1,002 research outputs found
What can be inferred from surrogate data testing?
Surrogate data testing for linearity is frequently applied to confirm the
results of nonlinear time series analysis. We argue that this, in general, is
not possible.Comment: 1 pag
On the birational section conjecture with local conditions
A birationally liftable Galois section s of a hyperbolic curve X/k over a
number field k yields an adelic point x(s) in the smooth completion of X. We
show that x(s) is X-integral outside a set of places of Dirichlet density 0, or
s is cuspidal. The proof relies on -quotients of for
some open U of X.
If k is totally real or imaginary quadratic, we prove that all birationally
adelic, non-cuspidal Galois sections come from rational points as predicted by
the section conjecture of anabelian geometry. As an aside we also obtain a
strong approximation result for rational points on hyperbolic curves over Q or
imaginary quadratic fields.Comment: Theorem C (and Section 7) of the original version have been deleted
due to a gap in the proof. This is the journal versio
A Self-Consistent Marginally Stable State for Parallel Ion Cyclotron Waves
We derive an equation whose solutions describe self-consistent states of
marginal stability for a proton-electron plasma interacting with
parallel-propagating ion cyclotron waves. Ion cyclotron waves propagating
through this marginally stable plasma will neither grow nor damp. The
dispersion relation of these waves, {\omega} (k), smoothly rises from the usual
MHD behavior at small |k| to reach {\omega} = {\Omega}p as k \rightarrow
\pm\infty. The proton distribution function has constant phase-space density
along the characteristic resonant surfaces defined by this dispersion relation.
Our equation contains a free function describing the variation of the proton
phase-space density across these surfaces. Taking this free function to be a
simple "box function", we obtain specific solutions of the marginally stable
state for a range of proton parallel betas. The phase speeds of these waves are
larger than those given by the cold plasma dispersion relation, and the
characteristic surfaces are more sharply peaked in the v\bot direction. The
threshold anisotropy for generation of ion cyclotron waves is also larger than
that given by estimates which assume bi-Maxwellian proton distributions.Comment: in press in Physics of Plasma
High Resolution Ionization of Ultracold Neutral Plasmas
Collective effects, such as waves and instabilities, are integral to our
understanding of most plasma phenomena. We have been able to study these in
ultracold neutral plasmas by shaping the initial density distribution through
spatial modulation of the ionizing laser intensity. We describe a relay imaging
system for the photoionization beam that allows us to create higher resolution
features and its application to extend the observation of ion acoustic waves to
shorter wavelengths. We also describe the formation of sculpted density
profiles to create fast expansion of plasma into vacuum and streaming plasmas
The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method
The relationship between two different asymptotic techniques developed in
order to describe the propagation of waves beyond the standard geometrical
optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex
geometrical optics method, is addressed. More specifically, a solution of the
wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which
yields the same wavefield intensity as the complex geometrical optics method.
Such a relationship is also discussed on the basis of the analytical solution
of the wave kinetic equation specific to Gaussian beams of electromagnetic
waves propagating in a ``lens-like'' medium for which the complex geometrical
optics solution is already available.Comment: Extended version comprising two new section
The Sun's Preferred Longitudes and the Coupling of Magnetic Dynamo Modes
Observations show that solar activity is distributed non-axisymmetrically,
concentrating at "preferred longitudes". This indicates the important role of
non-axisymmetric magnetic fields in the origin of solar activity. We
investigate the generation of the non-axisymmetric fields and their coupling
with axisymmetric solar magnetic field. Our kinematic generation (dynamo) model
operating in a sphere includes solar differential rotation, which approximates
the differential rotation obtained by inversion of helioseismic data, modelled
distributions of the turbulent resistivity, non-axisymmetric mean helicity, and
meridional circulation in the convection zone. We find that (1) the
non-axisymmetric modes are localised near the base of the convection zone,
where the formation of active regions starts, and at latitudes around
; (2) the coupling of non-axisymmetric and axisymmetric modes
causes the non-axisymmetric mode to follow the solar cycle; the phase relations
between the modes are found. (3) The rate of rotation of the first
non-axisymmetric mode is close to that determined in the interplanetary space.Comment: 22 pages, 18 figures. Accepted for publication in the Astrophysical
Journa
Kinetic instability of drift-Alfven waves in solar corona and stochastic heating
The solar atmosphere is structured and inhomogeneous both horizontally and
vertically. The omnipresence of coronal magnetic loops implies gradients of the
equilibrium plasma quantities like the density, magnetic field and temperature.
These gradients are responsible for the excitation of drift waves that grow
both within the two-component fluid description (in the presence of collisions
and without it) and within the two-component kinetic descriptions (due to
purely kinetic effects). In the present work the effects of the density
gradient in the direction perpendicular to the magnetic field vector are
investigated within the kinetic theory, in both electrostatic and
electromagnetic regimes. The electromagnetic regime implies the coupling of the
gradient-driven drift wave with the Alfven wave. The growth rates for the two
cases are calculated and compared. It is found that, in general, the
electrostatic regime is characterized by stronger growth rates, as compared
with the electromagnetic perturbations. Also discussed is the stochastic
heating associated with the drift wave. The released amount of energy density
due to this heating should be more dependent on the magnitude of the background
magnetic field than on the coupling of the drift and Alfven waves. The
stochastic heating is expected to be much higher in regions with a stronger
magnetic field. On the whole, the energy release rate caused by the stochastic
heating can be several orders of magnitude above the value presently accepted
as necessary for a sustainable coronal heating.Comment: To appear in ApJ (2010
Generation of femtosecond light pulses in the near infrared around λ = 850 nm
Femtosecond light pulses tunable between 840 nm and 880 nm are generated in a synchronously pumped ring dye laser. The laser emits nearly bandwidth-limited pulses (Δv tp = 0.45) with pulse durations down to 65 fs. At a pumping power of 450 mW of a mode-locked Ar-ion laser (λ = 514 nm) the infrared femtosecond dye laser has an output of up to 15 mW
A Kinetic Alfven wave cascade subject to collisionless damping cannot reach electron scales in the solar wind at 1 AU
(Abridged) Turbulence in the solar wind is believed to generate an energy
cascade that is supported primarily by Alfv\'en waves or Alfv\'enic
fluctuations at MHD scales and by kinetic Alfv\'en waves (KAWs) at kinetic
scales . Linear Landau damping of KAWs increases with
increasing wavenumber and at some point the damping becomes so strong that the
energy cascade is completely dissipated. A model of the energy cascade process
that includes the effects of linear collisionless damping of KAWs and the
associated compounding of this damping throughout the cascade process is used
to determine the wavenumber where the energy cascade terminates. It is found
that this wavenumber occurs approximately when ,
where and are, respectively, the real frequency and
damping rate of KAWs and the ratio is evaluated in the limit as
the propagation angle approaches 90 degrees relative to the direction of the
mean magnetic field.Comment: Submitted to Ap
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
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