14,057 research outputs found
Calibrated Sub-Bundles in Non-Compact Manifolds of Special Holonomy
This paper is a continuation of math.DG/0408005. We first construct special
Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on
the cotangent bundle of S^n by looking at the conormal bundle of appropriate
submanifolds of S^n. We find that the condition for the conormal bundle to be
special Lagrangian is the same as that discovered by Harvey-Lawson for
submanifolds in R^n in their pioneering paper. We also construct calibrated
submanifolds in complete metrics with special holonomy G_2 and Spin(7)
discovered by Bryant and Salamon on the total spaces of appropriate bundles
over self-dual Einstein four manifolds. The submanifolds are constructed as
certain subbundles over immersed surfaces. We show that this construction
requires the surface to be minimal in the associative and Cayley cases, and to
be (properly oriented) real isotropic in the coassociative case. We also make
some remarks about using these constructions as a possible local model for the
intersection of compact calibrated submanifolds in a compact manifold with
special holonomy.Comment: 20 pages; for Revised Version: Minor cosmetic changes, some
paragraphs rewritten for improved clarit
Closed trajectories of a particle model on null curves in anti-de Sitter 3-space
We study the existence of closed trajectories of a particle model on null
curves in anti-de Sitter 3-space defined by a functional which is linear in the
curvature of the particle path. Explicit expressions for the trajectories are
found and the existence of infinitely many closed trajectories is proved.Comment: 12 pages, 1 figur
An investigation of vegetation and other earth resource/feature parameters using LANDSAT and other remote sensing data. A: LANDSAT. B: Remote sensing of volcanic emissions
There are no author-identified significant results in this report
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Peopling the practices of sustainable consumption: eco-chic and the limits to the spaces of intention
Urban solar photovoltaics potential: An inventory and modelling study applied to the San Fernando Valley region of Los Angeles
Procedures for analyzing the potential of solar photovoltaic collectors to meet energy requirements in a metropolitan region are described and a modeling effort is applied to the San Fernando Valley region of Los Angeles. The procedure involves a series of steps designed to produce maps and tabulations revealing the amount of rooftop area available for establishing solar collectors and the proportion of energy requirement that could be potentially supplied by solar photovoltaics within each of the 533 mainline feeder service areas in the study area. For the sixty five square mile study area, the results showed that, with half the available flat and south facing roofs used and assuming the availability of energy storage, 52.7 percent of the actual kWh energy requirements could have been met in 1978 using photovoltaic collectors. Hourly, daily, weekly, and monthly fluctuations in potential supply and actual loads and recommendations of avenues for further research are discussed. Some further potential applications of the modeling technique are suggested
Integrable vortex-type equations on the two-sphere
We consider the Yang-Mills instanton equations on the four-dimensional
manifold S^2xSigma, where Sigma is a compact Riemann surface of genus g>1 or
its covering space H^2=SU(1,1)/U(1). Introducing a natural ansatz for the gauge
potential, we reduce the instanton equations on S^2xSigma to vortex-type
equations on the sphere S^2. It is shown that when the scalar curvature of the
manifold S^2xSigma vanishes, the vortex-type equations are integrable, i.e. can
be obtained as compatibility conditions of two linear equations (Lax pair)
which are written down explicitly. Thus, the standard methods of integrable
systems can be applied for constructing their solutions. However, even if the
scalar curvature of S^2xSigma does not vanish, the vortex equations are well
defined and have solutions for any values of the topological charge N. We show
that any solution to the vortex equations on S^2 with a fixed topological
charge N corresponds to a Yang-Mills instanton on S^2xSigma of charge (g-1)N.Comment: 14 pages; v2: clarifying comments added, published versio
Controlled complete suppression of single-atom inelastic spin and orbital cotunnelling
The inelastic portion of the tunnel current through an individual magnetic
atom grants unique access to read out and change the atom's spin state, but it
also provides a path for spontaneous relaxation and decoherence. Controlled
closure of the inelastic channel would allow for the latter to be switched off
at will, paving the way to coherent spin manipulation in single atoms. Here we
demonstrate complete closure of the inelastic channels for both spin and
orbital transitions due to a controlled geometric modification of the atom's
environment, using scanning tunnelling microscopy (STM). The observed
suppression of the excitation signal, which occurs for Co atoms assembled into
chain on a CuN substrate, indicates a structural transition affecting the
d orbital, effectively cutting off the STM tip from the spin-flip
cotunnelling path.Comment: 4 figures plus 4 supplementary figure
Parallelizing Synthesis from Temporal Logic Specifications by Identifying Equicontrollable States
For the synthesis of correct-by-construction control policies from temporal logic specifications the scalability of the synthesis algorithms is often a bottleneck. In this paper, we parallelize synthesis from specifications in the GR(1) fragment of linear temporal logic by introducing a hierarchical procedure that allows decoupling of the fixpoint computations. The state space is partitioned into equicontrollable sets using solutions to parametrized games that arise from decomposing the original GR(1) game into smaller reachability-persistence games. Following the partitioning, another synthesis problem is formulated for composing the strategies from the decomposed reachability games. The formulation guarantees that composing the synthesized controllers ensures satisfaction of the given GR(1) property. Experiments with robot planning problems demonstrate good performance of the approach
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