4,828 research outputs found
Origin of artificial electrodynamics in three-dimensional bosonic models
Several simple models of strongly correlated bosons on three-dimensional lattices have been shown to possess exotic fractionalized Mott insulating phases with a gapless "photon" excitation. In this paper we show how to view the physics of this "Coulomb" state in terms of the excitations of proximate superfluid. We argue for the presence of ordered vortex cores with a broken discrete symmetry in the nearby superfluid phase and that proliferating these degenerate but distinct vortices with equal amplitudes produces the Coulomb phase. This provides a simple physical description of the origin of the exotic excitations of the Coulomb state. The physical picture is formalized by means of a dual description of three-dimensional bosonic systems in terms of fluctuating quantum mechanical vortex loops. Such a dual formulation is extensively developed. It is shown how the Coulomb phase (as well as various other familiar phases) of three-dimensional bosonic systems may be described in this vortex loop theory. For bosons at half-filling and the closely related system of spin-1/2 quantum magnets on a cubic lattice, fractionalized phases as well as bond- or "box"-ordered states are possible. The latter are analyzed by an extension of techniques previously developed in two spatial dimensions. The relation between these "confining" phases with broken translational symmetry and the fractionalized Coulomb phase is exposed
Coverage and Connectivity in Three-Dimensional Networks
Most wireless terrestrial networks are designed based on the assumption that
the nodes are deployed on a two-dimensional (2D) plane. However, this 2D
assumption is not valid in underwater, atmospheric, or space communications. In
fact, recent interest in underwater acoustic ad hoc and sensor networks hints
at the need to understand how to design networks in 3D. Unfortunately, the
design of 3D networks is surprisingly more difficult than the design of 2D
networks. For example, proofs of Kelvin's conjecture and Kepler's conjecture
required centuries of research to achieve breakthroughs, whereas their 2D
counterparts are trivial to solve. In this paper, we consider the coverage and
connectivity issues of 3D networks, where the goal is to find a node placement
strategy with 100% sensing coverage of a 3D space, while minimizing the number
of nodes required for surveillance. Our results indicate that the use of the
Voronoi tessellation of 3D space to create truncated octahedral cells results
in the best strategy. In this truncated octahedron placement strategy, the
transmission range must be at least 1.7889 times the sensing range in order to
maintain connectivity among nodes. If the transmission range is between 1.4142
and 1.7889 times the sensing range, then a hexagonal prism placement strategy
or a rhombic dodecahedron placement strategy should be used. Although the
required number of nodes in the hexagonal prism and the rhombic dodecahedron
placement strategies is the same, this number is 43.25% higher than the number
of nodes required by the truncated octahedron placement strategy. We verify by
simulation that our placement strategies indeed guarantee ubiquitous coverage.
We believe that our approach and our results presented in this paper could be
used for extending the processes of 2D network design to 3D networks.Comment: To appear in ACM Mobicom 200
Onion Curve: A Space Filling Curve with Near-Optimal Clustering
Space filling curves (SFCs) are widely used in the design of indexes for
spatial and temporal data. Clustering is a key metric for an SFC, that measures
how well the curve preserves locality in moving from higher dimensions to a
single dimension. We present the {\em onion curve}, an SFC whose clustering
performance is provably close to optimal for the cube and near-cube shaped
query sets, irrespective of the side length of the query. We show that in
contrast, the clustering performance of the widely used Hilbert curve can be
far from optimal, even for cube-shaped queries. Since the clustering
performance of an SFC is critical to the efficiency of multi-dimensional
indexes based on the SFC, the onion curve can deliver improved performance for
data structures involving multi-dimensional data.Comment: The short version is published in ICDE 1
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