514 research outputs found
Group Theory of Circular-Polarization Effects in Chiral Photonic Crystals with Four-Fold Rotation Axes, Applied to the Eight-Fold Intergrowth of Gyroid Nets
We use group or representation theory and scattering matrix calculations to
derive analytical results for the band structure topology and the scattering
parameters, applicable to any chiral photonic crystal with body-centered cubic
symmetry I432 for circularly-polarised incident light. We demonstrate in
particular that all bands along the cubic [100] direction can be identified
with the irreducible representations E+/-,A and B of the C4 point group. E+ and
E- modes represent the only transmission channels for plane waves with wave
vector along the ? line, and can be identified as non-interacting transmission
channels for right- (E-) and left-circularly polarised light (E+),
respectively. Scattering matrix calculations provide explicit relationships for
the transmission and reflectance amplitudes through a finite slab which
guarantee equal transmission rates for both polarisations and vanishing
ellipticity below a critical frequency, yet allowing for finite rotation of the
polarisation plane. All results are verified numerically for the so-called
8-srs geometry, consisting of eight interwoven equal-handed dielectric Gyroid
networks embedded in air. The combination of vanishing losses, vanishing
ellipticity, near-perfect transmission and optical activity comparable to that
of metallic meta-materials makes this geometry an attractive design for
nanofabricated photonic materials
Second order analysis of geometric functionals of Boolean models
This paper presents asymptotic covariance formulae and central limit theorems
for geometric functionals, including volume, surface area, and all Minkowski
functionals and translation invariant Minkowski tensors as prominent examples,
of stationary Boolean models. Special focus is put on the anisotropic case. In
the (anisotropic) example of aligned rectangles, we provide explicit analytic
formulae and compare them with simulation results. We discuss which information
about the grain distribution second moments add to the mean values.Comment: Chapter of the forthcoming book "Tensor Valuations and their
Applications in Stochastic Geometry and Imaging" in Lecture Notes in
Mathematics edited by Markus Kiderlen and Eva B. Vedel Jensen. (The second
version mainly resolves minor LaTeX problems.
Group Theory of Chiral Photonic Crystals with 4-fold Symmetry: Band Structure and S-Parameters of Eight-Fold Intergrown Gyroid Nets
The Single Gyroid, or srs, nanostructure has attracted interest as a
circular-polarisation sensitive photonic material. We develop a group
theoretical and scattering matrix method, applicable to any photonic crystal
with symmetry I432, to demonstrate the remarkable chiral-optical properties of
a generalised structure called 8-srs, obtained by intergrowth of eight
equal-handed srs nets. Exploiting the presence of four-fold rotations, Bloch
modes corresponding to the irreducible representations E- and E+ are identified
as the sole and non-interacting transmission channels for right- and
left-circularly polarised light, respectively. For plane waves incident on a
finite slab of the 8-srs, the reflection rates for both circular polarisations
are identical for all frequencies and transmission rates are identical up to a
critical frequency below which scattering in the far field is restricted to
zero grating order. Simulations show the optical activity of the lossless
dielectric 8-srs to be large, comparable to metallic metamaterials,
demonstrating its potential as a nanofabricated photonic material
Thermal noise influences fluid flow in thin films during spinodal dewetting
Experiments on dewetting thin polymer films confirm the theoretical
prediction that thermal noise can strongly influence characteristic time-scales
of fluid flow and cause coarsening of typical length scales. Comparing the
experiments with deterministic simulations, we show that the Navier-Stokes
equation has to be extended by a conserved bulk noise term to accomplish the
observed spectrum of capillary waves. Due to thermal fluctuations the spectrum
changes from an exponential to a power law decay for large wavevectors. Also
the time evolution of the typical wavevector of unstable perturbations exhibits
noise induced coarsening that is absent in deterministic hydrodynamic flow.Comment: 4 pages, 3 figure
Primordial Non-Gaussianity and Analytical Formula for Minkowski Functionals of the Cosmic Microwave Background and Large-scale Structure
We derive analytical formulae for the Minkowski Functions of the cosmic
microwave background (CMB) and large-scale structure (LSS) from primordial
non-Gaussianity. These formulae enable us to estimate a non-linear coupling
parameter, f_NL, directly from the CMB and LSS data without relying on
numerical simulations of non-Gaussian primordial fluctuations. One can use
these formulae to estimate statistical errors on f_NL from Gaussian
realizations, which are much faster to generate than non-Gaussian ones, fully
taking into account the cosmic/sampling variance, beam smearing, survey mask,
etc. We show that the CMB data from the Wilkinson Microwave Anisotropy Probe
should be sensitive to |f_NL|\simeq 40 at the 68% confidence level. The Planck
data should be sensitive to |f_NL|\simeq 20. As for the LSS data, the late-time
non-Gaussianity arising from gravitational instability and galaxy biasing makes
it more challenging to detect primordial non-Gaussianity at low redshifts. The
late-time effects obscure the primordial signals at small spatial scales.
High-redshift galaxy surveys at z>2 covering \sim 10Gpc^3 volume would be
required for the LSS data to detect |f_NL|\simeq 100. Minkowski Functionals are
nicely complementary to the bispectrum because the Minkowski Functionals are
defined in real space and the bispectrum is defined in Fourier space. This
property makes the Minksowski Functionals a useful tool in the presence of
real-world issues such as anisotropic noise, foreground and survey masks. Our
formalism can be extended to scale-dependent f_NL easily.Comment: 16 pages, 5 figures, accepted for publication in ApJ (Vol. 653, 2006
Local orientations of fluctuating fluid interfaces
Thermal fluctuations cause the local normal vectors of fluid interfaces to
deviate from the vertical direction defined by the flat mean interface
position. This leads to a nonzero mean value of the corresponding polar tilt
angle which renders a characterization of the thermal state of an interface.
Based on the concept of an effective interface Hamiltonian we determine the
variances of the local interface position and of its lateral derivatives. This
leads to the probability distribution functions for the metric of the interface
and for the tilt angle which allows us to calculate its mean value and its mean
square deviation. We compare the temperature dependences of these quantities as
predicted by the simple capillary wave model, by an improved phenomenological
model, and by the microscopic effective interface Hamiltonian derived from
density functional theory. The mean tilt angle discriminates clearly between
these theoretical approaches and emphasizes the importance of the variation of
the surface tension at small wave lengths. Also the tilt angle two-point
correlation function is determined which renders an additional structural
characterization of interfacial fluctuations. Various experimental accesses to
measure the local orientational fluctuations are discussed.Comment: 29 pages, 12 figure
Using the filaments in the LCRS to test the LambdaCDM model
It has recently been established that the filaments seen in the Las Campanas
Redshift Survey (LCRS) are statistically significant at scales as large as 70
to 80 Mpc/h in the slice, and 50 to 70 Mpc/h in the five other
LCRS slices. The ability to produce such filamentary features is an important
test of any model for structure formation. We have tested the LCDM model with a
featureless, scale invariant primordial power spectrum by quantitatively
comparing the filamentarity in simulated LCRS slices with the actual data. The
filamentarity in an unbiased LCDM model, we find, is less than the LCRS.
Introducing a bias b=1.15, the model is in rough consistency with the data,
though in two of the slices the filamentarity falls below the data at a low
level of statistical significance. The filamentarity is very sensitive to the
bias parameter and a high value b=1.5, which enhances filamentarity at small
scales and suppresses it at large scales, is ruled out. A bump in the power
spectrum at k~0.05 Mpc/h is found to have no noticeable effect on the
filamentarity.Comment: 16 pages, 3 figures; Minor Changes, Accepted to Ap
Effects of Noise on Galaxy Isophotes
The study of shapes of the images of objects is an important issue not only
because it reveals its dynamical state but also it helps to understand the
object's evolutionary history. We discuss a new technique in cosmological image
analysis which is based on a set of non-parametric shape descriptors known as
the Minkowski Functionals (MFs). These functionals are extremely versatile and
under some conditions give a complete description of the geometrical properties
of objects. We believe that MFs could be a useful tool to extract information
about the shapes of galaxies, clusters of galaxies and superclusters. The
information revealed by MFs can be utilized along with the knowledge obtained
from currently popular methods and thus could improve our understanding of the
true shapes of cosmological objects.Comment: 3 pages, 1 figure, to appear in "The IGM/Galaxy Connection - The
Distribution of Baryons at z=0" Conference Proceeding
Percolation Analysis of a Wiener Reconstruction of the IRAS 1.2 Jy Redshift Catalog
We present percolation analyses of Wiener Reconstructions of the IRAS 1.2 Jy
Redshift Survey. There are ten reconstructions of galaxy density fields in real
space spanning the range to , where
, is the present dimensionless density and
is the bias factor. Our method uses the growth of the largest cluster
statistic to characterize the topology of a density field, where Gaussian
randomized versions of the reconstructions are used as standards for analysis.
For the reconstruction volume of radius, Mpc,
percolation analysis reveals a slight `meatball' topology for the real space,
galaxy distribution of the IRAS survey.
cosmology-galaxies:clustering-methods:numericalComment: Revised version accepted for publication in The Astrophysical
Journal, January 10, 1997 issue, Vol.47
Minkowski Tensors of Anisotropic Spatial Structure
This article describes the theoretical foundation of and explicit algorithms
for a novel approach to morphology and anisotropy analysis of complex spatial
structure using tensor-valued Minkowski functionals, the so-called Minkowski
tensors. Minkowski tensors are generalisations of the well-known scalar
Minkowski functionals and are explicitly sensitive to anisotropic aspects of
morphology, relevant for example for elastic moduli or permeability of
microstructured materials. Here we derive explicit linear-time algorithms to
compute these tensorial measures for three-dimensional shapes. These apply to
representations of any object that can be represented by a triangulation of its
bounding surface; their application is illustrated for the polyhedral Voronoi
cellular complexes of jammed sphere configurations, and for triangulations of a
biopolymer fibre network obtained by confocal microscopy. The article further
bridges the substantial notational and conceptual gap between the different but
equivalent approaches to scalar or tensorial Minkowski functionals in
mathematics and in physics, hence making the mathematical measure theoretic
method more readily accessible for future application in the physical sciences
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