2,528 research outputs found
On Minimum Average Stretch Spanning Trees in Polygonal 2-trees
A spanning tree of an unweighted graph is a minimum average stretch spanning
tree if it minimizes the ratio of sum of the distances in the tree between the
end vertices of the graph edges and the number of graph edges. We consider the
problem of computing a minimum average stretch spanning tree in polygonal
2-trees, a super class of 2-connected outerplanar graphs. For a polygonal
2-tree on vertices, we present an algorithm to compute a minimum average
stretch spanning tree in time. This algorithm also finds a
minimum fundamental cycle basis in polygonal 2-trees.Comment: 17 pages, 12 figure
Diffusion at constant speed in a model phase space
We reconsider the problem of diffusion of particles at constant speed and
present a generalization of the Telegrapher process to higher dimensional
stochastic media (), where the particle can move along directions.
We derive the equations for the probability density function using the
``formulae of differentiation'' of Shapiro and Loginov. The model is an
advancement over similiar models of photon migration in multiply scattering
media in that it results in a true diffusion at constant speed in the limit of
large dimensions.Comment: Final corrected version RevTeX, 6 pages, 1 figur
On the refractive index for a nonmagnetic two-component medium: resolution of a controversy
The refractive index of a dielectric medium comprising both passive and
inverted components in its permittivity was determined using two methods: (i)
in the time domain, a finite-difference algorithm to compute the
frequency-domain reflectance from reflection data for a pulsed plane wave that
is normally incident on a dielectric half-space, and (ii) in the frequency
domain, the deflection of an obliquely incident Gaussian beam on transmission
through a dielectric slab. The dielectric medium was found to be an active
medium with a negative real part for its refractive index. Thereby, a recent
controversy in the scientific literature was resolved.Comment: manuscript submitted to Optics Communication
Complete controllability of quantum systems
Sufficient conditions for complete controllability of -level quantum
systems subject to a single control pulse that addresses multiple allowed
transitions concurrently are established. The results are applied in particular
to Morse and harmonic-oscillator systems, as well as some systems with
degenerate energy levels. Morse and harmonic oscillators serve as models for
molecular bonds, and the standard control approach of using a sequence of
frequency-selective pulses to address a single transition at a time is either
not applicable or only of limited utility for such systems.Comment: 8 pages, expanded and revised versio
Near Field Lenses in Two Dimensions
It has been shown that a slab of materials with refractive index = -1 behaves
like a perfect lens focussing all light to an exact electromagnetic copy of an
object. The original lens is limited to producing images the same size as the
object, but here we generalise the concept so that images can be magnified. For
two dimensional systems, over distances much shorter than the free space
wavelength, we apply conformal transformations to the original parallel sided
slab generating a variety of new lenses. Although the new lenses are not
`perfect' they are able to magnify two dimensional objects. The results apply
equally to imaging of electric or magnetic sub wavelength objects in two
dimensions. The concepts have potential applications ranging from microwave
frequencies to the visible.Comment: PDF fil
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