8,524 research outputs found
On the Waring--Goldbach problem for eighth and higher powers
Recent progress on Vinogradov's mean value theorem has resulted in improved
estimates for exponential sums of Weyl type. We apply these new estimates to
obtain sharper bounds for the function in the Waring--Goldbach problem.
We obtain new results for all exponents , and in particular establish
that when is large, giving the first improvement
on the classical result of Hua from the 1940s
Conduction mechanism and magnetotransport in multi-walled carbon nanotubes
We report on a numerical study of quantum diffusion over micron lengths in
defect-free multi-walled nanotubes. The intershell coupling allows the electron
spreading over several shells, and when their periodicities along the nanotube
axis are incommensurate, which is likely in real materials, the electronic
propagation is shown to be non ballistic. This results in magnetotransport
properties which are exceptional for a disorder free system, and provides a new
scenario to understand the experiments (A. Bachtold et al. Nature 397, 673
(1999)).Comment: 4 page
Relaxation Scenarios in a Mixture of Large and Small Spheres: Dependence on the Size Disparity
We present a computational investigation on the slow dynamics of a mixture of
large and small soft spheres. By varying the size disparity at a moderate fixed
composition different relaxation scenarios are observed for the small
particles. For small disparity density-density correlators exhibit moderate
stretching. Only small quantitative differences are observed between dynamic
features for large and small particles. On the contrary, large disparity
induces a clear time scale separation between the large and the small
particles. Density-density correlators for the small particles become extremely
stretched, and display logarithmic relaxation by properly tuning the
temperature or the wavevector. Self-correlators decay much faster than
density-density correlators. For very large size disparity, a complete
separation between self- and collective dynamics is observed for the small
particles. Self-correlators decay to zero at temperatures where density-density
correlations are frozen. The dynamic picture obtained by varying the size
disparity resembles features associated to Mode Coupling transition lines of
the types B and A at, respectively, small and very large size disparity. Both
lines might merge, at some intermediate disparity, at a higher-order point, to
which logarithmic relaxation would be associated. This picture resembles
predictions of a recent Mode Coupling Theory for fluids confined in matrixes
with interconnected voids [V. Krakoviack, Phys. Rev. Lett. {\bf 94}, 065703
(2005)].Comment: Journal of Chemical Physics 125, 164507 (2006
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