Coupled Lugiato-Lefever equation for nonlinear frequency comb generation at an avoided crossing of a microresonator

Guided-mode coupling in a microresonator generally manifests itself through avoided crossings of the corresponding resonances. This coupling can strongly modify the resonator local effective dispersion by creating two branches that have dispersions of opposite sign in spectral regions that would otherwise be characterized by either positive (normal) or negative (anomalous) dispersion. In this paper, we study, both analytically and computationally, the general properties of nonlinear frequency comb generation at an avoided crossing using the coupled Lugiato-Lefever equation. In particular, we find that bright solitons and broadband frequency combs can be excited when both branches are pumped for a suitable choice of the pump powers and the detuning parameters. A deterministic path for soliton generation is found.Comment: 9 pages, 5 figure

Treaty Exit in the United States: Insights from the United Kingdom or South Africa?

This essay, a contribution to an AJIL Unbound symposium on “Treaty Exit at the Interface of Domestic and International Law,” compares treaty exit in the United States, the United Kingdom, and South Africa. After examining the longstanding practice of unilateral presidential withdrawals from treaties in the United States and the refusal to date of U.S. courts to review the constitutionality of that practice, the essay summarizes recent judicial decisions in the United Kingdom and South Africa holding that parliamentary approval was required before these nations could withdraw from treaties committing them, respectively, to the European Union and the International Criminal Court. We conclude that these decisions—while important and interesting in their own right—offer limited insights for debates in the United States over whether the President has unilateral treaty withdrawal authority and how such withdrawals might affect statutes implementing international agreements

Some reports of snowfall from fog during the UK winter of 2008/09

Snowfall during anticyclonic, non-frontal, and foggy conditions is surprising. Because it is often not forecast, it can present a hazard to transport and modify the surface albedo. In this report, we present some observations of snowfall during conditions of freezing fog in the UK during the winter of 2008/09

Spatiotemporal Model for Kerr Comb Generation in Whispering Gallery Mode Resonators

We establish an exact partial differential equation to model Kerr comb generation in whispering-gallery mode resonators. This equation is a variant of the Lugiato-Lefever equation that includes higher-order dispersion and nonlinearity. This spatio-temporal model, whose main variable is the total intracavity field, is significantly more suitable than the modal expansion approach for the theoretical understanding and the numerical simulation of wide-span combs. It allows us to explore pulse formation in which a large number of modes interact cooperatively. This versatile approach can be straightforwardly extended to include higher-order dispersion, as well as other phenomena like Raman, Brillouin and Rayleigh scattering. We demonstrate for the first time that when the dispersion is anomalous, Kerr comb generation can arise as the spectral signature of dissipative cavity solitons, leading to wide-span combs with low pumping.Comment: 5 pages, 2 figure

Bonding of reusable surface insulation with low density silicone foams

The development and evaluation of a reduced density, high reliable foamed bond strain isolation system for attaching reusable surface insulation to the space shuttle structure are reported. Included are data on virgin materials as well as on materials that received 100 cycles of exposure to 650 F for approximately 20 minutes per cycle. Room temperature vulcanizing silicon elastomers meet all the requirments for an adhesive bonding system

Differential equations for the cuspoid canonical integrals

Differential equations satisfied by the cuspoid canonical integrals I_n(a) are obtained for arbitrary values of n≥2, where n−1 is the codimension of the singularity and a=(ɑ_1,ɑ_2,...,ɑ_(n−1)). A set of linear coupled ordinary differential equations is derived for each step in the sequence I_n(0,0,...,0,0) →I_n(0,0,...,0,ɑ_(n−1)) →I_n(0,0,...,ɑ_(n−2),ɑ_(n−1)) →...→I_n(0,ɑ_2,...,ɑ_(n−2),ɑ_(n−1)) →I_n(ɑ_1,ɑ_2,...,ɑ_n−2,ɑ_(n−1)). The initial conditions for a given step are obtained from the solutions of the previous step. As examples of the formalism, the differential equations for n=2 (fold), n=3 (cusp), n=4 (swallowtail), and n=5 (butterfly) are given explicitly. In addition, iterative and algebraic methods are described for determining the parameters a that are required in the uniform asymptotic cuspoid approximation for oscillating integrals with many coalescing saddle points. The results in this paper unify and generalize previous researches on the properties of the cuspoid canonical integrals and their partial derivatives

OPTIMAL WATERFOWL HUNTING MANAGEMENT STRATEGIES FOR PRIVATE LANDOWNERS: A MINNESOTA CASE STUDY

A bio-economic model based upon waterfowl population, habitat, and hunting data in the state of Minnesota is used to examine the optimal management strategy of a waterfowl hunting enterprise on privately owned land. Various state sponsored incentive programs are then analyzed for their effect on hunting and waterfowl equilibrium levels, as well as the economic viability of the hunting enterprise. A waterfowl habitat and maintenance cost reimbursement incentive program is found to be the most effective at inducing additional hunting opportunities in Minnesota, while providing economic incentives for private landowners to actively manage their land.hunting enterprise, sustainable harvest, waterfowl, Resource /Energy Economics and Policy,