1,077 research outputs found
Properties and Applications of the Simplified Generalized Perpendicular Bisector
International audienceThis paper deals with the Simplified Generalized Perpendicular Bisector (SGBP) presented in [15,1]. The SGPB has some interesting properties that we explore. We show in particular that the SGPB can be used for the recognition and exhaustive parameter estimation of noisy discrete circles. A second application we are considering is the error estimation for a class of rotation reconstruction algorithms
Band Gap Modulation of Graphene on SiC
A recipe on how to engineer a band gap in the energy spectrum for the
carriers in graphene is conveyed. It is supported by a series of numerical
simulations inspired by an analytical result based on the opening of a band gap
in periodically corrugated graphene, e.g. the buffer layer grown on SiC at high
temperatures.Comment: accepted in EPJ
Time-Dependent Behavior of Linear Polarization in Unresolved Photospheres, With Applications for The Hanle Effect
Aims: This paper extends previous studies in modeling time varying linear
polarization due to axisymmetric magnetic fields in rotating stars. We use the
Hanle effect to predict variations in net line polarization, and use geometric
arguments to generalize these results to linear polarization due to other
mechanisms. Methods: Building on the work of Lopez Ariste et al., we use simple
analytic models of rotating stars that are symmetric except for an axisymmetric
magnetic field to predict the polarization lightcurve due to the Hanle effect.
We highlight the effects for the variable line polarization as a function of
viewing inclination and field axis obliquity. Finally, we use geometric
arguments to generalize our results to linear polarization from the weak
transverse Zeeman effect. Results: We derive analytic expressions to
demonstrate that the variable polarization lightcurve for an oblique magnetic
rotator is symmetric. This holds for any axisymmetric field distribution and
arbitrary viewing inclination to the rotation axis. Conclusions: For the
situation under consideration, the amplitude of the polarization variation is
set by the Hanle effect, but the shape of the variation in polarization with
phase depends largely on geometrical projection effects. Our work generalizes
the applicability of results described in Lopez Ariste et al., inasmuch as the
assumptions of a spherical star and an axisymmetric field are true, and
provides a strategy for separating the effects of perspective from the Hanle
effect itself for interpreting polarimetric lightcurves.Comment: 6 pages; 4 figures. Includes an extra figure found only in this
preprint versio
Geometry in Action: A Curriculum Unit Utilizing Dynamic Geometry Software to Enhance Students’ Comprehension
The paper identifies two critical obstacles to student success in a traditional geometry classroom and examines the role dynamic geometry software can play in overcoming these obstacles
Geometric phase and o-mode blue shift in a chiral anisotropic medium inside a Fabry-P\'erot cavity
Anomalous spectral shift of transmission peaks is observed in a
Fabry--P\'erot cavity filled with a chiral anisotropic medium. The effective
refractive index value resides out of the interval between the ordinary and the
extraordinary refractive indices. The spectral shift is explained by
contribution of a geometric phase. The problem is solved analytically using the
approximate Jones matrix method, numerically using the accurate Berreman method
and geometrically using the generalized Mauguin--Poincar\'e rolling cone
method. The -mode blue shift is measured for a
4-methoxybenzylidene-4'--butylaniline twisted--nematic layer inside the
Fabry--P\'erot cavity. The twist is electrically induced due to the
homeoplanar--twisted configuration transition in an ionic-surfactant-doped
liquid crystal layer. Experimental evidence confirms the validity of the
theoretical model.Comment: the text is available both in English (Timofeev2015en.tex) and in
Russian (download: other formats - source - Timofeev2015ru.tex,
Timofeev2015rus.pdf
Graph embeddings for low-stretch greedy routing
The simplest greedy geometric routing forwards packets to make most progress in terms of geometric distance within reach. Its notable advantages are low complexity, and the use of local information only. However, two problems of greedy routing are that delivery is not always guaranteed, and that the greedy routes may take more hops than the corresponding shortest paths. Additionally, in dynamic multihop networks, routing elements can join or leave during network operation or exhibit intermittent failures. Even a single link or node removal may invalidate the greedy routing success guarantees.
Greedy embedding is a graph embedding that makes the simple greedy packet forwarding successful for every source-destination pair. In this dissertation, we consider the problems of designing greedy graph embeddings that also yield low hop stretch of the greedy paths over the shortest paths and can accommodate network dynamics.
In the first part of the dissertation, we consider embedding and routing for arbitrary unweighted network graphs, based on greedy routing and utilizing virtual node coordinates. We propose an algorithm for online greedy graph embedding in the hyperbolic plane that enables incremental embedding of network nodes as they join the network, without disturbing the global embedding. As an alternative to frequent reembedding of temporally dynamic network graphs in order to retain the greedy embedding property, we propose a simple but robust generalization of greedy geometric routing called Gravity--Pressure (GP) routing. Our routing method always succeeds in finding a route to the destination provided that a path exists, even if a significant fraction of links or nodes is removed subsequent to the embedding. GP routing does not require precomputation or maintenance of special spanning subgraphs and is particularly suitable for operation in tandem with our proposed algorithm for online graph embedding.
In the second part of the dissertation we study how topological and geometric properties of embedded graphs influence the hop stretch. Based on the obtained insights, we synthesize embedding heuristics that yield minimal hop stretch greedy embeddings. Finally, we verify their effectiveness on models of synthetic graphs as well as instances of several classes of real-world network graphs
Optimal Point Placement for Mesh Smoothing
We study the problem of moving a vertex in an unstructured mesh of
triangular, quadrilateral, or tetrahedral elements to optimize the shapes of
adjacent elements. We show that many such problems can be solved in linear time
using generalized linear programming. We also give efficient algorithms for
some mesh smoothing problems that do not fit into the generalized linear
programming paradigm.Comment: 12 pages, 3 figures. A preliminary version of this paper was
presented at the 8th ACM/SIAM Symp. on Discrete Algorithms (SODA '97). This
is the final version, and will appear in a special issue of J. Algorithms for
papers from SODA '9
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