6,633 research outputs found
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
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
How model sets can be determined by their two-point and three-point correlations
We show that real model sets with real internal spaces are determined, up to
translation and changes of density zero by their two- and three-point
correlations. We also show that there exist pairs of real (even one
dimensional) aperiodic model sets with internal spaces that are products of
real spaces and finite cyclic groups whose two- and three-point correlations
are identical but which are not related by either translation or inversion of
their windows. All these examples are pure point diffractive.
Placed in the context of ergodic uniformly discrete point processes, the
result is that real point processes of model sets based on real internal
windows are determined by their second and third moments.Comment: 19 page
The Geometric Phase in Supersymmetric Quantum Mechanics
We explore the geometric phase in N=(2,2) supersymmetric quantum mechanics.
The Witten index ensures the existence of degenerate ground states, resulting
in a non-Abelian Berry connection. We exhibit a non-renormalization theorem
which prohibits the connection from receiving perturbative corrections.
However, we show that it does receive corrections from BPS instantons. We
compute the one-instanton contribution to the Berry connection for the massive
CP^1 sigma-model as the potential is varied. This system has two ground states
and the associated Berry connection is the smooth SU(2) 't Hooft-Polyakov
monopole.Comment: 28 pages, 2 figures, references added. v2: clarification of possible
corrections to Abelian Berry phase. v3: footnotes added to point the reader
towards later development
Random fields on model sets with localized dependency and their diffraction
For a random field on a general discrete set, we introduce a condition that
the range of the correlation from each site is within a predefined compact set
D. For such a random field omega defined on the model set Lambda that satisfies
a natural geometric condition, we develop a method to calculate the diffraction
measure of the random field. The method partitions the random field into a
finite number of random fields, each being independent and admitting the law of
large numbers. The diffraction measure of omega consists almost surely of a
pure-point component and an absolutely continuous component. The former is the
diffraction measure of the expectation E[omega], while the inverse Fourier
transform of the absolutely continuous component of omega turns out to be a
weighted Dirac comb which satisfies a simple formula. Moreover, the pure-point
component will be understood quantitatively in a simple exact formula if the
weights are continuous over the internal space of Lambda Then we provide a
sufficient condition that the diffraction measure of a random field on a model
set is still pure-point.Comment: 21 page
(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
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
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
On the effect of Ti on Oxidation Behaviour of a Polycrystalline Nickel-based Superalloy
Titanium is commonly added to nickel superalloys but has a well-documented
detrimental effect on oxidation resistance. The present work constitutes the
first atomistic-scale quantitative measurements of grain boundary and bulk
compositions in the oxide scale of a current generation polycrystalline nickel
superalloy performed through atom probe tomography. Titanium was found to be
particularly detrimental to oxide scale growth through grain boundary
diffusion
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