17,019 research outputs found
Programming of inhomogeneous resonant guided wave networks
Photonic functions are programmed by designing the interference of local waves in inhomogeneous resonant guided wave networks composed of power-splitting elements arranged at the nodes of a nonuniform waveguide network. Using a compact, yet comprehensive, scattering matrix representation of the network, the desired photonic function is designed by fitting structural parameters according to an optimization procedure. This design scheme is demonstrated for plasmonic dichroic and trichroic routers in the infrared frequency range
The Effect of Magnetic Field Tilt and Divergence on the Mass Flux and Flow Speed in a Line-Driven Stellar Wind
We carry out an extended analytic study of how the tilt and
faster-than-radial expansion from a magnetic field affect the mass flux and
flow speed of a line-driven stellar wind. A key motivation is to reconcile
results of numerical MHD simulations with previous analyses that had predicted
non-spherical expansion would lead to a strong speed enhancement. By including
finite-disk correction effects, a dynamically more consistent form for the
non-spherical expansion, and a moderate value of the line-driving power index
, we infer more modest speed enhancements that are in good quantitative
agreement with MHD simulations, and also are more consistent with observational
results. Our analysis also explains simulation results that show the
latitudinal variation of the surface mass flux scales with the square of the
cosine of the local tilt angle between the magnetic field and the radial
direction. Finally, we present a perturbation analysis of the effects of a
finite gas pressure on the wind mass loss rate and flow speed in both spherical
and magnetic wind models, showing that these scale with the ratio of the sound
speed to surface escape speed, , and are typically 10-20% compared
to an idealized, zero-gas-pressure model.Comment: Accepted for publication in ApJ, for the full version of the paper go
to: http://www.bartol.udel.edu/~owocki/preprints/btiltdiv-mdotvinf.pd
Antichain cutsets of strongly connected posets
Rival and Zaguia showed that the antichain cutsets of a finite Boolean
lattice are exactly the level sets. We show that a similar characterization of
antichain cutsets holds for any strongly connected poset of locally finite
height. As a corollary, we get such a characterization for semimodular
lattices, supersolvable lattices, Bruhat orders, locally shellable lattices,
and many more. We also consider a generalization to strongly connected
hypergraphs having finite edges.Comment: 12 pages; v2 contains minor fixes for publicatio
Some Combinatorial Properties of Hook Lengths, Contents, and Parts of Partitions
This paper proves a generalization of a conjecture of Guoniu Han, inspired
originally by an identity of Nekrasov and Okounkov. The main result states that
certain sums over partitions p of n, involving symmetric functions of the
squares of the hook lengths of p, are polynomial functions of n. A similar
result is obtained for symmetric functions of the contents and shifted parts of
n.Comment: 20 pages. Correction of some inaccuracies, and a new Theorem 4.
A density functional theory for general hard-core lattice gases
We put forward a general procedure to obtain an approximate free energy
density functional for any hard-core lattice gas, regardless of the shape of
the particles, the underlying lattice or the dimension of the system. The
procedure is conceptually very simple and recovers effortlessly previous
results for some particular systems. Also, the obtained density functionals
belong to the class of fundamental measure functionals and, therefore, are
always consistent through dimensional reduction. We discuss possible extensions
of this method to account for attractive lattice models.Comment: 4 pages, 1 eps figure, uses RevTeX
Negative refractive index in coaxial plasmon waveguides
We theoretically show that coaxial waveguides composed of a metallic core, surrounded by a dielectric cylinder and clad by a metal outer layer exhibit negative refractive index modes over a broad spectral range in the visible. For narrow dielectric gaps (10 nm GaP embedded in Ag) a figure-of-merit of 18 can be achieved at λ_0 = 460 nm. For larger dielectric gaps the negative index spectral range extends well below the surface plasmon resonance frequency. By fine-tuning the coaxial geometry the special case of n = −1 at a figure-of-merit of 5, or n = 0 for a decay length of 500 nm can be achieved
Three osculating walkers
We consider three directed walkers on the square lattice, which move
simultaneously at each tick of a clock and never cross. Their trajectories form
a non-crossing configuration of walks. This configuration is said to be
osculating if the walkers never share an edge, and vicious (or:
non-intersecting) if they never meet. We give a closed form expression for the
generating function of osculating configurations starting from prescribed
points. This generating function turns out to be algebraic. We also relate the
enumeration of osculating configurations with prescribed starting and ending
points to the (better understood) enumeration of non-intersecting
configurations. Our method is based on a step by step decomposition of
osculating configurations, and on the solution of the functional equation
provided by this decomposition
Scaling behavior in economics: I. Empirical results for company growth
We address the question of the growth of firm size. To this end, we analyze
the Compustat data base comprising all publicly-traded United States
manufacturing firms within the years 1974-1993. We find that the distribution
of firm sizes remains stable for the 20 years we study, i.e., the mean value
and standard deviation remain approximately constant. We study the distribution
of sizes of the ``new'' companies in each year and find it to be well
approximated by a log-normal. We find (i) the distribution of the logarithm of
the growth rates, for a fixed growth period of one year, and for companies with
approximately the same size displays an exponential form, and (ii) the
fluctuations in the growth rates -- measured by the width of this distribution
-- scale as a power law with , . We find
that the exponent takes the same value, within the error bars, for
several measures of the size of a company. In particular, we obtain:
for sales, for number of employees,
for assets, for cost of goods sold, and
for property, plant, & equipment.Comment: 16 pages LateX, RevTeX 3, 10 figures, to appear J. Phys. I France
(April 1997
Plasmon Dispersion in Coaxial Waveguides from Single-Cavity Optical Transmission Measurements
We determine the plasmon dispersion relation in coaxial waveguides composed of a circular channel separating a metallic core and cladding. Optical transmission measurements are performed on isolated coaxial nanoapertures fabricated on a Ag film using focused ion-beam lithography. The dispersion depends strongly on the dielectric material and layer thickness. Our experimental results agree well with an analytical model for plasmon dispersion in coaxial waveguides. We observe large phase shifts at reflection from the end facets of the coaxial cavity, which strongly affect the waveguide resonances and can be tuned by changing the coax geometry, composition, and surrounding dielectric index, enabling coaxial cavities with ultrasmall mode volumes
- …