A Combinatorial Formula for Macdonald Polynomials

We prove a combinatorial formula for the Macdonald polynomial H_mu(x;q,t) which had been conjectured by the first author. Corollaries to our main theorem include the expansion of H_mu(x;q,t) in terms of LLT polynomials, a new proof of the charge formula of Lascoux and Schutzenberger for Hall-Littlewood polynomials, a new proof of Knop and Sahi's combinatorial formula for Jack polynomials as well as a lifting of their formula to integral form Macdonald polynomials, and a new combinatorial rule for the Kostka-Macdonald coefficients K_{lambda,mu}(q,t) in the case that mu is a partition with parts less than or equal to 2.Comment: 29 page

A practical low-boom overpressure signature based on minimum sonic boom theory

A brief resume of sonic boom minimization methods is given to provide a background for a new, empirical modification of the Seebass and George minimum-nose-shock sonic boom F-function and signature. The new 'hybrid' F-function has all the inherent flexibility of application found with the Darden-modified Seebass and George F-function. In addition, it has enhanced this flexibility and applicability with neglegible increase in nose and/or tail shock strength. A description of this 'hybrid' F-function and signature is provided, and the benefits of using them to design high-performance, low-boom aircraft are discussed

Analysis of sonic boom measurements near shock wave extremities for flight near Mach 1.0 and for airplane accelerations

The analysis of the 14 low-altitude transonic flights showed that the prevailing meteorological consideration of the acoustic disturbances below the cutoff altitude during threshold Mach number flight has shown that a theoretical safe altitude appears to be valid over a wide range of meteorological conditions and provides a reasonable estimate of the airplane ground speed reduction to avoid sonic boom noise during threshold Mach number flight. Recent theoretical results for the acoustic pressure waves below the threshold Mach number caustic showed excellent agreement with observations near the caustic, but the predicted overpressure levels were significantly lower than those observed far from the caustic. The analysis of caustics produced by inadvertent low-magnitude accelerations during flight at Mach numbers slightly greater than the threshold Mach number showed that folds and associated caustics were produced by slight changes in the airplane ground speed. These caustic intensities ranged from 1 to 3 time the nominal steady, level flight intensity

Ultrafast Plasmonic Control of Second Harmonic Generation

Efficient frequency conversion techniques are crucial to the development of plasmonic metasurfaces for information processing and signal modulation. In principle, nanoscale electric-field confinement in nonlinear materials enables higher harmonic conversion efficiencies per unit volume than those attainable in bulk materials. Here we demonstrate efficient second-harmonic generation (SHG) in a serrated nanogap plasmonic geometry that generates steep electric field gradients on a dielectric metasurface. An ultrafast pump is used to control plasmon-induced electric fields in a thin-film material with inversion symmetry that, without plasmonic enhancement, does not exhibit an an even-order nonlinear optical response. The temporal evolution of the plasmonic near-field is characterized with ~100as resolution using a novel nonlinear interferometric technique. The ability to manipulate nonlinear signals in a metamaterial geometry as demonstrated here is indispensable both to understanding the ultrafast nonlinear response of nanoscale materials, and to producing active, optically reconfigurable plasmonic device