Sphere packing in a cylinder
three-dimensional packing problem
Sphere packing in a cylinder is a three-dimensional packing problem with the objective of packing a given number of identical spheres inside a cylinder of specified diameter and length. For cylinders with diameters on the same order of magnitude as the spheres, such packings result in what are called columnar structures.
These problems are studied extensively in the context of biology, nanoscience, materials science, and so forth due to the analogous assembly of small particles (like cells and atoms) into cylindrical crystalline structures.
Appearance in science
Columnar structures appear in various research fields on a broad range of length scales from metres down to the nanoscale. On the largest scale, such structures can be found in botany where seeds of a plant assemble around the stem. On a smaller scale bubbles of equal size crystallise to columnar foam structures when confined in a glass tube. In nanoscience such structures can be found in man-made objects which are on length scales from a micron to the nanoscale.
Botany
Columnar structures were first studied in botany due to their diverse appearances in plants. D'Arcy Thompson analysed such arrangement of plant parts around the stem in his book "On Growth and Form" (1917). But they are also of interest in other biological areas, including bacteria, viruses, microtubules, and the notochord of the zebra fish.
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