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On the quadrant theorem of Orowan

Authors
Journal
Surface Science
0039-6028
Publisher
Elsevier
Publication Date
Volume
232
Issue
3
Identifiers
DOI: 10.1016/0039-6028(90)90113-m
Disciplines
  • Mathematics

Abstract

Abstract Orowan's “quadrant theorem” is an important example of a general relation concerning interaction forces between macroscopic bodies. A more basic result, which is christened here the “column theorem”, concerns the interaction forces between any mass and a thin uniform semi-infinite column of material. A third “theorem”, which pertains to the same systems as are covered by these theorems, has been introduced recently under the mistaken impression that it was proved by Orowan; it is pointed out here that this third theorem is incorrect, and the correct relationship among the theorems is discussed. Also discussed is how these concepts depend on the assumptions of (a) superposition of forces and (b) negligible shielding of these forces due to the presence of other bodies: for example, these assumptions are incorrect in general, invalidating the quadrant theorem, although the column theorem holds in any case.

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