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Cubic superspace symmetry and inflation rules in metastable MgAl alloy

L. Elcoro, J.M. Perez-Mato
1999 European Physical Journal B : Condensed Matter Physics  
It is shown that the phase can be interpreted within the superspace 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  ... 
doi:10.1007/s100510050591 fatcat:j2itcm56vvdp5emjjdfpx4zfzm

HIGH RESOLUTION ELECTRON MICROSCOPY OF ICOSAHEDRAL PHASES

M. CORNIER, K. ZHANG, R. PORTIER, D. GRATIAS
1986 Le Journal de Physique Colloques  
In the second part, a 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.  ... 
doi:10.1051/jphyscol:1986345 fatcat:lglmhipv5zcx3c6afe4bxs2hf4

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.  ... 

Self-Similar One-Dimensional Quasilattices [article]

Latham Boyle, Paul J. Steinhardt
2016 arXiv   pre-print
We describe three equivalent geometric constructions 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).  ... 
arXiv:1608.08220v2 fatcat:t4vgdrnhnbgirmaxi4hr52nfsm

Stability of the hard-sphere icosahedral quasilattice

H. M. Cataldo, C. F. Tejero
1995 Physical Review B (Condensed Matter)  
The stability 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.  ... 
doi:10.1103/physrevb.52.13269 pmid:9980517 fatcat:lrji5sv7mvf2fdh2jv26vhv77y

STUDIES ON QUASILATTICES : MISTAKES AND LONG RANGE CORRELATION IN ONE DIMENSION

J. P. LU, J. L. BIRMAN
1986 Le Journal de Physique Colloques  
Mistakes in one dimensional 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.  ... 
doi:10.1051/jphyscol:1986327 fatcat:we75u6v5rre3ffftrldzbkzegu

Rows in two-dimensional quasilattices

S. Hoffmann, H.-R. Trebin
1992 Physica status solidi. B, Basic research  
We investigate the properties 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 .  ... 
doi:10.1002/pssb.2221740202 fatcat:hrz2pb2g2jde3gl7gca65gmi5y

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  ... 

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

V. G. Zhuravlev
2008 St. Petersburg Mathematical Journal  
It is proved that there exists a countable set 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.  ... 
doi:10.1090/s1061-0022-08-01005-4 fatcat:ls4ktpoekjcbdjibkarjdj5zuq

Applications of Group Cohomology to the Classification of Fourier-Space Quasicrystals [article]

Benji N. Fisher, David A. Rabson
2003 arXiv   pre-print
This duality is exploited to prove several results that were previously known only in special cases, including the classification 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  ... 
arXiv:math-ph/0105010v2 fatcat:ik4ud6k6h5gzvpfr27vqmmiyxm

Topological models in rotationally symmetric quasicrystals

Callum W. Duncan, Sourav Manna, Anne E. B. Nielsen
2020 Physical review B  
We investigate the physics 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] .  ... 
doi:10.1103/physrevb.101.115413 fatcat:s3efkrz3yfbmjk5iy5pb7cyawy

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.  ... 

A multigrid approach to the average lattices of quasicrystals

J. L. Aragón, Gerardo G. Naumis, M. Torres
2002 Acta Crystallographica Section A Foundations of Crystallography  
An average structure associated with a given 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.  ... 
doi:10.1107/s0108767302005202 pmid:12089458 fatcat:n7om6ri255hxvn2o4voxqtsfya

A novel algorithm for a quasiperiodic plane lattice with fivefold symmetry

P. Ramachandrarao, G. V. S. Sastry, L. Pandey, A. Sinha
1991 Acta Crystallographica Section A Foundations of Crystallography  
Conventionally, Penrose tilings with fivefold symmetry are constructed with the aid 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.  ... 
doi:10.1107/s0108767390011886 fatcat:xbrx6lqv6jcarl4jfgivlhzcte
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