WordNet

situated on or along or in the direction of an axis
of or relating to or resembling an axis of rotation

PrepTutorEJDIC

軸の,軸をなす / 軸上に位置した

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/05/09 23:30:54」(JST)

wiki en

[Wiki en表示]

In physics and mathematics, axiality and rhombicity are two characteristics of a symmetric second-rank tensor in three-dimensional Euclidean space, describing its directional asymmetry.

Let A denote a second-rank tensor in R³, which can be represented by a 3-by-3 matrix. We assume that A is symmetric. This implies that A has three real eigenvalues, which we denote by , and . We assume that they are ordered such that

The axiality of A is defined by

The rhombicity is the difference between the smallest and the second-smallest eigenvalue:

Other definitions of axiality and rhombicity differ from the ones given above by constant factors which depend on the context. For example, when using them as parameters in the irreducible spherical tensor expansion, it is most convenient to divide the above definition of axiality by and that of rhombicity by .

Applications [edit]

The description of physical interactions in terms of axiality and rhombicity is frequently encountered in spin dynamics and, in particular, in spin relaxation theory, where many traceless bilinear interaction Hamiltonians, having the (eigenframe) form

(hats denote spin projection operators) may be conveniently rotated using rank 2 irreducible spherical tensor operators:

where are Wigner functions, are Euler angles, and the expressions for the rank 2 irreducible spherical tensor operators are:

Defining Hamiltonian rotations in this way (axiality, rhombicity, three angles) significantly simplifies calculations, since the properties of Wigner functions are well understood.

References [edit]

D.M. Brink and G.R. Satchler, Angular momentum, 3rd edition, 1993, Oxford: Clarendon Press.

D.A. Varshalovich, A.N. Moskalev, V.K. Khersonski, Quantum theory of angular momentum: irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols, 1988, Singapore: World Scientific Publications.

I. Kuprov, N. Wagner-Rundell, P.J. Hore, J. Magn. Reson., 2007 (184) 196-206. Article

English Journal

Delineating the vascular territory (perforasome) of a perforator in the lower extremity of the rabbit with four-dimensional computed tomographic angiography.

Nie JY, Lu LJ, Gong X, Li Q, Nie JJ.SourceChangchun and Jilin, People's Republic of China From the Department of Hand Surgery, First Affiliated Hospital of Jilin University, and the Departments of Plastic Surgery, Neurology, and Radiology, The People's Hospital.
Plastic and reconstructive surgery.Plast Reconstr Surg.2013 Mar;131(3):565-71. doi: 10.1097/PRS.0b013e31827c6e49.
BACKGROUND: : The anatomy of any particular vascular perforator relative to its vascular territory (perforasome) and flow characteristics is unique and complex. This arterial perforasome study with laboratory rabbits was conducted to assess four-dimensional computed tomographic angiography as an ima
PMID 23446568

Ytterbium can relax slowly too: a field-induced Yb2 single-molecule magnet.

Lin PH, Sun WB, Tian YM, Yan PF, Ungur L, Chibotaru LF, Murugesu M.SourceDepartment of Chemistry, University of Ottawa, 10 Marie-Curie, Ottawa, ON, Canada K1N 6N5.
Dalton transactions (Cambridge, England : 2003).Dalton Trans.2012 Oct 28;41(40):12349-52.
An unusual dinuclear Yb(2) complex isolated using a mixed ligand strategy leads to field-induced SMM behaviour. Low magnetic axiality and a large tunnelling gap lead to significant quantum tunnelling of the magnetisation, which was reduced under an applied static optimum field of 1600 Oe.
PMID 22968654

Electric field control of the magnetic chiralities in ferroaxial multiferroic RbFe(MoO4)2.

Hearmon AJ, Fabrizi F, Chapon LC, Johnson RD, Prabhakaran D, Streltsov SV, Brown PJ, Radaelli PG.SourceClarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom. a.hearmon@physics.ox.ac.uk
Physical review letters.Phys Rev Lett.2012 Jun 8;108(23):237201. Epub 2012 Jun 4.
The coupling of magnetic chiralities to the ferroelectric polarization in multiferroic RbFe(MoO4)2 is investigated by neutron spherical polarimetry. Because of the axiality of the crystal structure below T(c)=190 K, helicity and triangular chirality are symmetric-exchange coupled, explaining
PMID 23003983

Japanese Journal

G0301-6-4 円周切欠き丸棒引張試験片を用いた破壊靭性試験における先端部破壊起点と加工変質層(材料力学部門一般(6))

佐藤雅史,笠場孝一,風巻直人,村上嵩
年次大会講演論文集 : JSME annual meeting 2009(1), 65-66, 2009-09-12
… Comparing the thickness with numerically obtained high stress tri-axiality region where a fracture is likely to initiate is needed to substitute a EDM notch for a fatigue crack. …
NAID 110007866504

溶接熱影響部におけるクリープき裂成長挙動に及ぼす局所応力多軸効果

杉浦隆次,横堀壽光,鈴木和人,田淵正明
鉄と鋼 95(4), 361-368, 2009
… In the present study, for the welded joint of the W-added 9Cr ferritic heat-resistant steel, ASME Code Case 2179/ASTM A335 P92, creep crack growth tests and 3-dimensional elastic-plastic creep finite element analyses were conducted to clarify the effect of stress multi-axiality on creep crack growth. …
NAID 130000136714