1,807 research outputs found
Complexity of the General Chromatic Art Gallery Problem
In the original Art Gallery Problem (AGP), one seeks the minimum number of
guards required to cover a polygon . We consider the Chromatic AGP (CAGP),
where the guards are colored. As long as is completely covered, the number
of guards does not matter, but guards with overlapping visibility regions must
have different colors. This problem has applications in landmark-based mobile
robot navigation: Guards are landmarks, which have to be distinguishable (hence
the colors), and are used to encode motion primitives, \eg, "move towards the
red landmark". Let , the chromatic number of , denote the minimum
number of colors required to color any guard cover of . We show that
determining, whether is \NP-hard for all . Keeping
the number of colors minimal is of great interest for robot navigation, because
less types of landmarks lead to cheaper and more reliable recognition
On Three-Dimensional Space Groups
An entirely new and independent enumeration of the crystallographic space
groups is given, based on obtaining the groups as fibrations over the plane
crystallographic groups, when this is possible. For the 35 ``irreducible''
groups for which it is not, an independent method is used that has the
advantage of elucidating their subgroup relationships. Each space group is
given a short ``fibrifold name'' which, much like the orbifold names for
two-dimensional groups, while being only specified up to isotopy, contains
enough information to allow the construction of the group from the name.Comment: 26 pages, 8 figure
Schroedinger operators with singular interactions: a model of tunneling resonances
We discuss a generalized Schr\"odinger operator in , with an attractive singular interaction supported by a
-dimensional hyperplane and a finite family of points. It can be
regarded as a model of a leaky quantum wire and a family of quantum dots if
, or surface waves in presence of a finite number of impurities if .
We analyze the discrete spectrum, and furthermore, we show that the resonance
problem in this setting can be explicitly solved; by Birman-Schwinger method it
is cast into a form similar to the Friedrichs model.Comment: LaTeX2e, 34 page
Well-posedness of boundary layer equations for time-dependent flow of non-Newtonian fluids
We consider the flow of an upper convected Maxwell fluid in the limit of high
Weissenberg and Reynolds number. In this limit, the no-slip condition cannot be
imposed on the solutions. We derive equations for the resulting boundary layer
and prove the well-posedness of these equations. A transformation to Lagrangian
coordinates is crucial in the argument
Binary black hole spacetimes with a helical Killing vector
Binary black hole spacetimes with a helical Killing vector, which are
discussed as an approximation for the early stage of a binary system, are
studied in a projection formalism. In this setting the four dimensional
Einstein equations are equivalent to a three dimensional gravitational theory
with a sigma model as the material source. The sigma
model is determined by a complex Ernst equation. 2+1 decompositions of the
3-metric are used to establish the field equations on the orbit space of the
Killing vector. The two Killing horizons of spherical topology which
characterize the black holes, the cylinder of light where the Killing vector
changes from timelike to spacelike, and infinity are singular points of the
equations. The horizon and the light cylinder are shown to be regular
singularities, i.e. the metric functions can be expanded in a formal power
series in the vicinity. The behavior of the metric at spatial infinity is
studied in terms of formal series solutions to the linearized Einstein
equations. It is shown that the spacetime is not asymptotically flat in the
strong sense to have a smooth null infinity under the assumption that the
metric tends asymptotically to the Minkowski metric. In this case the metric
functions have an oscillatory behavior in the radial coordinate in a
non-axisymmetric setting, the asymptotic multipoles are not defined. The
asymptotic behavior of the Weyl tensor near infinity shows that there is no
smooth null infinity.Comment: to be published in Phys. Rev. D, minor correction
The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids
The Rosensweig instability is the phenomenon that above a certain threshold
of a vertical magnetic field peaks appear on the free surface of a horizontal
layer of magnetic fluid. In contrast to almost all classical hydrodynamical
systems, the nonlinearities of the Rosensweig instability are entirely
triggered by the properties of a deformed and a priori unknown surface. The
resulting problems in defining an adjoint operator for such nonlinearities are
illustrated. The implications concerning amplitude equations for pattern
forming systems with a deformed surface are discussed.Comment: 11 pages, 1 figur
Added Value of Combining Multiple Optical and Acoustic Instruments When Characterizing Fine-Grained Estuarine Suspensions
Various optical and acoustic instruments have specific advantages and limitations for characterizing suspensions, and when used together more information can be obtained than with one instrument alone. The LISST 100X, for example, is a powerful tool for estimating particle size distribution, but because of the inversion method used to determine the size distribution, it is difficult to distinguish two dominate populations that peak close to one another, especially among larger grain sizes. In the York River estuary, VA, additional information obtained through the deployment of a RIPScam camera system and an ADV along with the LISST 100X allowed differentiation between populations of resilient pellets and flocs in suspension close to the bed and how the populations varied over a tidal cycle. A second example of instrument pairing providing additional information was the use of a PICS video imaging system in the York River to verify the conditions under which use of the ADV Reynolds flux method was valid for estimating settling velocity of suspended particle populations
Surface Instabilities on Liquid Oxygen in an Inhomogeneous Magnetic Field
Liquid oxygen exhibits surface instabilities when subjected to a sufficiently
strong magnetic field. A vertically oriented magnetic field gradient both
increases the magnetic field value at which the pattern forms and shrinks the
length scale of the surface patterning. We show that these effects of the field
gradient may be described in terms of an ``effective gravity'', which in our
experiments may be varied from 1g to 360g.Comment: 4 pages, 5 embedded figures in eps forma
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