380 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
Three‐periodic nets and tilings: regular and quasiregular nets
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/115935/1/S0108767302018494.pd
Three‐periodic nets and tilings: semiregular nets
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/115982/1/S0108767303017100.pd
The Multipole Resonance Probe: Simultaneous Determination of Electron Density and Electron Temperature Using Spectral Kinetic Simulation
The investigation of the spectral kinetic model of the Multipole Resonance
Probe (MRP) is presented and discussed in this paper. The MRP is a
radio-frequency driven probe of the particular spherical design, which is
suitable for the supervision and control of low-temperature plasma. The
importance of the kinetic effects was introduced in the previous study of the
spectral kinetic model of the idealized MRP. Such effects particularly dominate
the energy loss in a low-pressure regime. Unfortunately, they are absent in the
Drude model. With the help of the spectral kinetic scheme, those energy losses
can be predicted, and it enables us to obtain the electron temperature from the
FWHM in the simulated resonance curve. Simultaneously, the electron density can
be derived from the simulated resonance frequency. Good agreements in the
comparison between the simulation and the measurement demonstrate the
suitability of the presented model
Minimal nets and minimal minimal surfaces
The 3-periodic nets of genus 3 ('minimal nets') are reviewed and their symmetries re-examined. Although they are all crystallographic, seven of the 15 only have maximum-symmetry embeddings if some links are allowed to have zero length. The connection bet
Three‐periodic nets and tilings: minimal nets
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/116005/1/S0108767304015442.pd
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
Isogonal non-crystallographic periodic graphs based on knotted sodalite cages
This work considers non-crystallographic periodic nets obtained from multiple identical copies of an underlying crystallographic net by adding or flipping edges so that the result is connected. Such a structure is called a `ladder' net here because the 1-periodic net shaped like an ordinary (infinite) ladder is a particularly simple example. It is shown how ladder nets with no added edges between layers can be generated from tangled polyhedra. These are simply related to the zeolite nets SOD, LTA and FAU. They are analyzed using new extensions of algorithms in the program Systre that allow unambiguous identification of locally stable ladder nets
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