# trifurcation

## Definitions

• WordNet 3.6
• n trifurcation the act of splitting into three branches
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Century Dictionary and Cyclopedia
• n trifurcation The state of being trifurcate; a trifurcate shape, formation, or arrangement.
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## Usage

### In literature:

Tendrils may be long or short, stout or slender; simple, bifurcated or trifurcated; or smooth, pubescent or warty.
"Manual of American Grape-Growing" by U. P. Hedrick
When the road had traversed the width of the valley, it trifurcated.
"Sinister Street, vol. 2" by Compton Mackenzie
The genital duct is now trifurcated or triaulic, a condition which is confined to certain Nudibranchs, viz.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 5" by Various
There are two dorsal fins, slightly connected; the caudal fin is double concave or trifurcate.
"Bass, Pike, Perch, and Others" by James Alexander Henshall
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### In science:

Tile all of Zd with boxes of size Λn . A given box is called a trifurcation box if removing a connected cluster of vertices inside of the box causes a single inﬁnite cluster to break into three or more pieces.
Random Surfaces
Now, for a large value of k, let Λkn be a box of side length kn; observe that for each trifurcation box of an inﬁnite cluster C, we can choose a partition of the ∂Λn ∩ C into three sets, each of which is the intersection of ∂Λn with one of the three components of the inﬁnite cluster that is broken apart.
Random Surfaces
In fact, as Burton and Keane observe (again, see Lemma 8.5 of or ), the set of partitions corresponding to the trifurcation points of the intersection with any particular cluster forms a compatible family of partitions of the intersection of ∂Λn with that inﬁnite cluster.
Random Surfaces
This implies that the total number of trifurcation points in Λn is less than |∂Λn |.
Random Surfaces
To handle the latter possibility, the rough idea is to build a trifurcation point (see Deﬁnition 3.3) using the interlacement paths; this is done in what follows Lemma 3.4 In both cases, the diﬃculty is due to the fact that the measures Qu fail to satisfy the so-called ﬁnite energy condition (1.5) used in .
On the uniqueness of the infinite cluster of the vacant set of random interlacements
We follow the broad strategy of Burton and Keane (see ), but in the absence of the ﬁnite energy property, a speciﬁc proof for the existence of trifurcation points needs to be developed.
On the uniqueness of the infinite cluster of the vacant set of random interlacements
We call y a trifurcation point at level u if it belongs to an inﬁnite component of V u which is split into three distinct inﬁnite components by the removal of y .
On the uniqueness of the infinite cluster of the vacant set of random interlacements
We now begin the construction of the trifurcation associated to this triple.
On the uniqueness of the infinite cluster of the vacant set of random interlacements
Ra jagopal elucidated that, reducing µq from large values, the ﬁrst transition is probably from the u-d-s symmetric CFL ground state into a “gapless” CFL phase : the asymmetry induced by ms trifurcates the gap value and induces “blocking” regions on the d- and s- Fermi surfaces where their pairing is inhibited.
Theory Highlights of Quark Matter 2004
Inside each main subband the fragmentation scheme follows a trifurcation pattern in which each subband further trifurcates obeying a hierarchy of splitting from one to three subsubbands.
Energy spectra of quasiperiodic systems via information entropy
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