21,173 research outputs found
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
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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 as the sum of four -th powers of integers of size at most ,
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 , whereas earlier
versions of the Determinant method would produce an exponent for of order
in this case. Furthermore, we prove that the number of
representations of a positive integer as a sum of four -th powers of
non-negative integers is at most for
, improving upon bounds by Wisdom.Comment: 18 pages. Mistake corrected in the statement of Theorem 1.2. To
appear in Monatsh. Mat
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