2,261 research outputs found
KAM-tori near an analytic elliptic fixed point
We study the accumulation of an elliptic fixed point of a real analytic
Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with
Diophantine frequency vector \o_0 is always accumulated by invariant complex
analytic KAM-tori. Indeed, the following alternative holds: If the Birkhoff
normal form of the Hamiltonian at the invariant point satisfies a R\"ussmann
transversality condition, the fixed point is accumulated by real analytic
KAM-tori which cover positive Lebesgue measure in the phase space (in this part
it suffices to assume that \o_0 has rationally independent coordinates). If
the Birkhoff normal form is degenerate, there exists an analytic subvariety of
complex dimension at least passing through 0 that is foliated by complex
analytic KAM-tori with frequency . This is an extension of previous
results obtained in \cite{EFK} to the case of an elliptic fixed point
Fractional Lindstedt series
The parametric equations of the surfaces on which highly resonant
quasi-periodic motions develop (lower-dimensional tori) cannot be analytically
continued, in general, in the perturbation parameter, i.e. they are not
analytic functions of the perturbation parameter. However rather generally
quasi-periodic motions whose frequencies satisfy only one rational relation
("resonances of order 1") admit formal perturbation expansions in terms of a
fractional power of the perturbation parameter, depending on the degeneration
of the resonance. We find conditions for this to happen, and in such a case we
prove that the formal expansion is convergent after suitable resummation.Comment: 40 pages, 6 figure
Amaranthus interruptus R. Br. on Jarvis Island in the Central Pacific
Amaranthus interruptus R. Br.,' a principally Australian species,
has been recorded on Jarvis Island in the Central Pacific. The plant is supposed
to have been introduced to the island some time between 1924 and 1935. It
evidently became well established and was still there in 1964
Converging Perturbative Solutions of the Schroedinger Equation for a Two-Level System with a Hamiltonian Depending Periodically on Time
We study the Schroedinger equation of a class of two-level systems under the
action of a periodic time-dependent external field in the situation where the
energy difference 2epsilon between the free energy levels is sufficiently small
with respect to the strength of the external interaction. Under suitable
conditions we show that this equation has a solution in terms of converging
power series expansions in epsilon. In contrast to other expansion methods,
like in the Dyson expansion, the method we present is not plagued by the
presence of ``secular terms''. Due to this feature we were able to prove
absolute and uniform convergence of the Fourier series involved in the
computation of the wave functions and to prove absolute convergence of the
epsilon-expansions leading to the ``secular frequency'' and to the coefficients
of the Fourier expansion of the wave function
Food Tailoring bilberry powder functionality by processing: effects of preprocessing.
Berry powders are popular as ingredients in a range of food products, where they
naturally provide flavor, color, texture, polyphenols, fiber, and other nutrients. The
choices regarding processing techniques and conditions influence the quality attrib-
utes of berry powders. The aim of this study was to study the effects on bilberry
powder functionalities of applying different preprocessing techniques (purée mixing
and juice pressing vs. untreated whole berries) prior to hot air drying and milling.
Drying of press cake reduced the drying time by 72% and increased the total appar-
ent phenolic content of the final powder by 44%, as compared to the powder of dried
whole berries. The press cake powder showed an easier flowing behavior than the
powders from whole berries and puréed berries. Dispersibility (in water and dairy
cream) was 60% higher for powders from whole berries and puréed berries, as com-
pared to press cake. The total phenolic content of the dispersed powders was highest
for whole berries and puréed berries. Bilberry powder functionality can be modu-
lated through the selection of an appropriate preprocessing technique before drying
and milling. This tailors the powder properties into food ingredients ready for differ-
ent applications, without the need for additives
Almost reducibility for finitely differentiable SL(2,R)-valued quasi-periodic cocycles
Quasi-periodic cocycles with a diophantine frequency and with values in
SL(2,R) are shown to be almost reducible as long as they are close enough to a
constant, in the topology of k times differentiable functions, with k great
enough. Almost reducibility is obtained by analytic approximation after a loss
of differentiability which only depends on the frequency and on the constant
part. As in the analytic case, if their fibered rotation number is diophantine
or rational with respect to the frequency, such cocycles are in fact reducible.
This extends Eliasson's theorem on Schr\"odinger cocycles to the differentiable
case
Numerical simulations of the Fourier transformed Vlasov-Maxwell system in higher dimensions --- Theory and applications
We present a review of recent developments of simulations of the
Vlasov-Maxwell system of equations using a Fourier transform method in velocity
space. In this method, the distribution functions for electrons and ions are
Fourier transformed in velocity space, and the resulting set of equations are
solved numerically. In the original Vlasov equation, phase mixing may lead to
an oscillatory behavior and sharp gradients of the distribution function in
velocity space, which is problematic in simulations where it can lead to
unphysical electric fields and instabilities and to the recurrence effect where
parts of the initial condition recur in the simulation. The particle
distribution function is in general smoother in the Fourier transformed
velocity space, which is desirable for the numerical approximations. By
designing outflow boundary conditions in the Fourier transformed velocity
space, the highest oscillating terms are allowed to propagate out through the
boundary and are removed from the calculations, thereby strongly reducing the
numerical recurrence effect. The outflow boundary conditions in higher
dimensions including electromagnetic effects are discussed. The Fourier
transform method is also suitable to solve the Fourier transformed Wigner
equation, which is the quantum mechanical analogue of the Vlasov equation for
classical particles.Comment: 41 pages, 19 figures. To be published in Transport Theory and
Statistical Physics. Proceedings of the VLASOVIA 2009 Workshop, CIRM, Luminy,
Marseilles, France, 31 August - 4 September 200
Kolmogorov condition near hyperbolic singularities of integrable Hamiltonian systems
In this paper we show that, if an integrable Hamiltonian system admits a
nondegenerate hyperbolic singularity then it will satisfy the Kolmogorov
condegeneracy condition near that singularity (under a mild additional
condition, which is trivial if the singularity contains a fixed point)Comment: revised version, 11p, accepted for publication in a sepecial volume
in Regular and Chaotic Dynamics in honor of Richard Cushma
Predictions of local ground geomagnetic field fluctuations during the 7-10 November 2004 events studied with solar wind driven models
The 7-10 November 2004 period contains two events for which the local ground magnetic field was severely disturbed and simultaneously, the solar wind displayed several shocks and negative <i>B<sub>z</sub></i> periods. Using empirical models the 10-min RMS and at Brorfelde (BFE, 11.67&deg; E, 55.63&deg; N), Denmark, are predicted. The models are recurrent neural networks with 10-min solar wind plasma and magnetic field data as inputs. The predictions show a good agreement during 7 November, up until around noon on 8 November, after which the predictions become significantly poorer. The correlations between observed and predicted log RMS is 0.77 during 7-8 November but drops to 0.38 during 9-10 November. For RMS the correlations for the two periods are 0.71 and 0.41, respectively. Studying the solar wind data for other L1-spacecraft (WIND and SOHO) it seems that the ACE data have a better agreement to the near-Earth solar wind during the first two days as compared to the last two days. Thus, the accuracy of the predictions depends on the location of the spacecraft and the solar wind flow direction. Another finding, for the events studied here, is that the and models showed a very different dependence on <i>B<sub>z</sub></i>. The model is almost independent of the solar wind magnetic field <i>B<sub>z</sub></i>, except at times when <i>B<sub>z</sub></i> is exceptionally large or when the overall activity is low. On the contrary, the model shows a strong dependence on <i>B<sub>z</sub></i> at all times
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