402 research outputs found
Symmetry properties of Penrose type tilings
The Penrose tiling is directly related to the atomic structure of certain
decagonal quasicrystals and, despite its aperiodicity, is highly symmetric. It
is known that the numbers 1, , , , ..., where
, are scaling factors of the Penrose tiling. We show that
the set of scaling factors is much larger, and for most of them the number of
the corresponding inflation centers is infinite.Comment: Paper submitted to Phil. Mag. (for Proceedings of Quasicrystals: The
Silver Jubilee, Tel Aviv, 14-19 October, 2007
Conceptual mechanization studies for a horizon definition spacecraft attitude control subsystem, phase A, part II, 10 October 1966 - 29 May 1967
Attitude control subsystem for spin stabilized spacecraft for mapping earths infrared horizon radiance profiles in 15 micron carbon dioxide absorption ban
Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons
We present a unified approach for qualitative and quantitative analysis of
stability and instability dynamics of positive bright solitons in
multi-dimensional focusing nonlinear media with a potential (lattice), which
can be periodic, periodic with defects, quasiperiodic, single waveguide, etc.
We show that when the soliton is unstable, the type of instability dynamic that
develops depends on which of two stability conditions is violated.
Specifically, violation of the slope condition leads to an amplitude
instability, whereas violation of the spectral condition leads to a drift
instability. We also present a quantitative approach that allows to predict the
stability and instability strength
Chiral Quasicrystalline Order and Dodecahedral Geometry in Exceptional Families of Viruses
On the example of exceptional families of viruses we i) show the existence of
a completely new type of matter organization in nanoparticles, in which the
regions with a chiral pentagonal quasicrystalline order of protein positions
are arranged in a structure commensurate with the spherical topology and
dodecahedral geometry, ii) generalize the classical theory of quasicrystals
(QCs) to explain this organization, and iii) establish the relation between
local chiral QC order and nonzero curvature of the dodecahedral capsid faces.Comment: 8 pages, 3 figure
Modelling quasicrystals at positive temperature
We consider a two-dimensional lattice model of equilibrium statistical
mechanics, using nearest neighbor interactions based on the matching conditions
for an aperiodic set of 16 Wang tiles. This model has uncountably many ground
state configurations, all of which are nonperiodic. The question addressed in
this paper is whether nonperiodicity persists at low but positive temperature.
We present arguments, mostly numerical, that this is indeed the case. In
particular, we define an appropriate order parameter, prove that it is
identically zero at high temperatures, and show by Monte Carlo simulation that
it is nonzero at low temperatures
Local Complexity of Delone Sets and Crystallinity
This paper characterizes when a Delone set X is an ideal crystal in terms of
restrictions on the number of its local patches of a given size or on the
hetereogeneity of their distribution. Let N(T) count the number of
translation-inequivalent patches of radius T in X and let M(T) be the minimum
radius such that every closed ball of radius M(T) contains the center of a
patch of every one of these kinds. We show that for each of these functions
there is a `gap in the spectrum' of possible growth rates between being bounded
and having linear growth, and that having linear growth is equivalent to X
being an ideal crystal. Explicitly, for N(T), if R is the covering radius of X
then either N(T) is bounded or N(T) >= T/2R for all T>0. The constant 1/2R in
this bound is best possible in all dimensions. For M(T), either M(T) is bounded
or M(T) >= T/3 for all T>0. Examples show that the constant 1/3 in this bound
cannot be replaced by any number exceeding 1/2. We also show that every
aperiodic Delone set X has M(T) >= c(n)T for all T>0, for a certain constant
c(n) which depends on the dimension n of X and is greater than 1/3 when n > 1.Comment: 26 pages. Uses latexsym and amsfonts package
A symmetry group of a Thue-Morse quasicrystal
We present a method of coding general self-similar structures. In particular,
we construct a symmetry group of a one-dimensional Thue-Morse quasicrystal,
i.e., of a nonperiodic ground state of a certain translation-invariant,
exponentially decaying interaction.Comment: 6 pages, Late
Diffusive limits on the Penrose tiling
In this paper random walks on the Penrose lattice are investigated. Heat
kernel estimates and the invariance principle are shown
Symmetry Breaking in the Double-Well Hermitian Matrix Models
We study symmetry breaking in symmetric large matrix models. In the
planar approximation for both the symmetric double-well model and the
symmetric Penner model, we find there is an infinite family of broken symmetry
solutions characterized by different sets of recursion coefficients and
that all lead to identical free energies and eigenvalue densities. These
solutions can be parameterized by an arbitrary angle , for each
value of . In the double scaling limit, this class reduces to a
smaller family of solutions with distinct free energies already at the torus
level. For the double-well theory the double scaling string equations
are parameterized by a conserved angular momentum parameter in the range and a single arbitrary phase angle.Comment: 23 pages and 4 figures, Preprint No. CERN-TH.6611/92, Brown HET-863,
HUTP -- 92/A035, LPTHE-Orsay: 92/2
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