Monte Carlo Calculations of Phase Diagrams of Magnetic Alloys on the Body-Centered Cubic Lattice

1989 ◽  
pp. 263-268
Author(s):  
B. Dünweg ◽  
K. Binder
Keyword(s):  
Monte Carlo ◽  
Phase Diagrams ◽  
The Body ◽  
Body Centered Cubic ◽  
Magnetic Alloys ◽  
Cubic Lattice ◽  
Monte Carlo Calculations ◽  
Body Centered Cubic Lattice

MINIMAL KNOTTING NUMBERS

2009 ◽  
Vol 18 (08) ◽  
pp. 1159-1173 ◽  
Author(s):  
CASEY MANN ◽  
JENNIFER MCLOUD-MANN ◽  
RAMONA RANALLI ◽  
NATHAN SMITH ◽  
BENJAMIN MCCARTY
Keyword(s):  
The Body ◽  
Computer Algorithm ◽  
Face Centered Cubic ◽  
Body Centered Cubic ◽  
Cubic Lattice ◽  
The Face ◽  
Face Centered ◽  
Body Centered Cubic Lattice

This article concerns the minimal knotting number for several types of lattices, including the face-centered cubic lattice (fcc), two variations of the body-centered cubic lattice (bcc-14 and bcc-8), and simple-hexagonal lattices (sh). We find, through the use of a computer algorithm, that the minimal knotting number in sh is 20, in fcc is 15, in bcc-14 is 13, and bcc-8 is 18.

SOLID HARMONICS AS BASIS FUNCTIONS FOR CUBIC CRYSTALS

1959 ◽  
Vol 37 (3) ◽  
pp. 350-361 ◽  
Author(s):  
D. D. Betts
Keyword(s):  
Basis Functions ◽  
The Body ◽  
New Method ◽  
Face Centered Cubic ◽  
Body Centered Cubic ◽  
Cubic Crystals ◽  
Cubic Lattice ◽  
The Face ◽  
Face Centered ◽  
Body Centered Cubic Lattice

The various sets of basis functions useful in discussing cubic crystals must include sets of symmetrized combinations of powers of the co-ordinates ortho-gonalized over the cellular polyhedron. Such polynomials are here called solid harmonics. A study of the actual solid harmonics reveals the limitations of the spherical cell approximation. The solid harmonics can be used to develop a new method over the cellular polyhedron of the body-centered cubic lattice or of the face-centered cubic lattice.

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