Symbolic algorithms for the Painlevé test, special solutions, and recursion operators for nonlinear PDEs

This paper discusses the algorithms and implementations of three MATHEMATICA packages for the study of integrability and the computation of closed-form solutions of nonlinear polynomial PDEs. The first package, PainleveTest.m, symbolically performs the Painlevé integrability test. The second package, PDESpecialSolutions.m, computes exact solutions expressible in hyperbolic or elliptic functions. The third package, PDERecursionOperator.m, generates and tests recursion operators

Development of large, horizontal-axis wind turbines

A program to develop large, horizontal-axis wind turbines is discussed. The program is directed toward developing the technology for safe, reliable, environmentally acceptable large wind turbines that can generate a significant amount of electricity at costs competitive with those of conventional electricity-generating systems. In addition, these large wind turbines must be fully compatible with electric utility operations and interface requirements. Several ongoing projects in large-wind-turbine development are directed toward meeting the technology requirements for utility applications. The machines based on first-generation technology (Mod-OA and Mod-1) successfully completed their planned periods of experimental operation in June, 1982. The second-generation machines (Mod-2) are in operation at selected utility sites. A third-generation machine (Mod-5) is under contract. Erection and initial operation of the Mod-5 in Hawaii should take place in 1986. Each successive generation of technology increased reliability and energy capture while reducing the cost of electricity. These advances are being made by gaining a better understanding of the system-design drivers, improving the analytical design tools, verifying design methods with operating field data, and incorporating new technology and innovative designs. Information is given on the results from the first- and second-generation machines (Mod-OA, - 1, and -2), the status of the Department of Interior, and the status of the third-generation wind turbine (Mod-5)

Diffraction-limited CCD imaging with faint reference stars

By selecting short exposure images taken using a CCD with negligible readout noise we obtained essentially diffraction-limited 810 nm images of faint objects using nearby reference stars brighter than I=16 at a 2.56 m telescope. The FWHM of the isoplanatic patch for the technique is found to be 50 arcseconds, providing ~20% sky coverage around suitable reference stars.Comment: 4 page letter accepted for publication in Astronomy and Astrophysic

Functional design for operational earth resources ground data processing

The author has identified the following significant results. Study emphasis was on developing a unified concept for the required ground system, capable of handling data from all viable acquisition platforms and sensor groupings envisaged as supporting operational earth survey programs. The platforms considered include both manned and unmanned spacecraft in near earth orbit, and continued use of low and high altitude aircraft. The sensor systems include both imaging and nonimaging devices, operated both passively and actively, from the ultraviolet to the microwave regions of the electromagnetic spectrum

Economic and demographic issues related to deployment of the Satellite Power System (SPS)

Growth in energy consumption stimulated interest in exploitation of renewable sources of electric energy. One technology that was proposed is the Satellite Power System (SPS). Before committing the U.S. to such a large program, the Department of Energy and the National Aeronautics and Space Administration are jointly participating in an SPS Concept Development and Evaluation Program. This white paper on industrial and population relocation is part of the FY 78 preliminary evaluation of related socio-economic issues. Results of four preliminary assessment activities are documented

Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs

Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and PDEs in terms of Jacobi's elliptic functions. For systems with parameters, the algorithms determine the conditions on the parameters so that the differential equations admit polynomial solutions in tanh, sech, combinations thereof, Jacobi's sn or cn functions. Examples illustrate key steps of the algorithms. The new algorithms are implemented in Mathematica. The package DDESpecialSolutions.m can be used to automatically compute new special solutions of nonlinear PDEs. Use of the package, implementation issues, scope, limitations, and future extensions of the software are addressed. A survey is given of related algorithms and symbolic software to compute exact solutions of nonlinear differential equations.Comment: 39 pages. Software available from Willy Hereman's home page at http://www.mines.edu/fs_home/whereman

Self-Consistent Response of a Galactic Disk to an Elliptical Perturbation Halo Potential

We calculate the self-consistent response of an axisymmetric galactic disk perturbed by an elliptical halo potential of harmonic number m = 2, and obtain the net disk ellipticity. Such a potential is commonly expected to arise due to a galactic tidal encounter and also during the galaxy formation process. The self-gravitational potential corresponding to the self-consistent, non-axisymmetric density response of the disk is obtained by inversion of Poisson equation for a thin disk. This response potential is shown to oppose the perturbation potential, because physically the disk self-gravity resists the imposed potential. This results in a reduction in the net ellipticity of the perturbation halo potential in the disk plane. The reduction factor denoting this decrease is independent of the strength of the perturbation potential, and has a typical minimum value of 0.75 - 0.9 for a wide range of galaxy parameters. The reduction is negligible at all radii for higher harmonics (m > or = 3) of the halo potential. (abridged).Comment: 26 pages (LaTex- aastex style), 3 .eps figures. To appear in the Astrophysical Journal, Vol. 542, Oct. 20, 200