Pieri's Formula for Generalized Schur Polynomials

Young's lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young tableaux. We define a generalization of Schur polynomials as expansion coefficients of generalized Schur operators. We show that the commutating relation of generalized Schur operators implies Pieri's formula to generalized Schur polynomials

Secondary pattern computation of an arbitrarily shaped main reflector

The secondary pattern of a perfectly conducting offset main reflector being illuminated by a point feed at an arbitrary location was studied. The method of analysis is based upon the application of the Fast Fourier Transform (FFT) to the aperture fields obtained using geometrical optics (GO) and geometrical theory of diffraction (GTD). Key features of the reflector surface is completely arbitrary, the incident field from the feed is most general with arbitrary polarization and location, and the edge diffraction is calculated by either UAT or by UTD. Comparison of this technique for an offset parabolic reflector with the Jacobi-Bessel and Fourier-Bessel techniques shows good agreement. Near field, far field, and scan data of a large reflector are presented

Early time dynamics of laser-ablated silicon using ultrafast grazing incidence X-ray scattering

Controlling the morphology of laser-derived nanomaterials is dependent on developing a better understanding of the particle nucleation dynamics in the ablation plume. Here, we utilize the femtosecond-length pulses from an x-ray free electron laser to perform time-resolved grazing incidence x-ray scattering measurements on a laser-produced silicon plasma plume. At 20 ps we observe a dramatic increase in the scattering amplitude at small scattering vectors, which we attribute to incipient formation of liquid silicon droplets. These results demonstrate the utility of XFELs as a tool for characterizing the formation dynamics of nanomaterials in laser-produced plasma plumes on ultrafast timescales

Compensation of relector antenna surface distortion using an array feed

The dimensional stability of the surface of a large reflector antenna is important when high gain or low sidelobe performance is desired. If the surface is distorted due to thermal or structural reasons, antenna performance can be improved through the use of an array feed. The design of the array feed and its relation to the surface distortion are examined. The sensitivity of antenna performance to changing surface parameters for fixed feed array geometries is also studied. This allows determination of the limits of usefulness for feed array compensation

Schubert Polynomials for the affine Grassmannian of the symplectic group

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and Q-functions. An explicit combinatorial description is obtained for the Schubert basis of the cohomology of Gr, and this is extended to a definition of the affine type C Stanley symmetric functions. A homology Pieri rule is also given for the product of a special Schubert class with an arbitrary one.Comment: 45 page

Implementing Unitarity in Perturbation Theory

Unitarity cannot be perserved order by order in ordinary perturbation theory because the constraint UU^\dagger=\1 is nonlinear. However, the corresponding constraint for $K=\ln U$, being $K=-K^\dagger$, is linear so it can be maintained in every order in a perturbative expansion of $K$. The perturbative expansion of $K$ may be considered as a non-abelian generalization of the linked-cluster expansion in probability theory and in statistical mechanics, and possesses similar advantages resulting from separating the short-range correlations from long-range effects. This point is illustrated in two QCD examples, in which delicate cancellations encountered in summing Feynman diagrams of are avoided when they are calculated via the perturbative expansion of $K$. Applications to other problems are briefly discussed.Comment: to appear in Phys. Rev.

Near-field spillover from a subreflector: Theory and experiment

In a dual reflector antenna, the spillover from the subreflector is important in determining the accuracy of near-field measurements. This is especially so when some of the feed elements are placed far away from the focus. A high-frequency GTD analysis of the spillover field over a plane just behind the subreflector is presented. Special attention is given to the field near the incident shadow boundary and the role played by the slope diffraction term. Computations are in excellent agreement with experimental results