Solutions of Penrose's Equation

The computational use of Killing potentials which satisfy Penrose's equation is discussed. Penrose's equation is presented as a conformal Killing-Yano equation and the class of possible solutions is analyzed. It is shown that solutions exist in spacetimes of Petrov type O, D or N. In the particular case of the Kerr background, it is shown that there can be no Killing potential for the axial Killing vector.Comment: To appear in J. Math. Phy

Orthogonal, solenoidal, three-dimensional vector fields for no-slip boundary conditions

Viscous fluid dynamical calculations require no-slip boundary conditions. Numerical calculations of turbulence, as well as theoretical turbulence closure techniques, often depend upon a spectral decomposition of the flow fields. However, such calculations have been limited to two-dimensional situations. Here we present a method that yields orthogonal decompositions of incompressible, three-dimensional flow fields and apply it to periodic cylindrical and spherical no-slip boundaries.Comment: 16 pages, 2 three-part figure

Assessing access of galactic cosmic rays at Moon\u27s orbit

[1] Characterizing the lunar radiation environment is essential for preparing future robotic and human explorations on lunar bases. Galactic cosmic rays (GCR) represent one source of ionizing radiation at the Moon that poses a biological risk. Because GCR are charged particles, their paths are affected by the magnetic fields along their trajectories. Unlike the Earth, the Moon has no strong, shielding magnetic field of its own. However, as it orbits Earth, the Moon traverses not only the weak interplanetary magnetic field but also the distant magnetic tail of Earth\u27s magnetosphere. We combine an empirical magnetic field model of Earth\u27s magnetosphere with a fully-relativistic charged particle trajectory code to model and assess the access of GCR at the Moon\u27s orbit. We follow protons with energies of 1, 10 and 100 MeV starting from an isotropic distribution at large distances outside a volume of space including Earth\u27s magnetosphere and the lunar orbit. The simulation result shows that Earth\u27s magnetosphere does not measurably modify protons of energy greater than 1 MeV at distances outside the geomagnetic cutoff imposed by Earth\u27s strong dipole field very near to the planet. Therefore, in contrast to Winglee and Harnett (2007), we conclude that Earth\u27s magnetosphere does not provide any substantial magnetic shielding at the Moon\u27s orbit. These simulation results will be compared to LRO/CRaTER data after its planned launch in June 2009

Getting grants

Attracting financial support is a critical element of success in science, but we have entered a time of cost constraint with little hope of relief coming soon. For principal investigators, developing a broad base of research support is a valuable strategy for attaining financial stability for the laboratory. New investigators working on problems related to virulence and just beginning to build their careers and laboratories must attain NIH funding. But they should also look beyond that agency to the other federal organizations, state and regional agencies, and non-profits that support research. This review will discuss the general principles of how to understand funders, their intentions, and their funding programs. An investigator who grasps what drives the funders will be better able to write fundable proposals

Magnetohydrodynamic activity inside a sphere

We present a computational method to solve the magnetohydrodynamic equations in spherical geometry. The technique is fully nonlinear and wholly spectral, and uses an expansion basis that is adapted to the geometry: Chandrasekhar-Kendall vector eigenfunctions of the curl. The resulting lower spatial resolution is somewhat offset by being able to build all the boundary conditions into each of the orthogonal expansion functions and by the disappearance of any difficulties caused by singularities at the center of the sphere. The results reported here are for mechanically and magnetically isolated spheres, although different boundary conditions could be studied by adapting the same method. The intent is to be able to study the nonlinear dynamical evolution of those aspects that are peculiar to the spherical geometry at only moderate Reynolds numbers. The code is parallelized, and will preserve to high accuracy the ideal magnetohydrodynamic (MHD) invariants of the system (global energy, magnetic helicity, cross helicity). Examples of results for selective decay and mechanically-driven dynamo simulations are discussed. In the dynamo cases, spontaneous flips of the dipole orientation are observed.Comment: 15 pages, 19 figures. Improved figures, in press in Physics of Fluid