Integers represented as a sum of primes and powers of two

It is shown that every sufficiently large even integer is a sum of two primes and exactly 13 powers of 2. Under the Generalized Rieman Hypothesis one can replace 13 by 7. Unlike previous work on this problem, the proof avoids numerical calculations with explicit zero-free regions of Dirichlet L-functions. The argument uses a new technique to bound the measure of the set on which the exponential sum formed from powers of 2 is large.Comment: 32 Pages; typos correcte

Nanocrystal seeding: A low temperature route to polycrystalline Si films

A novel method is presented for growth of polycrystalline silicon films on amorphous substrates at temperatures of 540–575 °C. Grain nucleation and grain growth are performed in two steps, using Si nanocrystals as nuclei ("seeds"). The nanocrystal seeds are produced by excimer laser photolysis of disilane in a room temperature flow cell. Film (grain) growth occurs epitaxially on the seeds in a separate thermal chemical vapor deposition (CVD) step, with growth rates 10–100 times higher than similar CVD growth rates on crystal Si. Grain size and CVD growth rates are dependent on seed coverage, for seed coverage <0.2 monolayers

Radioisotope thermionic power supply for spacecraft

Power supply design for unmanned electric propulsion missions to outer planets utilizes a store of curium-244 in compact array of capsules as energy source. Supply subassemblies are: heat source, converter equipment which supplies power, and safety equipment. System is designed for a 72,000 hour mission

Thermionic reactor power system: Effects of radiation on integration with Manned Space Station

The application of a thermionic reactor power system to the modular space station is described. The nominal net power is 40 kWe, with the power system designed to be applicable over the power range from 25 to 60 kWe. The power system is designed to be launched by the space shuttle. Radiation protection is provided by LiH neutron shielding and W gamma shielding in a shaped 4 pion configuration, i.e., the reactor is shielded on all sides but not to equal extent. Isodose contours are presented for the region around the modular space station. Levels and spectral distribution of radiation are given for later evaluation of effects on space station experiments. Parametric data on the effects of separation distance on power system mass are presented

A discontinuous Galerkin method for the Vlasov-Poisson system

A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity of the electron distribution function and weakly enforces continuity of the electric field through mesh interfaces and boundary conditions. The performance of the method is investigated by computing several examples and error estimates associated system's approximation are stated. In particular, computed results are benchmarked against established theoretical results for linear advection and the phenomenon of linear Landau damping for both the Maxwell and Lorentz distributions. Moreover, two nonlinear problems are considered: nonlinear Landau damping and a version of the two-stream instability are computed. For the latter, fine scale details of the resulting long-time BGK-like state are presented. Conservation laws are examined and various comparisons to theory are made. The results obtained demonstrate that the discontinuous Galerkin method is a viable option for integrating the Vlasov-Poisson system.Comment: To appear in Journal for Computational Physics, 2011. 63 pages, 86 figure

Variations in the stratospheric ozone field inferred from Nimbus satellite observations

The ultraviolet earth radiance data from the Backscatter Ultraviolet Experiment on Nimbus 4 have been inverted to infer ozone profiles using a single Rayleigh scattering model. Two methods of solution give essentially the same results. Comparisons of these profiles with simultaneous rocket sounding data shows satisfactory agreement at low and middle latitudes. Vertical cross sections of ozone mixing ratio along the orbital tracks indicate that while the gross characteristics of the ozone field above 10 mb are under photochemical control, the influence of atmospheric motions can be found up to the 4 mb level

Sums and differences of four k-th powers

We prove an upper bound for the number of representations of a positive integer $N$ as the sum of four $k$-th powers of integers of size at most $B$, using a new version of the Determinant method developed by Heath-Brown, along with recent results by Salberger on the density of integral points on affine surfaces. More generally we consider representations by any integral diagonal form. The upper bound has the form $O_{N}(B^{c/\sqrt{k}})$, whereas earlier versions of the Determinant method would produce an exponent for $B$ of order $k^{-1/3}$ in this case. Furthermore, we prove that the number of representations of a positive integer $N$ as a sum of four $k$-th powers of non-negative integers is at most $O_{\epsilon}(N^{1/k+2/k^{3/2}+\epsilon})$ for $k \geq 3$, improving upon bounds by Wisdom.Comment: 18 pages. Mistake corrected in the statement of Theorem 1.2. To appear in Monatsh. Mat