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In this regards, the use of periodic open cellular structures (POCS) is a recent and very promising structuring concept, as packings of these structures offer superior and adjustable properties (e.g. low pressure drop, high surface area, good liquid distribution, advanced heat transfer) [[4], [5], [6], [7], [8]].
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We have implemented the algorithms and applied them to ordered as well as random packings of circular disks and spheres with periodic boundary conditions.
The algorithm is based on linear programming and is applicable to regular as well as random packings of finite size with hard-wall and periodic boundary conditions.
Various microstructures including lamellae, hexagonal packings of PS and PI cylinders as well as a gyroid phase were obtained by varying the volume fraction of polystyrene (fPS) of the branches, leading to the formation of ordered, periodic and localized nanoscale dispersions of the C60 in a polymer matrix including planes, threads and a 3D bicontinuous network of C60.
This problem is connected with other important problems such as packings in Grassmannian spaces and antipodal spherical codes.
Also, we prove that the height-to-width ratio of rectangles of minimum perimeter containing packings of n congruent circles tends to 1 as n→∞.
A statistical geometrical theory of packings of particles is given.
Packings of various sizes and shapes are employed.
Special attention is given to a comparison of the test results with other modern and standard random packings as well as to structured packings.
Section System networks as a language of description with its sub-sections leaves no doubt that the description presented in a contextual sys-net is an 'un-packing' of simply some aspect of these terms.
Yet as this arrangement, called hexagonal close packing (HCP ), cannot be described by three vectors, it does not define a lattice (see Figure 5D), even though it is as tightly packed as the F C C. Such packings, defined as an arrangement of equal non-overlapping balls (Conway and Sloane, 1992; Hales, 2012), generalize lattices.
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