Acupuncture treatment for piriformis syndrome

Oscillating carbon nanotori along carbon nanotubes

“…3 we plot the Lennard-Jones potential energy given by Eq. ͑8͒ against the nanotorus position Z, where we use c =55 Å, b = 3.39 Å from results of Han 19 and we choose a nanotube with radius a = 48.21 Å and half length L = 500 Å. These dimensions are such that Eq.…”

“…It has been shown to be possible to form these toroidal nanotubes from straight single-walled carbon nanotubes, 17 where the ring circumference is therefore equal to the initial tube length. Using molecular dynamics simulations Huhtala et al 18 and Han 19 investigated the stability of these toroidal carbon nanotubes and found much smaller ring diameters are possible than those discovered experimentally. For example, Huhtala et al 18 found that a ring diameter of 220 Å must have a tube diameter below 13 Å for the nanotorus to remain stable and similarly Han 19 found ring diameters must be greater than 100, 200, and 400 Å for a nanotorus ͑5,5͒, ͑8,8͒, and ͑10,10͒, respectively to remain energetically stable.…”

“…Using molecular dynamics simulations Huhtala et al 18 and Han 19 investigated the stability of these toroidal carbon nanotubes and found much smaller ring diameters are possible than those discovered experimentally. For example, Huhtala et al 18 found that a ring diameter of 220 Å must have a tube diameter below 13 Å for the nanotorus to remain stable and similarly Han 19 found ring diameters must be greater than 100, 200, and 400 Å for a nanotorus ͑5,5͒, ͑8,8͒, and ͑10,10͒, respectively to remain energetically stable. Effectively the toroidal nanotube structure can be viewed as a single-walled carbon nanotube closed around onto itself into a perfect torus.…”

Bioinformatics

“…55 Clustering techniques used in analyzing gene expression data can be categorized according to the internal algorithms used 55 as follows: Clustering is the process of grouping the data into classes or clusters so that objects within a cluster have high similarity in comparison to one another but are very dissimilar to objects in other clusters.…”

“…55 Agrawal et al 69 present a density-based clustering algorithm called CLIQUE to partition the data space into nonoverlapping rectangular cells by treating the attribute of each data record as one dimension. It grows clusters either according to the density of neighborhood clusters or according to some estimated density functions.…”