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Cubic superspace symmetry and inflation rules in metastable MgAl alloy

1999
*
European Physical Journal B : Condensed Matter Physics
*

It is shown that the phase can be interpreted within the superspace

doi:10.1007/s100510050591
fatcat:j2itcm56vvdp5emjjdfpx4zfzm
*formalism*as an ordinary incommensurately modulated structure. ... the modulus*of*the modulation wave vectors, which is composition dependent. ... According to the general*formalism**of*superspace symmetry, a rotational symmetry operation in superspace, R s (R), is then given by a 6×6 integer matrix representing the rotational transformation R*of*...##
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HIGH RESOLUTION ELECTRON MICROSCOPY OF ICOSAHEDRAL PHASES

1986
*
Le Journal de Physique Colloques
*

In the second part, a

doi:10.1051/jphyscol:1986345
fatcat:lglmhipv5zcx3c6afe4bxs2hf4
*formalism*for dynamical simulations will be illustrated with examples*of*simulated images compared to the experimental ones. ... The first part*of*the paper is devoted to the elementary interpretation*of*the images based on the mathematical description*of*the cut and projection method (hereafter called CPM)C3-83. ... Cahn for his critical comments during the redaction*of*the present paper; we thank Drs. A. Katz and M. Duneau for many fruitful discussions and Dr. C. L. ...##
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Page 3471 of Mathematical Reviews Vol. , Issue 92f
[page]

1992
*
Mathematical Reviews
*

)
Special lines

*of**quasilattices*. ... The pseudomechanics and the quantum statistical mechanics*of*the model are studied. The per- turbative*formalism*for a general interacting potential and the Feynman rules are given. ...##
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Self-Similar One-Dimensional Quasilattices
[article]

2016
*
arXiv
*
pre-print

We describe three equivalent geometric constructions

arXiv:1608.08220v2
fatcat:t4vgdrnhnbgirmaxi4hr52nfsm
*of*these*quasilattices*and show how they can be subdivided into various types*of*equivalence classes: (i) lattice equivalent, where any two*quasilattices*... Finally, we sketch the extension*of*our results from degree two to degree N (i.e to 1D*quasilattices*built from N different intervals). ... n (regarded as an infinite string*of*primed letters S and L ) by a*formal*substitution rule in which each primed letter (S or L ) is replaced by a fixed finite string*of*unprimed letters (S and L). ...##
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Stability of the hard-sphere icosahedral quasilattice

1995
*
Physical Review B (Condensed Matter)
*

The stability

doi:10.1103/physrevb.52.13269
pmid:9980517
fatcat:lrji5sv7mvf2fdh2jv26vhv77y
*of*the hard-sphere icosahedral*quasilattice*is analyzed using the differential formulation*of*the generalized effective liquid approximation. ... We find that the icosahedral*quasilattice*is metastable with respect to the hard-sphere crystal structures. Our results agree with recent findings by McCarley and Ashcroft [Phys. Rev. ... By starting with the 6D simple cubic lattice, we construct the*quasilattice*using the projection*formalism*described in Sec. II. ...##
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STUDIES ON QUASILATTICES : MISTAKES AND LONG RANGE CORRELATION IN ONE DIMENSION

1986
*
Le Journal de Physique Colloques
*

Mistakes in one dimensional

doi:10.1051/jphyscol:1986327
fatcat:we75u6v5rre3ffftrldzbkzegu
*quasilattices*are studied. The effect*of*mistakes on the diffraction intensity is calculated exactly: we show that the diffraction pattern is changed qualitatively. ... Detailed calculations*of*Fourier transform and configuration average are given. Also the density-density correlation for both perfect and imperfect*quasilattices*have been studied. ... Also we will examine the long range order*of*a*quasilattice*from the point*of*view*of*the density-density correlation function. ...##
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Rows in two-dimensional quasilattices

1992
*
Physica status solidi. B, Basic research
*

We investigate the properties

doi:10.1002/pssb.2221740202
fatcat:hrz2pb2g2jde3gl7gca65gmi5y
*of*rows, which are the analogues to lattice lines*of*periodic lattices, by a method based on the projection*formalism*. ... It enables us to derive the vertex pattern and the mean vertex density*of*an arbitrary row as well as the mean vertex density*of*the corresponding family and its dependence on the row direction. ... q/5 + 1) being the golden mean, and the mean vertex density*of*the tiling amounts to C!v = r ~ = tan (2n/ 5). In the projection*formalism*one starts with a lattice Z 5 . ...##
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Page 7714 of Mathematical Reviews Vol. , Issue 2001K
[page]

2001
*
Mathematical Reviews
*

We prove that, if the cardinality

*of*a free n-*quasilattice*Fy(r) is m, then the cardinality*of*the corresponding free n-*quasilattice*with 0 and | is 2+3m. ... We also investigate the relationship between the semilattice orders*of*n-*quasilattices*and show that each n-*quasilattice*is a subalgebra*of*a reduct*of*a ‘quasimedian’ algebra, answering a question asked ...##
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Page 7885 of Mathematical Reviews Vol. , Issue 98M
[page]

1998
*
Mathematical Reviews
*

components

*of*Int(P), A the number*of**formal*holes*of*P and e the so-called effective number*of*P (relative ¥ ). ... In many*of*the well-known types*of**quasilattices*, the entire quasilat- tice can be built up starting from a finite set*of*points by repeatedly applying this quasiaddition The second type*of*algebraic structure ...##
###
One-dimensional Fibonacci quasilattices and their application to the Euclidean algorithm and Diophantine equations

2008
*
St. Petersburg Mathematical Journal
*

It is proved that there exists a countable set

doi:10.1090/s1061-0022-08-01005-4
fatcat:ls4ktpoekjcbdjibkarjdj5zuq
*of*similarity classes*of**quasilattices*L in F 2 (fine classification), and also four classes*of*local equivalence (rough classification). ... Asymptotic distributions*of*points in*quasilattices*L are found and then applied to Diophantine equations involving the function [α] (the integral part*of*α) and to equations*of*the form A 1 • X 1 − A ... This fact allows us to*formally*use the*quasilattice*F 1 in the division algorithm instead*of*the ring*of*rational integers Z. Suppose r 0 ≥ r 1 > 0, where r i ∈ O. ...##
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Applications of Group Cohomology to the Classification of Fourier-Space Quasicrystals
[article]

2003
*
arXiv
*
pre-print

This duality is exploited to prove several results that were previously known only in special cases, including the classification

arXiv:math-ph/0105010v2
fatcat:ik4ud6k6h5gzvpfr27vqmmiyxm
*of*space groups for*quasilattices**of*arbitrary rank in two dimensions. ... A certain cohomology group classifies the space groups associated to a given point group and*quasilattice*, and the dual homology group gives all gauge invariants. ... A Fourier quasicrystalρ is defined as the coefficients*of*a*formal*Fourier series (0.1) ρ(x) = k∈Lρ (k)e 2πik·x , where L is a*quasilattice*: a finitely generated additive group that spans R d * but is ...##
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Topological models in rotationally symmetric quasicrystals

2020
*
Physical review B
*

We investigate the physics

doi:10.1103/physrevb.101.115413
fatcat:s3efkrz3yfbmjk5iy5pb7cyawy
*of*quasicrystalline lattices in the presence*of*a uniform magnetic field, focusing on the presence and construction*of*topological states. ... This introduces two competing scales; the uniform magnetic field and the incommensurate scale*of*the cells*of*the lattice. ... Note, this higher dimensional space is a superspace and it was recently utilized to develop a Hamiltonian*formalism*in superspace to obtain the eigenstates*of*a quaisperiodic model [53] . ...##
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Page 920 of Mathematical Reviews Vol. 45, Issue 4
[page]

1973
*
Mathematical Reviews
*

A. 5040 Subdirect decomposition

*of*distributive*quasilattices*. Fund. Math. 71 (1971), no. 2, 161-163. ... (Amherst, Mass.) 5039 Equational classes*of*relative Stone algebras. Notre Dame J.*Formal*Logic 13 (1972), 248-254. A relative Stone algebra [the reviewer and E. T. Schmidt, Acta Math. Acad. Sci. ...##
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A multigrid approach to the average lattices of quasicrystals

2002
*
Acta Crystallographica Section A Foundations of Crystallography
*

An average structure associated with a given

doi:10.1107/s0108767302005202
pmid:12089458
fatcat:n7om6ri255hxvn2o4voxqtsfya
*quasilattice*is a system composed*of*several average lattices that in reciprocal space produces strong main re¯ections. ... Here we calculate average structures for arbitrary two-and three-dimensional*quasilattices*using the dual generalized method. ... To keep things as simple as possible, we introduce our*formalism*for two-dimensional*quasilattices*. ...##
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A novel algorithm for a quasiperiodic plane lattice with fivefold symmetry

1991
*
Acta Crystallographica Section A Foundations of Crystallography
*

Conventionally, Penrose tilings with fivefold symmetry are constructed with the aid

doi:10.1107/s0108767390011886
fatcat:xbrx6lqv6jcarl4jfgivlhzcte
*of*two characteristic rhombic tiles and sets*of*rules based on either matching*of*markings on the tiles or their subdivision ... In the present communication, a fool-proof method*of*producing Penrose tilings using a set*of*operations that can be repeated ad infinitum is described. ... They also acknowledge with thanks the financial assistance received from the Department*of*Science and Technology, Government*of*India. ...
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