Large-scale computation of pseudospectra using ARPACK and eigs

ARPACK and its MATLAB counterpart, eigs, are software packages that calculate some eigenvalues of a large non-symmetric matrix by Arnoldi iteration with implicit restarts. We show that at a small additional cost, which diminishes relatively as the matrix dimension increases, good estimates of pseudospectra in addition to eigenvalues can be obtained as a by-product. Thus in large-scale eigenvalue calculations it is feasible to obtain routinely not just eigenvalue approximations, but also information as to whether or not the eigenvalues are likely to be physically significant. Examples are presented for matrices with dimension up to 200,000

Effect of reactor coolant radioactivity upon configuration feasibility for a nuclear electric propulsion vehicle

A preliminary shielding analysis was carried out for a conceptual nuclear electric propulsion vehicle designed to transport payloads from low earth orbit to synchronous orbit. The vehicle employed a thermionic nuclear reactor operating at 1575 kilowatts and generated 120 kilowatts of electricity for a round-trip mission time of 2000 hours. Propulsion was via axially directed ion engines employing 3300 pounds of mercury as a propellant. The vehicle configuration permitted a reactor shadow shield geometry using LiH and the mercury propellant for shielding. However, much of the radioactive NaK reactor coolant was unshielded and in close proximity to the power conditioning electronics. An estimate of the radioactivity of the NaK coolant was made and its unshielded dose rate to the power conditioning equipment calculated. It was found that the activated NaK contributed about three-fourths of the gamma dose constraint. The NaK dose was considered a sufficiently high fraction of the allowable gamma dose to necessitate modifications in configuration

Evidence for extended IR emission in NGC2798 and NGC6240

Extended emission at 10 and 20 microns can be used to distinguish starbursts from monsters as the underlying energy source driving the luminous infrared emission in the central regions of galaxies. The spatial extent of the mid infrared emission in the interacting galaxy NCG 2798 and the merger NGC 6240 were investigated. The 10 and 20 micron profiles of the IR source in NGC 2798 are significantly wider than beam profiles measured on a standard star, supporting a starburst interpretation of its IR luminosity. For NGC 6240 there is marginal evidence for an extended 10 micron source, suggesting that a significant fraction of its IR luminosity could be produced by a burst of star formation

Computing Lyapunov constants for random recurrences with smooth coefficients

In recent years, there has been much interest in the growth and decay rates (Lyapunov constants) of solutions to random recurrences such as the random Fibonacci sequence $x_{n+1} = \pm x_{n} \pm x_{n-1}$. Many of these problems involve non-smooth dynamics (nondifferentiable invariant measures), making computations hard. Here, however, we consider recurrences with smooth random coefficients and smooth invariant measures. By computing discretised invariant measures and applying Richardson extrapolation, we can compute Lyapunov constants to ten digits of accuracy. In particular, solutions to the recurrence $x_{n+1} = x_{n} + c_{n+1} x_{n-1}$, where the $\{c_{n}\}$ are independent standard normal variables, increase exponentially (almost surely) at the asymptotic rate $(1.0574735537...)^{n}$. Solutions to the related recurrences $x_{n+1} = c_{n+1}x_{n} + x_{n-1}$, and $x_{n+1} = c_{n+1}x_{n} + d_{n+1}x_{n-1}$ (where the $\{d_{n}\}$ are also independent standard normal variables) increase (decrease) at the rates $(1.1149200917...)^{n}$ and $(0.9949018837...)^(n)$ respectively

Eigenvalues and Pseudospectra of Rectangular Matrices

Pseudospectra of rectangular matrices vary continuously with the matrix entries, a feature that eigenvalues of rectangular matrices do not have. Some properties of eigenvalues and pseudospectra of rectangular matrices are explored, and an efficient algorithm for the computation of pseudospectra is given. Applications are given in (square) eigenvalue computation (Lanczos and Arnoldi iteration), square pseudospectra approximation, control theory (nearest uncontrollable system) and game theory

High-Tip-Speed, Low-Loading Transonic Fan Stage. Part 1: Aerodynamic and Mechanical Design

A high-tip-speed, low-loading transonic fan stage was designed to deliver an overall pressure ratio of 1.5 with an adiabatic efficiency of 86 percent. The design flow per unit annulus area is 42.0 pounds per square foot. The fan features a hub/tip ratio of 0.46, a tip diameter of 28.74 in. and operates at a design tip speed of 1600 fps. For these design conditions, the rotor blade tip region operates with supersonic inlet and supersonic discharge relative velocities. A sophisticated quasi-three-dimensional characteristic section design procedure was used for the all-supersonic sections and the inlet of the midspan transonic sections. For regions where the relative outlet velocities are supersonic, the blade operates with weak oblique shocks only

Optical photometric GTC/OSIRIS observations of the young massive association Cygnus OB2

In order to fully understand the gravitational collapse of molecular clouds, the star formation process and the evolution of circumstellar disks, these phenomena must be studied in different Galactic environments with a range of stellar contents and positions in the Galaxy. The young massive association Cygnus OB2, in the Cygnus-X region, is an unique target to study how star formation and the evolution of circumstellar disks proceed in the presence of a large number of massive stars. We present a catalog obtained with recent optical observations in r,i,z filters with OSIRIS, mounted on the $10.4\,m$ GTC telescope, which is the deepest optical catalog of Cyg OB2 to date. The catalog consist of 64157 sources down to M=0.15 solar masses at the adopted distance and age of Cyg OB2. A total of 38300 sources have good photometry in all three bands. We combined the optical catalog with existing X-ray data of this region, in order to define the cluster locus in the optical diagrams. The cluster locus in the r-i vs. i-z diagram is compatible with an extinction of the optically selected cluster members in the 2.64<AV<5.57 range. We derive an extinction map of the region, finding a median value of AV=4.33 in the center of the association, decreasing toward the north-west. In the color-magnitude diagrams, the shape of the distribution of main sequence stars is compatible with the presence of an obscuring cloud in the foreground at about 850+/-25 pc from the Sun.Comment: Accepted for publication ApJS 201