Gauge-invariant Formulation of the Second-order Cosmological Perturbations

Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the Einstein equations in the case where the first order vector and tensor modes are negligible. These equations imply that the tensor and the vector mode of the second order metric perturbations may be generated by the scalar-scalar mode coupling of the linear order perturbations as the result of the non-linear effects of the Einstein equations.Comment: 5 pages, no figure. RevTeX; short letter version of gr-qc/0605108; some details of explanations are adde

Automatic holographic droplet analysis for liquid fuel sprays

The basic scheme for automated holographic analysis involves an optical system for reconstruction of the three dimensional real image of the droplet field, a spatial scanning system to transport a digitizing X-y image sensor through the real image, and processing algorithms for droplet recognition which establish the droplet sizes and positions. The hardware for system demonstrated includes the expanded and collimated beam from a 5 mW helium-neon laser for hologram reconstruction, an imaging lens for magnification of the real image field, and a video camera and digitizer providing 512-by-512 pixel resolution with 8-bit digitization. A mechanical stage is used to scan the hologram in three dimensional space, maintaining constant image magnification. A test droplet hologram is used for development and testing of the image processing algorithms

Multivariate Diophantine equations with many solutions

We show that for each n-tuple of positive rational integers (a_1,..,a_n) there are sets of primes S of arbitrarily large cardinality s such that the solutions of the equation a_1x_1+...+a_nx_n=1 with the x_i all S-units are not contained in fewer than exp((4+o(1))s^{1/2}(log s)^{-1/2}) proper linear subspaces of C^n. This generalizes a result of Erdos, Stewart and Tijdeman for m=2 [Compositio 36 (1988), 37-56]. Furthermore we prove that for any algebraic number field K of degree n, any integer m with 1<=m<n, and any sufficiently large s there are integers b_0,...,b_m in a number field which are linearly independent over the rationals, and prime numbers p_1,...,p_s, such that the norm polynomial equation |N_{K/Q}(b_0+b_1x_1+...+b_mx_m)|=p_1^{z_1}...p_s^{z_s} has at least exp{(1+o(1)){n/m}s^{m/n}(log s)^{-1+m/n}) solutions in integers x_1,..,x_m,z_1,..,z_s. This generalizes a result of Moree and Stewart [Indag. Math. 1 (1990), 465-472]. Our main tool, also established in this paper, is an effective lower bound for the number of ideals in a number field K of norm <=X composed of prime ideals which lie outside a given finite set of prime ideals T and which have norm <=Y. This generalizes a result of Canfield, Erdos and Pomerance [J. Number Th. 17 (1983), 1-28], and of Moree and Stewart (see above).Comment: 29 page

The Costs of Wrongful-Discharge Laws

We estimate the effects on employment and wages of wrongful-discharge protections in the United States. Over the last three decades, most U.S. state courts have adopted one or more common law wrongful discharge doctrines that limit employers' discretion to terminate workers at-will. Using this cross-state variation with a difference-in-difference framework, we find robust evidence of a modest negative impact ( 0.8 to 1.6 percentage points) of one wrongful-discharge doctrine, the implied-contract exception, on employment to population rates in state labor markets. The short-term impact is most pronounced for female, younger, and less-skilled workers, while the longer term costs appear to be borne by older and more-educated workers those most likely to litigate under this doctrine. We find no robust employment or wage effects of two other widely recognized wrongful-discharge laws: the public -policy and good-faith exceptions. Published findings in the literature range from no effect to very large negative effects. We reanalyze the two leading studies and find the discrepancies can be explained by methodological shortcomings in the one case and limitations in the coding of key court decisions in the other.

A review of NASA's propulsion programs for aviation

A review of five NASA engine-oriented propulsion programs of major importance to civil aviation are presented and discussed. Included are programs directed at exploring propulsion system concepts for (1) energy conservation subsonic aircraft (improved current turbofans, advanced turbofans, and advanced turboprops); (2) supersonic cruise aircraft (variable cycle engines); (3) general aviation aircraft (improved reciprocating engines and small gas turbines); (4) powered lift aircraft (advanced turbofans); and (5) advanced rotorcraft

The Marysville, Montana Geothermal Project

Drilling the first geothermal well in Montana presented many challenges, not only in securing materials and planning strategies for drilling the wildcat well but also in addressing the environmental, legal, and institutional issues raised by the request for permission to explore a resource which lacked legal definition. The Marysville Geothermal Project was to investigate a dry hot rock heat anomaly. The well was drilled to a total depth of 6790 feet and many fractured water bearing zones were encountered below 1800 feet

INITIAL WEIGHT LOSS OF PLASTICS IN A VACUUM AT TEMPERATURES FROM 80 DEG TO 500 DEG F

Initial weight loss of plastics in a vacuu

Specific Heat of Ce(1-x)La(x)RhIn(5) in Zero and Applied Magnetic Field: A Very Rich Phase Diagram

Specific heat and magnetization results as a function of field on single- and poly-crystalline samples of Ce(1-x)La(x)RhIn(5) show 1.) a specific heat gamma of about 100 mJ/moleK^2 (in agreement with recent dHvA results of Alvers et al.); 2.) upturns at low temperatures in C/T and chi that fit a power law behavior ( Griffiths phase non-Fermi liquid behavior); 3.) a field induced anomaly in C/T as well as M vs H behavior in good agreement with the recent Griffiths phase theory of Castro Neto and Jones, where M~H at low field, M ~ H^lambda above a crossover field, C/T ~ T^(-1+lambda) at low field, and C/T ~ (H^(2+lambda/2)/T^(3-lambda/2))*exp(-mu(eff)H/T) above the same crossover field as determined in the magnetization and where lambda is independently determined from the temperature dependence of chi at low temperatures, chi ~ T^(-1+lambda) and low fields.Comment: 13 pages, 9 figures, to be published in Physical Review

Exact diagonalization of the S=1/2 Heisenberg antiferromagnet on finite bcc lattices to estimate properties on the infinite lattice

Here we generate finite bipartite body-centred cubic lattices up to 32 vertices. We have studied the spin one half Heisenberg antiferromagnet by diagonalizing its Hamiltonian on each of the finite lattices and hence computing its ground state properties. By extrapolation of these data we obtain estimates of the T = 0 properties on the infinite bcc lattice. Our estimate of the T = 0 energy agrees to five parts in ten thousand with third order spin wave and series expansion method estimates, while our estimate of the staggered magnetization agrees with the spin wave estimate to within a quarter of one percent.Comment: 16 pages, LaTeX, 1 ps figure, to appear in J.Phys.