foliation

Definitions

  • WordNet 3.6
    • n foliation the work of coating glass with metal foil
    • n foliation the production of foil by cutting or beating metal into thin leaves
    • n foliation (architecture) leaf-like architectural ornament
    • n foliation (geology) the arrangement of leaflike layers in a rock
    • n foliation (botany) the process of forming leaves
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Webster's Revised Unabridged Dictionary
    • Foliation The act of beating a metal into a thin plate, leaf, foil, or lamina.
    • Foliation The act of coating with an amalgam of tin foil and quicksilver, as in making looking-glasses.
    • Foliation (Arch) The enrichment of an opening by means of foils, arranged in trefoils, quatrefoils, etc.; also, one of the ornaments. See Tracery.
    • Foliation The manner in which the young leaves are disposed within the bud. "The . . . foliation must be in relation to the stem."
    • Foliation The process of forming into a leaf or leaves.
    • Foliation (Geol) The property, possessed by some crystalline rocks, of dividing into plates or slabs, which is 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.
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Century Dictionary and Cyclopedia
    • n foliation The leafing of plants; vernation; the disposition of the nascent leaves within the bud; also, leafage; foliage.
    • n foliation A leaf or scale.
    • n foliation The act of beating a metal into a thin plate, leaf, or foil.
    • n foliation The act or operation of spreading foil over the surface of a piece of glass to form a mirror.
    • n foliation The state of being foliaceous or foliated.
    • n foliation In geology, an arrangement of the constituent minerals of a rock in thinly lamellar or often scale-like forms, the result of which is that the mass splits easily in a certain definite direction. Foliation may be congenital with the formation of the rock itself, or posterior to it: in the latter case the epithet foliated indicates a structure not essentially different from that more generally designated as schistose. The relations of foliation to cleavage are somewhat obscure. The essential difference between them appears to be that cleavage is rarely well developed except in fine-grained, argillaceous rock, which by its effects is usually rendered capable of almost indefinite subdivision in one direction, while foliation separates the rock into bands sometimes quite distinct from each other in mineral character, these bands being also not infrequently more or less irregular in thickness and rather lenticular in form. By some geologists it is thought that in foliation a more advanced stage of metamorphism has been reached than that indicated by cleavage; but it is also highly probable that the original lithological and structural character of the mass had much to do with bringing about the observed differences. See schist and schistose.
    • n foliation In architecture, enrichment with ornamental cusps or groups of cusps, as in the tracery of medieval windows; foils collectively; feathering.
    • n foliation Arrangement by leaves; specifically, a numbering of the leaves of a book instead of the pages.
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Chambers's Twentieth Century Dictionary
    • ns Foliation the leafing, esp. of plants: the act of beating a metal into a thin plate, or of spreading foil over a piece of glass to form a mirror: :
    • ns Foliation (geol.) the alternating and more or less parallel layers or folia of different mineralogical nature, of which the crystalline schists are composed
    • ns Foliation (archit.) decoration with cusps, lobes, or foliated tracery
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Etymology

Webster's Revised Unabridged Dictionary
Cf. F. foliation,
Chambers's Twentieth Century Dictionary
O. Fr. fueillage—L. folium, a leaf.

Usage

In literature:

On the west side is a recess with shafts of Purbeck marble and foliated cusps.
"Bournemouth, Poole & Christchurch" by Sidney Heath
On the lower row are interlacing semicircles in high relief forming foliated cusps and painted blue.
"Portuguese Architecture" by Walter Crum Watson
Some are of wood, others of stone; the former are mostly polygonal, with the panels enriched with foliation or tracery.
"Our Homeland Churches and How to Study Them" by Sidney Heath
I would rather have him show me an acanthus than a finished drawing of the foliation of a capital.
"Émile" by Jean Jacques Rousseau
Now observe: those old Greeks gave the shaft; Rome gave the arch; the Arabs pointed and foliated the arch.
"The Stones of Venice, Volume I (of 3)" by John Ruskin
No Gothic is either good or characteristic which is not foliated either in its arches or apertures.
"The Stones of Venice, Volume II (of 3)," by John Ruskin
The recesses on the sides of the other cusps indicate their single or double lines of foliation.
"The Stones of Venice, Volume III (of 3)" by John Ruskin
The smaller spaces are filled with carvings of animals, birds, flowers and foliated ornament.
"Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 7" by Various
Cusping and foliation (which see) are features of tracery.
"Architecture" by Thomas Roger Smith
APOPH'YLLITE, a species of mineral of a foliated structure and pearly lustre, called also fish-eye stone.
"The New Gresham Encyclopedia. Vol. 1 Part 2" by Various
Side balls below the line of the top of the letters of "Prov., R. I.," and lower point of left foliation cuts into the left ball.
"History of the Postage Stamps of the United States of America" by John Kerr Tiffany
DYS'ODILE, a yellowish or greenish foliated carbonaceous substance found in Sicily originally, and derived from the decay of minute organisms.
"The New Gresham Encyclopedia" by Various
Foliated masses of this mineral occur in the river cliffs in St. Clair county, Illinois.
"Scenes and Adventures in the Semi-Alpine Region of the Ozark Mountains of Missouri and Arkansas" by Henry Rowe Schoolcraft
In Titian's portrait of Ariosto there is a dark foliated background which gives great brilliancy to the picture, but no sky is visible.
"The Evolution of Photography" by John Werge
The AISLE-ARCADE is often very elegant; the arches are usually foliated, and covered with a straight-sided canopy.
"The Seven Periods of English Architecture" by Edmund Sharpe
Stem from a fibrous root, 2-foliate.
"The Manual of the Botany of the Northern United States" by Asa Gray
Each of these foliations is a permanent record of a certain epoch.
"Omphalos" by Philip Henry Gosse
In Gothic, again, with its grove-like ranges of clustered columns, we find rich foliated ornaments abundantly employed.
"Illustrations of Universal Progress" by Herbert Spencer
Dikes of igneous rocks may be followed into a region where they have been foliated by pressure.
"The Elements of Geology" by William Harmon Norton
Mr. Stillingfleet is the only person that has made correct observations upon the foliation of the trees and shrubs of this kingdom.
"Woodland Gleanings" by Charles Tilt
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In poetry:

The greens of the Ganges delta foliate.
Of heartless youth made late aware he pled:
Brownies, please come.
To Henry in his sparest times sometimes
the little people spread, & did friendly things;
then he was glad.
"Dream Song 27: "The greens of the Ganges delta foliate."" by John Berryman

In news:

The remnant of volcanic mayhem, where jagged peaks and spires plunge into densely foliated and impenetrable valleys, heart-shaped Moorea is where Polynesian dreams begin to come true.
Here's a look at smartphone applications to foliate a family tree, digitize and post old family snapshots, and probe for family connections among obituaries published around the world.
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In science:

Recall that, by Theorem 1.2, B 1 is foliated by fibres, B 0 is foliated by vertical lines and there is a diffeomorphism between the space of fibres and the space of vertical lines.
Morin singularities and global geometry in a class of ordinary differential operators
In the process, explicitness is lost: from the theorem (and its proof ), in the H case the domain and image are foliated by smooth surfaces, diffeomorphic to R2 , which are in turn foliated by fibres.
Morin singularities and global geometry in a class of ordinary differential operators
In Mukohyama and Hayward define a double null foliation based on two foliations of null hypersurfaces labeled by ξ+ and ξ− .
Dynamical surface gravity
Instead of using a pseudo-foliation as Vickers and Wilson (the three dimensional submanifolds intersect in a two dimensional submanifold of space-time) we use the natural foliation Στ := {t = τ } stemming from the static coordinates.
The wave equation on static singular space-times
This foliation is called the Koszul foliation and we denote it by F∇ .
The complexifications of pseudo-Riemannian manifolds and anti-Kaehler geometry
Andersson, Mars and Simon [2, 3] showed that for a spacelike foliation of spacetime, if an initial slice contains a strictly stably outermost marginally outer trapped surface then that surface will be part of a horizon that can be foliated by marginally outer trapped surfaces.
Black holes and black hole thermodynamics without event horizons
The proportion of elements of a random walk of length n which are pseudo-Anosov with stable foliation in A and unstable foliation in B is asymptotic to ν (A)eν (B ).
Random Heegaard splittings
The Gromov boundary of the complex of curves, and hence the relative space, is the set formed by taking the foliations in PMF , the space of pro jective measured foliations on the surface, whose tra jectories contain no closed curves, and forgetting the measures, as shown by Klarreich , see also Hamensd¨adt .
Random Heegaard splittings
D stack families S I are said to be linearly independent provided that there exist D linearly independent foliations FI such that the leaves of the foliation FI is transverse to every stack in S I .
Semiclassical analysis of the Loop Quantum Gravity volume operator: I. Flux Coherent States
The arbitrariness in the choice of foliation is encoded in the lapse scalar N and the shift vector (tangent to the foliation) N a which imply that the time vector ta (defined by ta (t) = 1) takes the form ta = N a + N na .
4d Lorentzian Holst action with topological terms
If P is a 2-plane in general position then the foliations Fr and Fρ are also Lyapunov foliations for α0,P .
Local Rigidity of Partially Hyperbolic Actions
If m ≥ n + 1, neutral foliation of the full split Cartan action, as well as any generic restriction contains not only the orbit foliation, but also compact part of the centralizer of the maximal split Cartan subgroup.
Local Rigidity of Partially Hyperbolic Actions
The neutral foliation for a generic restriction α0,G is a smooth foliation, we may use the Hirsch-Pugh-Shub structural stability theorem [, Chapter 6].
Local Rigidity of Partially Hyperbolic Actions
Notice that the latter foliations have only H¨older leaves but we are justified in calling them Lyapunov foliations since they are images of Lyapunov foliations for a smooth perturbed action under a H¨older conjugacy.
Local Rigidity of Partially Hyperbolic Actions
If P is a generic 2-plane with respect to Φ then the foliations Fr and Fρ are also Lyapunov foliations for α0,P .
New Cases of Differential Rigidity for Non-Generic Partially Hyperbolic Actions
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