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Sphere Packing In A Cylinder
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Notochord
In anatomy, the notochord is a flexible rod which is similar in structure to the stiffer cartilage. If a species has a notochord at any stage of its life cycle (along with 4 other features), it is, by definition, a chordate. The notochord consists of inner, vacuolated cells covered by fibrous and elastic sheaths, lies along the anteroposterior axis (''front to back''), is usually closer to the dorsal than the ventral surface of the embryo, and is composed of cells derived from the mesoderm. The most commonly cited functions of the notochord are: as a midline tissue that provides directional signals to surrounding tissue during development, as a skeletal (structural) element, and as a vertebral precursor. In lancelets the notochord persists throughout life as the main structural support of the body. In tunicates the notochord is present only in the larval stage, being completely absent in the adult animal. In these invertebrate chordates, the notochord is not vacuolated. In all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nanotubes
file:Chiraltube.png, A scanning tunneling microscopy image of a single-walled carbon nanotube file:Kohlenstoffnanoroehre Animation.gif, Rotating single-walled zigzag carbon nanotube A carbon nanotube (CNT) is a tube made of carbon with diameters typically measured in nanometers. ''Single-wall carbon nanotubes'' (''SWCNTs'') are one of the allotropes of carbon, intermediate between fullerene cages and flat graphene, with diameters in the range of a nanometre. Although not made this way, single-wall carbon nanotubes can be idealized as cutouts from a two-dimensional Hexagonal tiling, hexagonal lattice of carbon atoms rolled up along one of the Bravais lattice vectors of the hexagonal lattice to form a hollow cylinder. In this construction, periodic boundary conditions are imposed over the length of this roll-up vector to yield a helical lattice of seamlessly bonded carbon atoms on the cylinder surface. ''Multi-wall carbon nanotubes'' (''MWCNTs'') consisting of nested single-wall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CT Scan
A computed tomography scan (CT scan; formerly called computed axial tomography scan or CAT scan) is a medical imaging technique used to obtain detailed internal images of the body. The personnel that perform CT scans are called radiographers or radiology technologists. CT scanners use a rotating X-ray tube and a row of detectors placed in a gantry (medical), gantry to measure X-ray Attenuation#Radiography, attenuations by different tissues inside the body. The multiple X-ray measurements taken from different angles are then processed on a computer using tomographic reconstruction algorithms to produce Tomography, tomographic (cross-sectional) images (virtual "slices") of a body. CT scans can be used in patients with metallic implants or pacemakers, for whom magnetic resonance imaging (MRI) is Contraindication, contraindicated. Since its development in the 1970s, CT scanning has proven to be a versatile imaging technique. While CT is most prominently used in medical diagnosis, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weaire–Phelan Structure
In geometry, the Weaire–Phelan structure is a three-dimensional structure representing an idealised foam of equal-sized bubbles, with two different shapes. In 1993, Denis Weaire and Robert Phelan found that this structure was a better solution of the Kelvin problem of tiling space by equal volume cells of minimum surface area than the previous best-known solution, the Kelvin structure. History and the Kelvin problem In two dimensions, the subdivision of the plane into cells of equal area with minimum average perimeter is given by the hexagonal tiling, but although the first record of this honeycomb conjecture goes back to the ancient Roman scholar Marcus Terentius Varro, it was not proven until the work of Thomas C. Hales in 1999. In 1887, Lord Kelvin asked the corresponding question for three-dimensional space: how can space be partitioned into cells of equal volume with the least area of surface between them? Or, in short, what was the most efficient soap bubble foam? This ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dodecahedron
In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120. Some dodecahedra have the same combinatorial structure as the regular dodecahedron (in terms of the graph formed by its vertices and edges), but their pentagonal faces are not regular: The pyritohedron, a common crystal form in pyrite, has pyritohedral symmetry, while the tetartoid has tetrahedral symmetry. The rhombic dodecahedron can be seen as a limiting case of the pyritohedron, and it has octahedral symmetry. The elongated dodecahedron and trapezo-rhombic dodecahedron variations, along with the rhombic dodecahedra, are space-filling. There ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cylinder Sphere Packing
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hard Spheres
Hard spheres are widely used as model particles in the statistical mechanical theory of fluids and solids. They are defined simply as impenetrable spheres that cannot overlap in space. They mimic the extremely strong ("infinitely elastic bouncing") repulsion that atoms and spherical molecules experience at very close distances. Hard spheres systems are studied by analytical means, by molecular dynamics simulations, and by the experimental study of certain colloidal model systems. The hard-sphere system provides a generic model that explains the quasiuniversal structure and dynamics of simple liquids. Formal definition Hard spheres of diameter \sigma are particles with the following pairwise interaction potential: :V(\mathbf_1,\mathbf_2)=\left\{ \begin{matrix}0 & \mbox{if}\quad , \mathbf{r}_1-\mathbf{r}_2, \geq \sigma \\ \infty & \mbox{if}\quad, \mathbf{r}_1-\mathbf{r}_2, < \sigma \end{matrix} \right. where and are the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Evolver
Surface Evolver is an interactive program for the study of surfaces shaped by surface tension and other energies, and subject to various constraints. A surface is implemented as a simplicial complex. The user defines an initial surface in a datafile. The Evolver evolves the surface toward minimal energy by a gradient descent method. The aim can be to find a minimal energy surface, or to model the process of evolution by mean curvature. The energy in the Evolver can be a combination of surface tension, gravitational energy, squared mean curvature, user-defined surface integrals, or knot energies. The Evolver can handle arbitrary topology, volume constraints, boundary constraints, boundary contact angles, prescribed mean curvature, crystalline integrands, gravity, and constraints expressed as surface integrals. The surface can be in an ambient space of arbitrary dimension, which can have a Riemannian metric, and the ambient space can be a quotient space under a group action. Evo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on the same plane. Cubes and pyramids are examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions. Definition Convex polyhedra are well-defined, with several equivalent standard definitions. However, the formal mathematical definition of polyhedra that are not required to be convex has been problematic. Many definitions of "polyhedron" have been given within particular contexts,. some more rigorous than others, and there is not universal agreement over which of these to choose. Some of these definitions exclude shapes that have often been counted as polyhedra (such as the self-crossing polyhedra) or include shapes that are often not considered as valid polyhedr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columnar Structure Of A Foam
Epithelium or epithelial tissue is one of the four basic types of animal tissue, along with connective tissue, muscle tissue and nervous tissue. It is a thin, continuous, protective layer of compactly packed cells with a little intercellular matrix. Epithelial tissues line the outer surfaces of organs and blood vessels throughout the body, as well as the inner surfaces of cavities in many internal organs. An example is the epidermis, the outermost layer of the skin. There are three principal shapes of epithelial cell: squamous (scaly), columnar, and cuboidal. These can be arranged in a singular layer of cells as simple epithelium, either squamous, columnar, or cuboidal, or in layers of two or more cells deep as stratified (layered), or ''compound'', either squamous, columnar or cuboidal. In some tissues, a layer of columnar cells may appear to be stratified due to the placement of the nuclei. This sort of tissue is called pseudostratified. All glands are made up of epithelia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Callistemon
''Callistemon'' is a genus of shrubs in the family Myrtaceae, first described as a genus in 1814. The entire genus is endemic to Australia but widely cultivated in many other regions and naturalised in scattered locations. Their status as a separate taxon is in doubt, some authorities accepting that the difference between callistemons and melaleucas is not sufficient for them to be grouped in a separate genus. Description ''Callistemon'' species have commonly been referred to as bottlebrushes because of their cylindrical, brush like flowers resembling a traditional bottle brush. They are mostly found in the more temperate regions of Australia, especially along the east coast and typically favour moist conditions so when planted in gardens thrive on regular watering. However, two species are found in Tasmania and several others in the south-west of Western Australia. At least some species are drought-resistant and some are used in ornamental landscaping elsewhere in the world. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
