Eigenvalues of the Laplacian of a graph

Let G be a finite undirected graph with no loops or multiple edges. The Laplacian matrix of G, Delta(G), is defined by Delta sub ii = degree of vertex i and Delta sub ij = -1 if there is an edge between vertex i and vertex j. The structure of the graph G is related to the eigenvalues of Delta(G); in particular, it is proved that all the eigenvalues of Delta(G) are nonnegative, less than or equal to the number of vertices, and less than or equal to twice the maximum vertex degree. Precise conditions for equality are given

Methods for the evaluation of alternative disaster warning systems

For each of the methods identified, a theoretical basis is provided and an illustrative example is described. The example includes sufficient realism and detail to enable an analyst to conduct an evaluation of other systems. The methods discussed in the study include equal capability cost analysis, consumers' surplus, and statistical decision theory

Methods for the evaluation of alternative disaster warning systems. Executive summary

Methods for estimating the economic costs and benefits of the transmission-reception and reception-action segments of a disaster warning system (DWS) are described. Methods were identified for the evaluation of the transmission and reception portions of alternative disaster warning systems. Example analyses using the methods identified were performed

Semiclassical charged black holes with a quantized massive scalar field

Semiclassical perturbations to the Reissner-Nordstrom metric caused by the presence of a quantized massive scalar field with arbitrary curvature coupling are found to first order in \epsilon = \hbar/M^2. The DeWitt-Schwinger approximation is used to determine the vacuum stress-energy tensor of the massive scalar field. When the semiclassical perturbation are taken into account, we find extreme black holes will have a charge-to-mass ratio that exceeds unity, as measured at infinity. The effects of the perturbations on the black hole temperature (surface gravity) are studied in detail, with particular emphasis on near extreme ``bare'' states that might become precisely zero temperature ``dressed'' semiclassical black hole states. We find that for minimally or conformally coupled scalar fields there are no zero temperature solutions among the perturbed black holes.Comment: 19 pages; 1 figure; ReVTe

Size Gap for Zero Temperature Black Holes in Semiclassical Gravity

We show that a gap exists in the allowed sizes of all zero temperature static spherically symmetric black holes in semiclassical gravity when only conformally invariant fields are present. The result holds for both charged and uncharged black holes. By size we mean the proper area of the event horizon. The range of sizes that do not occur depends on the numbers and types of quantized fields that are present. We also derive some general properties that both zero and nonzero temperature black holes have in all classical and semiclassical metric theories of gravity.Comment: 4 pages, ReVTeX, no figure

Calculation of AGARD Wing 445.6 Flutter Using Navier-Stokes Aerodynamics

An unsteady, 3D, implicit upwind Euler/Navier-Stokes algorithm is here used to compute the flutter characteristics of Wing 445.6, the AGARD standard aeroelastic configuration for dynamic response, with a view to the discrepancy between Euler characteristics and experimental data. Attention is given to effects of fluid viscosity, structural damping, and number of structural model nodes. The flutter characteristics of the wing are determined using these unsteady generalized aerodynamic forces in a traditional V-g analysis. The V-g analysis indicates that fluid viscosity has a significant effect on the supersonic flutter boundary for this wing

Explicitly correlated trial wave functions in Quantum Monte Carlo calculations of excited states of Be and Be-

We present a new form of explicitly correlated wave function whose parameters are mainly linear, to circumvent the problem of the optimization of a large number of non-linear parameters usually encountered with basis sets of explicitly correlated wave functions. With this trial wave function we succeeded in minimizing the energy instead of the variance of the local energy, as is more common in quantum Monte Carlo methods. We applied this wave function to the calculation of the energies of Be 3P (1s22p2) and Be- 4So (1s22p3) by variational and diffusion Monte Carlo methods. The results compare favorably with those obtained by different types of explicitly correlated trial wave functions already described in the literature. The energies obtained are improved with respect to the best variational ones found in literature, and within one standard deviation from the estimated non-relativistic limitsComment: 19 pages, no figures, submitted to J. Phys.

Semiclassical effects in black hole interiors

First-order semiclassical perturbations to the Schwarzschild black hole geometry are studied within the black hole interior. The source of the perturbations is taken to be the vacuum stress-energy of quantized scalar, spinor, and vector fields, evaluated using analytic approximations developed by Page and others (for massless fields) and the DeWitt-Schwinger approximation (for massive fields). Viewing the interior as an anisotropic collapsing cosmology, we find that minimally or conformally coupled scalar fields, and spinor fields, decrease the anisotropy as the singularity is approached, while vector fields increase the anisotropy. In addition, we find that massless fields of all spins, and massive vector fields, strengthen the singularity, while massive scalar and spinor fields tend to slow the growth of curvature.Comment: 29 pages, ReVTeX; 4 ps figure

The Near-Infrared and Optical Spectra of Methane Dwarfs and Brown Dwarfs

We identify the pressure--broadened red wings of the saturated potassium resonance lines at 7700 \AA as the source of anomalous absorption seen in the near-infrared spectra of Gliese 229B and, by extension, of methane dwarfs in general. This conclusion is supported by the recent work of Tsuji {\it et al.} 1999, though unlike them we find that dust need not be invoked to explain the spectra of methane dwarfs shortward of 1 micron. We find that a combination of enhanced alkali abundances due to rainout and a more realistic non-Lorentzian theory of resonant line shapes may be all that is needed to properly account for these spectra from 0.5 to 1.0 microns. The WFPC2 $I$ measurement of Gliese 229B is also consistent with this theory. Furthermore, a combination of the blue wings of this K I resonance doublet, the red wings of the Na D lines at 5890 \AA, and, perhaps, the Li I line at 6708 \AA can explain in a natural way the observed WFPC2 $R$ band flux of Gliese 229B. Hence, we conclude that the neutral alkali metals play a central role in the near-infrared and optical spectra of methane dwarfs and that their lines have the potential to provide crucial diagnostics of brown dwarfs. We speculate on the systematics of the near-infrared and optical spectra of methane dwarfs, for a given mass and composition, that stems from the progressive burial with decreasing \teff of the alkali metal atoms to larger pressures and depths.Comment: Revised and accepted to Ap.J. volume 531, March 1, 2000, also available at http://jupiter.as.arizona.edu/~burrows/papers/BMS.p

Ferromagnetism in a lattice of Bose condensates

We show that an ensemble of spinor Bose-Einstein condensates confined in a one dimensional optical lattice can undergo a ferromagnetic phase transition and spontaneous magnetization arises due to the magnetic dipole-dipole interaction. This phenomenon is analogous to ferromagnetism in solid state physics, but occurs with bosons instead of fermions.Comment: 4 pages, 2 figure