5,635 research outputs found
Diophantine approximation by conjugate algebraic integers
Building on work of Davenport and Schmidt, we mainly prove two results. The
first one is a version of Gel'fond's transcendence criterion which provides a
sufficient condition for a complex or -adic number to be algebraic in
terms of the existence of polynomials of bounded degree taking small values at
together with most of their derivatives. The second one, which follows
from this criterion by an argument of duality, is a result of simultaneous
approximation by conjugate algebraic integers for a fixed number that is
either transcendental or algebraic of sufficiently large degree. We also
present several constructions showing that these results are essentially
optimal.Comment: The section 4 of this new version has been rewritten to simplify the
proof of the main result. Other results in Sections 9 and 10 have been
improved. To appear in Compositio Mat
Asymptotics of eigenstates of elliptic problems with mixed boundary data on domains tending to infinity
We analyze the asymptotic behavior of eigenvalues and eigenfunctions of an
elliptic operator with mixed boundary conditions on cylindrical domains when
the length of the cylinder goes to infinity. We identify the correct limiting
problem and show in particular, that in general the limiting behavior is very
different from the one for the Dirichlet boundary conditions.Comment: Asymptotic Analysis, 201
Non-adiabatic pulsations in ESTER models
One of the greatest challenges in interpreting the pulsations of rapidly
rotating stars is mode identification, i.e. correctly matching theoretical
modes to observed pulsation frequencies. Indeed, the latest observations as
well as current theoretical results show the complexity of pulsation spectra in
such stars, and the lack of easily recognisable patterns. In the present
contribution, the latest results on non-adiabatic effects in such pulsations
are described, and we show how these come into play when identifying modes.
These calculations fully take into account the effects of rapid rotation,
including centrifugal distortion, and are based on models from the ESTER
project, currently the only rapidly rotating models in which the energy
conservation equation is satisfied, a prerequisite for calculating
non-adiabatic effects. Non-adiabatic effects determine which modes are excited
and play a key role in the near-surface pulsation-induced temperature
variations which intervene in multi-colour amplitude ratios and phase
differences, as well as line profile variations.Comment: Proceedings for the Joint TASC2 & KASC9 Workshop, Terceira, Azores,
201
Asymmetric frequency conversion in nonlinear systems driven by a biharmonic pump
A novel mechanism of asymmetric frequency conversion is investigated in
nonlinear dispersive devices driven parametrically with a biharmonic pump. When
the relative phase between the first and second harmonics combined in a
two-tone pump is appropriately tuned, nonreciprocal frequency conversion,
either upward or downward, can occur. Full directionality and efficiency of the
conversion process is possible, provided that the distribution of pump power
over the harmonics is set correctly. While this asymmetric conversion effect is
generic, we describe its practical realization in a model system consisting of
a current-biased, resistively-shunted Josephson junction (RSJ). Here, the
multiharmonic Josephson oscillations, generated internally from the static
current bias, provide the pump drive.Comment: 5+ pages, 4 pages supplement. Expanded and modified discussion,
additional references and a new appendix in supplemental material detailing
the calculation of Josephson harmonics in the RS
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