16 research outputs found
Hyperuniformity of Quasicrystals
Hyperuniform systems, which include crystals, quasicrystals and special
disordered systems, have attracted considerable recent attention, but rigorous
analyses of the hyperuniformity of quasicrystals have been lacking because the
support of the spectral intensity is dense and discontinuous. We employ the
integrated spectral intensity, , to quantitatively characterize the
hyperuniformity of quasicrystalline point sets generated by projection methods.
The scaling of as tends to zero is computed for one-dimensional
quasicrystals and shown to be consistent with independent calculations of the
variance, , in the number of points contained in an interval of
length . We find that one-dimensional quasicrystals produced by projection
from a two-dimensional lattice onto a line of slope fall into distinct
classes determined by the width of the projection window. For a countable dense
set of widths, ; for all others, . This
distinction suggests that measures of hyperuniformity define new classes of
quasicrystals in higher dimensions as well.Comment: 12 pages, 14 figure
The effect of boundary adaptivity on hexagonal ordering and bistability in circularly confined quasi hard discs
The behaviour of materials under spatial confinement is sensitively dependent
on the nature of the confining boundaries. In two dimensions, confinement
within a hard circular boundary inhibits the hexagonal ordering observed in
bulk systems at high density. Using colloidal experiments and Monte Carlo
simulations, we investigate two model systems of quasi hard discs under
circularly symmetric confinement. The first system employs an adaptive circular
boundary, defined experimentally using holographic optical tweezers. We show
that deformation of this boundary allows, and indeed is required for, hexagonal
ordering in the confined system. The second system employs a circularly
symmetric optical potential to confine particles without a physical boundary.
We show that, in the absence of a curved wall, near perfect hexagonal ordering
is possible. We propose that the degree to which hexagonal ordering is
suppressed by a curved boundary is determined by the `strictness' of that wall.Comment: 10 pages, 8 figure
Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings
We consider the scaling properties characterizing the hyperuniformity (or
anti-hyperuniformity) of long wavelength fluctuations in a broad class of
one-dimensional substitution tilings. We present a simple argument that
predicts the exponent governing the scaling of Fourier intensities at
small wavenumbers, tilings with being hyperuniform, and confirm with
numerical computations that the predictions are accurate for quasiperiodic
tilings, tilings with singular continuous spectra, and limit-periodic tilings.
Tilings with quasiperiodic or singular continuous spectra can be constructed
with arbitrarily close to any given value between and .
Limit-periodic tilings can be constructed with between and or
with Fourier intensities that approach zero faster than any power law.Comment: 13 pages, 9 figures, to be submitted to Acta Crystallographica
special issue: Aperiodic 201
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Local-order metric for condensed-phase environments
We introduce a local order metric (LOM) that measures the degree of order in the neighborhood of an atomic or molecular site in a condensed medium. The LOM maximizes the overlap between the spatial distribution of sites belonging to that neighborhood and the corresponding distribution in a suitable reference system. The LOM takes a value tending to zero for completely disordered environments and tending to one for environments that perfectly match the reference. The site-averaged LOM and its standard deviation define two scalar order parameters, and , that characterize with excellent resolution crystals, liquids, and amorphous materials. We show with molecular dynamics simulations that , , and the LOM provide very insightful information in the study of structural transformations, such as those occurring when ice spontaneously nucleates from supercooled water or when a supercooled water sample becomes amorphous upon progressive cooling