Distributional Energy-Momentum Densities of Schwarzschild Space-Time

For Schwarzschild space-time, distributional expressions of energy-momentum densities and of scalar concomitants of the curvature tensors are examined for a class of coordinate systems which includes those of the Schwarzschild and of Kerr-Schild types as special cases. The energy-momentum density $\tilde T_\mu^{\nu}(x)$ of the gravitational source and the gravitational energy-momentum pseudo-tensor density $\tilde t_\mu^{\nu}$ have the expressions $\tilde T_\mu^{\nu}(x) =-Mc^2\delta_\mu^0\delta_0^{\nu} \delta^{(3)}x)$ and $\tilde t_\mu^{\nu}=0$, respectively. In expressions of the curvature squares for this class of coordinate systems, there are terms like $\delta^{(3)}(x)/r^3$ and [\delta^{(3)}(x)}]^2, as well as other terms, which are singular at $x=0$. It is pointed out that the well-known expression $R^{\rho\sigma\mu\nu}({}) R_{\rho\sigma\mu\nu}({})$ $=48G^{2}M^{2}/c^{4}r^{6}$ is not correct, if we define $1/r^6 = \lim_{\epsilon\to 0}1/(r^2+\epsilon^2)^3$.}Comment: 21 pages, LaTeX, uses amssymb.sty. To appear in Prog. Theor. Phys. 98 (1997

An Isotopic analysis of the hydrology and riparian vegetation water sources on Bishop Creek

Five power generation plants along an eleven kilometer stretch divert Bishop Creek water for hydro-electric power. Stream diversion may be adversely affecting the riparian vegetation. Stable isotopic analysis is employed to determine surface water/ground-water interactions along the creek. surface water originates primarily from three headwater lakes. Discharge into Bishop Creek below the headwaters is primarily derived from ground water. The average δD and δ18O values are significantly different for surface water and ground water that an isotopic analysis can delineate between these two components of flow. Therefore isotopic shifts along the creek can determine gaining reaches. In addition, by knowing the isotopic signatures of various waters in the watershed, it may be possible to examine tree waters to determine their water source(s)

The Final Count Down: A Review of Three Decades of Flight Controller Training Methods for Space Shuttle Mission Operations

Operations of human spaceflight systems is extremely complex; therefore, the training and certification of operations personnel is a critical piece of ensuring mission success. Mission Control Center (MCC-H), at the Lyndon B. Johnson Space Center in Houston, Texas, manages mission operations for the Space Shuttle Program, including the training and certification of the astronauts and flight control teams. An overview of a flight control team s makeup and responsibilities during a flight, and details on how those teams are trained and certified, reveals that while the training methodology for developing flight controllers has evolved significantly over the last thirty years the core goals and competencies have remained the same. In addition, the facilities and tools used in the control center have evolved. Changes in methodology and tools have been driven by many factors, including lessons learned, technology, shuttle accidents, shifts in risk posture, and generational differences. Flight controllers share their experiences in training and operating the space shuttle. The primary training method throughout the program has been mission simulations of the orbit, ascent, and entry phases, to truly train like you fly. A review of lessons learned from flight controller training suggests how they could be applied to future human spaceflight endeavors, including missions to the moon or to Mars. The lessons learned from operating the space shuttle for over thirty years will help the space industry build the next human transport space vehicle

Electromagnetic form factor via Bethe-Salpeter amplitude in Minkowski space

For a relativistic system of two scalar particles, we find the Bethe-Salpeter amplitude in Minkowski space and use it to compute the electromagnetic form factor. The comparison with Euclidean space calculation shows that the Wick rotation in the form factor integral induces errors which increase with the momentum transfer Q^2. At JLab domain (Q^2=10 GeV^2/c^2), they are about 30%. Static approximation results in an additional and more significant error. On the contrary, the form factor calculated in light-front dynamics is almost indistinguishable from the Minkowski space one.Comment: 8 pages, 7 figures, to be published in Eur. Phys. J. A; Reference [15] is adde