22,668 research outputs found
A novel view of plane wave expansion method in photonic crystals
We propose a method derived from the simple plane wave expansion that can
easily solve the interface problem between vacuum and a semi-infinite photonic
crystal. The method is designed to find the complete set of all the
eigenfunctions, propagating or evanescent, of the translation operators , at a fixed frequency. With these eigenfunctions and their
eigenvalues, the transmitted and reflected waves can be determined. Two kinds
of applications are presented for 2D photonic crystals. The first is a
selection rule for determine the normal direction of the vacuum-photonic
crystal interface to achieve the highest attenuation effect at a gap frequency.
The second is to calculate the transmittance and reflectance for a light
incident from vacuum to an semi-infinite photonic crystal. As an example we
recalculate a system studied previously by K. Sakoda et al. and get results in
agreement with theirs
Adjacency labeling schemes and induced-universal graphs
We describe a way of assigning labels to the vertices of any undirected graph
on up to vertices, each composed of bits, such that given the
labels of two vertices, and no other information regarding the graph, it is
possible to decide whether or not the vertices are adjacent in the graph. This
is optimal, up to an additive constant, and constitutes the first improvement
in almost 50 years of an bound of Moon. As a consequence, we
obtain an induced-universal graph for -vertex graphs containing only
vertices, which is optimal up to a multiplicative constant,
solving an open problem of Vizing from 1968. We obtain similar tight results
for directed graphs, tournaments and bipartite graphs
Peeling from a patterned thin elastic film
Inspired by the observation that many naturally occurring adhesives arise as
textured thin films, we consider the displacement controlled peeling of a
flexible plate from an incision-patterned thin adhesive elastic layer. We find
that crack initiation from an incision on the film occurs at a load much higher
than that required to propagate it on a smooth adhesive surface; multiple
incisions thus cause the crack to propagate intermittently. Microscopically,
this mode of crack initiation and propagation in geometrically confined thin
adhesive films is related to the nucleation of cavitation bubbles behind the
incision which must grow and coalesce before a viable crack propagates. Our
theoretical analysis allows us to rationalize these experimental observations
qualitatively and quantitatively and suggests a simple design criterion for
increasing the interfacial fracture toughness of adhesive films.Comment: 8 pages, To appear in Proceedings of Royal Society London, Ser.
Bidirectional PageRank Estimation: From Average-Case to Worst-Case
We present a new algorithm for estimating the Personalized PageRank (PPR)
between a source and target node on undirected graphs, with sublinear
running-time guarantees over the worst-case choice of source and target nodes.
Our work builds on a recent line of work on bidirectional estimators for PPR,
which obtained sublinear running-time guarantees but in an average-case sense,
for a uniformly random choice of target node. Crucially, we show how the
reversibility of random walks on undirected networks can be exploited to
convert average-case to worst-case guarantees. While past bidirectional methods
combine forward random walks with reverse local pushes, our algorithm combines
forward local pushes with reverse random walks. We also discuss how to modify
our methods to estimate random-walk probabilities for any length distribution,
thereby obtaining fast algorithms for estimating general graph diffusions,
including the heat kernel, on undirected networks.Comment: Workshop on Algorithms and Models for the Web-Graph (WAW) 201
Induced Lorentz- and CPT-violating Chern-Simons term in QED: Fock-Schwinger proper time method
Using the Fock-Schwinger proper time method, we calculate the induced
Chern-Simons term arising from the Lorentz- and CPT-violating sector of quantum
electrodynamics with a term. Our
result to all orders in coincides with a recent linear-in- calculation
by Chaichian et al. [hep-th/0010129 v2]. The coincidence was pointed out by
Chung [Phys. Lett. {\bf B461} (1999) 138] and P\'{e}rez-Victoria [Phys. Rev.
Lett. {\bf 83} (1999) 2518] in the standard Feynman diagram calculation with
the nonperturbative-in- propagator.Comment: 11 pages, no figur
Lorentz invariance violation in top-down scenarios of ultrahigh energy cosmic ray creation
The violation of Lorentz invariance (LI) has been invoked in a number of ways
to explain issues dealing with ultrahigh energy cosmic ray (UHECR) production
and propagation. These treatments, however, have mostly been limited to
examples in the proton-neutron system and photon-electron system. In this paper
we show how a broader violation of Lorentz invariance would allow for a series
of previously forbidden decays to occur, and how that could lead to UHECR
primaries being heavy baryonic states or Higgs bosons.Comment: Replaced with heavily revised (see new Abstract) version accepted by
Phys. Rev. D. 6 page
Uncertainty Estimates for Theoretical Atomic and Molecular Data
Sources of uncertainty are reviewed for calculated atomic and molecular data
that are important for plasma modeling: atomic and molecular structure and
cross sections for electron-atom, electron-molecule, and heavy particle
collisions. We concentrate on model uncertainties due to approximations to the
fundamental many-body quantum mechanical equations and we aim to provide
guidelines to estimate uncertainties as a routine part of computations of data
for structure and scattering.Comment: 65 pages, 18 Figures, 3 Tables. J. Phys. D: Appl. Phys. Final
accepted versio
Multiple Scattering of Fractionally-Charged Quasiparticles
We employ shot noise measurements to characterize the effective charge of
quasiparticles, at filling factor nu=1/3 of the fractional quantum Hall regime,
as they scatter from an array of identical weak backscatterers. Upon
scattering, quasiparticles are known to bunch, e.g., only three e/3 charges, or
'electrons' are found to traverse a rather opaque potential barrier. We find
here that the effective charge scattered by an array of scatterers is
determined by the scattering strength of an individual scatterer and not by the
combined scattering strength of the array, which can be very small. Moreover,
we also rule out intra-edge equilibration of e/3 quasiparticles over length
scale of hundreds microns.Comment: 4 pages, 4 figure
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