Small-distance behaviour in field theory

In polyethylene single crystals pairs of black and white lines spaced 700-3,000Å apart, parallel to the [100] and [010] directions, have been identified as microsector boundaries. A microsector is formed when the plane of chain folding changes over a small distance within a polymer crystal. In order for the different types of folds to accommodate at the boundary between the 2 fold domains, a staggering along the chain direction and a rotation of the chains in the plane of the boundary occurs. The black-white contrast from a microsector boundary can be explained in terms of these chain rotations. We demonstrate that microsectors can terminate within the crystal and interpret the observed terminal strain contrast in terms of a screw dislocation dipole model.

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Unbiased estimation of particle number and sizes using the new stereological tools: the disector, the fractionator, the selector, and the nucleator — or just point-sampled intercepts

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100104200 ◽

1988 ◽

Vol 46 ◽

pp. 428-429

Author(s):

H.J.G. Gundersen

Keyword(s):

Particle Number ◽

Small Distance ◽

Parallel Plane ◽

Unbiased Estimation ◽

Severe Problem ◽

New Era ◽

Size And Shape ◽

Distinct Property ◽

Sectioned Tissue

Previously, all stereological estimation of particle number and sizes were based on models and notoriously gave biased results, were very inefficient to use and difficult to justify. For all references to old methods and a direct comparison with unbiased methods see recent reviews.The publication in 1984 of the DISECTOR, the first unbiased stereological probe for sampling and counting 3—D objects irrespective of their size and shape, signalled the new era in stereology — and give rise to a number of remarkably simple and efficient techniques based on its distinct property: It is the only known way to obtain an unbiased sample of 3-D objects (cells, organelles, etc). The principle is simple: within a 2-D unbiased frame count or sample only cells which are not hit by a parallel plane at a known, small distance h.The area of the frame and h must be known, which might sometimes in itself be a problem, albeit usually a small one. A more severe problem may arise because these constants are known at the scale of the fixed, embedded and sectioned tissue which is often shrunken considerably.

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