}, m_{13})\). Before tackling a SUSY physics example in Sect.4, we consider several analogous toy examples of increasing complexity in Sects.2and3. This helps develop the reader’s intuition and motivates some ...
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The BCC is a more compact system and have a low energy structure, is therefore more common in nature. Examples of BCC structures include Fe, Cr, W, and Nb. Finally, thanks to its extremal properties in terms of packing fraction and the resulting high density, FCC crystals are fairly ...