Numerical Techniques for the Study of Long-Time Correlations

In the study of long-time correlations extremely long orbits must be calculated. This may be accomplished much more reliably using fixed-point arithmetic. Use of this arithmetic on the Cray-1 computer is illustrated.Comment: Plain TeX, 10 pages. Proc. Workshop on Orbital Dynamics and Applications to Accelerators, Lawrence Berkeley Laboratory, Berkeley, California, March 7-12, 198

Temporal Evolution of Lower Hybrid Waves in the Presence of Ponderomotive Density Fluctuations

The propagation of lower hybrid waves in the presence of ponderomotive density fluctuations is considered. The problem is treated in two dimensions and, in order to be able to correctly impose the boundary conditions, the waves are allowed to evolve in time. The fields are described by i v_tau - \int v_xi dzeta + v_{zeta zeta} + |v|^2 v = 0 where v is proportional to the electric field, tau to time, and zeta and xi measure distances across and along the lower hybrid ray. The behavior of the waves is investigated numerically. If the amplitude of the waves is large enough, the spectrum of the waves broadens and their parallel wavelength becomes shorter. The assumptions made in the formulation preclude the application of these results to the lower hybrid heating experiment on Alcator-A. Nevertheless, there are indications that the physics embodied in this problem are responsible for some of the results of that experiment.Comment: Plain TeX, 24 pages, 11 figure

Geodesics on an ellipsoid of revolution

Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems involving geodesics (triangulation, projections, maritime boundaries, and polygonal areas) are investigated.Comment: LaTex, 29 pages, 16 figures. Supplementary material is available at http://geographiclib.sourceforge.net/geod.htm

Symmetric and Antisymmetric Vector-valued Jack Polynomials

Polynomials with values in an irreducible module of the symmetric group can be given the structure of a module for the rational Cherednik algebra, called a standard module. This algebra has one free parameter and is generated by differential-difference ("Dunkl") operators, multiplication by coordinate functions and the group algebra. By specializing Griffeth's (arXiv:0707.0251) results for the G(r,p,n) setting, one obtains norm formulae for symmetric and antisymmetric polynomials in the standard module. Such polynomials of minimum degree have norms which involve hook-lengths and generalize the norm of the alternating polynomial.Comment: 22 pages, added remark about the Gordon-Stafford Theorem, corrected some typo