foliation

plural foliations

1. countableuncountablebiologyThe process of forming into a leaf or leaves.

   Synonyms: vernation

2. countableuncountablemediaThe process of forming into pages; pagination.

   Synonyms: pagination

3. countableuncountablecodicologyThe numbering of the folios of a manuscript or a book.
4. countableuncountablebiologyThe manner in which the young leaves are disposed within the bud.
5. countableuncountableThe act of beating a metal into a thin plate, leaf, foil, or lamina.
6. countableuncountableThe act of coating with an amalgam of tin foil and quicksilver, as in making looking-glasses.
7. countableuncountableThe enrichment of an opening by means of foils, arranged in trefoils, quatrefoils, etc.; also, one of the ornaments.

   The house was a big elaborate limestone affair, evidently new. Winter sunshine sparkled on lace-hung casement, on glass marquise, and the burnished bronze foliations of grille and door.

   1907 August, Robert W[illiam] Chambers, chapter I, in The Younger Set, New York, N.Y.: D. Appleton & Company, →OCLC

8. countableuncountablegeographyThe property, possessed by some crystalline rocks, of being divided into plates or layers, due to the cleavage structure of one of the constituents, as mica or hornblende. It may sometimes include slaty structure or cleavage, though the latter is usually independent of any mineral constituent, and transverse to the bedding, it having been produced by pressure.

   The dominant strike orientation of both bedding and foliation of Vermont bedrock is north or northeasterly.

   1993, Charles A. Baskerville, Fitzhugh T. Lee, Charles A. Ratté, “Landslide Hazards in Vermont”, in U.S. Geological Survey Bulletin, published 2043, page 18

   3 more examples

   Formation of alteration minerals in the host rock during deformation within the shear zone is indicated by the parallel foliation within the secondary micaceous minerals and the unmineralized host schist.

   1983, Warren C. Day, Richard M. Tosdal, E.L. Acosta, J.C. Aruspon, L. Carvajal, E. Cedeño, Glenda Lowry, L.F. Martinez, J.A. Noriega, Fernanco J. Niñez, J. Rojas, F. Prieto, “Geology of the Lo Indreíble Mining District and U-Pb Age of the Early Proterozoic Yuruari Formation of the Pastora Supergroup, Guayana Shield, Venezuela”, in U.S. Geological Survey Bulletin, numbers 2122-2127, page E-12

   They show that curved inclusion trails may form even with no coupling, as the porphyroblast overgrows foliation that is deflected around it.

   1996, Eric C. Beam, Modeling Growth and Rotation of Porphyroblasts and Inclusion Trails, D.G. De Paor, Structural Geology and Personal Computers, p.249

   In sedimentary rocks, the magnetic foliation results from a combination of depositional processes and diagenetic compaction.

   2004, F. Martín-Hernández, C. M. Lüneburg, C. Aubourg, M. Jackson, “Magnetic fabric: methods and applications - an introduction”, in Magnetic Fabric: Methods and Applications, Geological Society of London, page 3

9. countableuncountablemathematicsA set of submanifolds of a given manifold, each of which is of lower dimension than it, but which, taken together, are coextensive with it.

   The simplest example of a foliation is provided by a single submersion F : M → N, M and N being manifolds.

   2004, Paweł Grzegorz Walczak, Dynamics Of Foliations, Groups And Pseudogroups, Monografie Matematyczne: Vol.64, New Series, p.6

   2 more examples

   Historically, the formalism which first arose for the material we discuss is that of measured foliations in surfaces.

   1992, R. C. Penner, Combinatorics of Train Tracks, page 204

   We will show that every closed 3-manifold has a foliation of codimension one. In 1952, G. Reeb published his construction of a foliation of the 3-sphere. About twelve years later, W. Lickorish [123] exhibited foliations of codimension one on every closed, orientable 3-manifold.

   2003, Alberto Candel, Lawrence Conlon, Foliations, Vol.2, p.253