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 $\alpha$, 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, $a/v_{esc}$, 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: II. Modeling of company growth

In the preceding paper we presented empirical results describing the growth of publicly-traded United States manufacturing firms within the years 1974--1993. Our results suggest that the data can be described by a scaling approach. Here, we propose models that may lead to some insight into these phenomena. First, we study a model in which the growth rate of a company is affected by a tendency to retain an ``optimal'' size. That model leads to an exponential distribution of the logarithm of the growth rate in agreement with the empirical results. Then, we study a hierarchical tree-like model of a company that enables us to relate the two parameters of the model to the exponent $\beta$, which describes the dependence of the standard deviation of the distribution of growth rates on size. We find that $\beta = -\ln \Pi / \ln z$, where $z$ defines the mean branching ratio of the hierarchical tree and $\Pi$ is the probability that the lower levels follow the policy of higher levels in the hierarchy. We also study the distribution of growth rates of this hierarchical model. We find that the distribution is consistent with the exponential form found empirically.Comment: 19 pages LateX, RevTeX 3, 6 figures, to appear J. Phys. I France (April 1997

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 $S$ displays an exponential form, and (ii) the fluctuations in the growth rates -- measured by the width of this distribution $\sigma_1$ -- scale as a power law with $S$, $\sigma_1\sim S^{-\beta}$. We find that the exponent $\beta$ takes the same value, within the error bars, for several measures of the size of a company. In particular, we obtain: $\beta=0.20\pm0.03$ for sales, $\beta=0.18\pm0.03$ for number of employees, $\beta=0.18\pm0.03$ for assets, $\beta=0.18\pm0.03$ for cost of goods sold, and $\beta=0.20\pm0.03$ for property, plant, & equipment.Comment: 16 pages LateX, RevTeX 3, 10 figures, to appear J. Phys. I France (April 1997