5,687 research outputs found
The rings of n-dimensional polytopes
Points of an orbit of a finite Coxeter group G, generated by n reflections
starting from a single seed point, are considered as vertices of a polytope
(G-polytope) centered at the origin of a real n-dimensional Euclidean space. A
general efficient method is recalled for the geometric description of G-
polytopes, their faces of all dimensions and their adjacencies. Products and
symmetrized powers of G-polytopes are introduced and their decomposition into
the sums of G-polytopes is described. Several invariants of G-polytopes are
found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers
and congruence classes of the polytopes. The definitions apply to
crystallographic and non-crystallographic Coxeter groups. Examples and
applications are shown.Comment: 24 page
Six types of functions of the Lie groups O(5) and G(2)
New families of -functions are described in the context of the compact
simple Lie groups O(5) and G(2). These functions of two real variables
generalize the common exponential functions and for each group, only one family
is currently found in the literature. All the families are fully characterized,
their most important properties are described, namely their continuous and
discrete orthogonalities and decompositions of their products.Comment: 25 pages, 13 figure
Icosahedral multi-component model sets
A quasiperiodic packing Q of interpenetrating copies of C, most of them only
partially occupied, can be defined in terms of the strip projection method for
any icosahedral cluster C. We show that in the case when the coordinates of the
vectors of C belong to the quadratic field Q[\sqrt{5}] the dimension of the
superspace can be reduced, namely, Q can be re-defined as a multi-component
model set by using a 6-dimensional superspace.Comment: 7 pages, LaTeX2e in IOP styl
(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
Four families of special functions, depending on n variables, are studied. We
call them symmetric and antisymmetric multivariate sine and cosine functions.
They are given as determinants or antideterminants of matrices, whose matrix
elements are sine or cosine functions of one variable each. These functions are
eigenfunctions of the Laplace operator, satisfying specific conditions at the
boundary of a certain domain F of the n-dimensional Euclidean space. Discrete
and continuous orthogonality on F of the functions within each family, allows
one to introduce symmetrized and antisymmetrized multivariate Fourier-like
transforms, involving the symmetric and antisymmetric multivariate sine and
cosine functions.Comment: 25 pages, no figures; LaTaX; corrected typo
Perfection of materials technology for producing improved Gunn-effect devices
Chemical vapor deposition system for improved Gunn effect devices using arsenic chloride 3 metho
From solid solution to cluster formation of Fe and Cr in -Zr
To understand the mechanisms by which Fe and Cr additions increase the
corrosion rate of irradiated Zr alloys, a combination of experimental (atom
probe tomography, x-ray diffraction and thermoelectric power measurements) and
modelling (density functional theory) techniques are employed to investigate
the non-equilibrium solubility and clustering of Fe and Cr in binary Zr alloys.
Cr occupies both interstitial and substitutional sites in the {\alpha}-Zr
lattice, Fe favours interstitial sites, and a low-symmetry site that was not
previously modelled is found to be the most favourable for Fe. Lattice
expansion as a function of alloying concentration (in the dilute regime) is
strongly anisotropic for Fe additions, expanding the -axis while contracting
the -axis. Defect clusters are observed at higher solution concentrations,
which induce a smaller amount of lattice strain compared to the dilute defects.
In the presence of a Zr vacancy, all two-atom clusters are more soluble than
individual point defects and as many as four Fe or three Cr atoms could be
accommodated in a single Zr vacancy. The Zr vacancy is critical for the
increased solubility of defect clusters, the implications for irradiation
induced microstructure changes in Zr alloys are discussed.Comment: 15 pages including figure, 9 figures, 2 tables. Submitted for
publication in Acta Mater, Journal of Nuclear Materials (2015
Quantum theory of large amplitude collective motion and the Born-Oppenheimer method
We study the quantum foundations of a theory of large amplitude collective
motion for a Hamiltonian expressed in terms of canonical variables. In previous
work the separation into slow and fast (collective and non-collective)
variables was carried out without the explicit intervention of the Born
Oppenheimer approach. The addition of the Born Oppenheimer assumption not only
provides support for the results found previously in leading approximation, but
also facilitates an extension of the theory to include an approximate
description of the fast variables and their interaction with the slow ones.
Among other corrections, one encounters the Berry vector and scalar potential.
The formalism is illustrated with the aid of some simple examples, where the
potentials in question are actually evaluated and where the accuracy of the
Born Oppenheimer approximation is tested. Variational formulations of both
Hamiltonian and Lagrangian type are described for the equations of motion for
the slow variables.Comment: 29 pages, 1 postscript figure, preprint no UPR-0085NT. Latex + epsf
styl
Affine extension of noncrystallographic Coxeter groups and quasicrystals
Unique affine extensions H^{\aff}_2, H^{\aff}_3 and H^{\aff}_4 are
determined for the noncrystallographic Coxeter groups , and .
They are used for the construction of new mathematical models for quasicrystal
fragments with 10-fold symmetry. The case of H^{\aff}_2 corresponding to
planar point sets is discussed in detail. In contrast to the cut-and-project
scheme we obtain by construction finite point sets, which grow with a model
specific growth parameter.Comment: (27 pages, to appear in J. Phys. A
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