2,466 research outputs found
On the Origin of the Slow Speed Solar Wind: Helium Abundance Variations
The First Ionization Potential (FIP) effect is the by now well known
enhancement in abundance over photospheric values of Fe and other elements with
first ionization potential below about 10 eV observed in the solar corona and
slow speed solar wind. In our model, this fractionation is achieved by means of
the ponderomotive force, arising as Alfv\'en waves propagate through or reflect
from steep density gradients in the solar chromosphere. This is also the region
where low FIP elements are ionized, and high FIP elements are largely neutral
leading to the fractionation as ions interact with the waves but neutrals do
not. Helium, the element with the highest FIP and consequently the last to
remain neutral as one moves upwards can be depleted in such models. Here, we
investigate this depletion for varying loop lengths and magnetic field
strengths.
Variations in this depletion arise as the concentration of the ponderomotive
force at the top of the chromosphere varies in response to Alfv\'en wave
frequency with respect to the resonant frequency of the overlying coronal loop,
the magnetic field, and possibly also the loop length. We find that stronger
depletions of He are obtained for weaker magnetic field, at frequencies close
to or just above the loop resonance. These results may have relevance to
observed variations of the slow wind solar He abundance with wind speed, with
slower slow speed solar wind having a stronger depletion of He.Comment: 28 pages, 12 figures, accepted to Ap
Non-WKB Models of the FIP Effect: The Role of Slow Mode Waves
A model for element abundance fractionation between the solar chromosphere
and corona is further developed. The ponderomotive force due to Alfven waves
propagating through, or reflecting from the chromosphere in solar conditions
generally accelerates chromospheric ions, but not neutrals, into the corona.
This gives rise to what has become known as the First Ionization Potential
(FIP) Effect. We incorporate new physical processes into the model. The
chromospheric ionization balance is improved, and the effect of different
approximations is discussed. We also treat the parametric generation of slow
mode waves by the parallel propagating Alfven waves. This is also an effect of
the ponderomotive force, arising from the periodic variation of the magnetic
pressure driving an acoustic mode, which adds to the background longitudinal
pressure. This can have subtle effects on the fractionation, rendering it
quasi-mass independent in the lower regions of the chromosphere. We also
briefly discuss the change in the fractionation with Alfven wave frequency,
relative to the frequency of the overlying coronal loop resonance.Comment: 32 pages, 8 figures, accepted by Ap
Oracle-order Recovery Performance of Greedy Pursuits with Replacement against General Perturbations
Applying the theory of compressive sensing in practice always takes different
kinds of perturbations into consideration. In this paper, the recovery
performance of greedy pursuits with replacement for sparse recovery is analyzed
when both the measurement vector and the sensing matrix are contaminated with
additive perturbations. Specifically, greedy pursuits with replacement include
three algorithms, compressive sampling matching pursuit (CoSaMP), subspace
pursuit (SP), and iterative hard thresholding (IHT), where the support
estimation is evaluated and updated in each iteration. Based on restricted
isometry property, a unified form of the error bounds of these recovery
algorithms is derived under general perturbations for compressible signals. The
results reveal that the recovery performance is stable against both
perturbations. In addition, these bounds are compared with that of oracle
recovery--- least squares solution with the locations of some largest entries
in magnitude known a priori. The comparison shows that the error bounds of
these algorithms only differ in coefficients from the lower bound of oracle
recovery for some certain signal and perturbations, as reveals that
oracle-order recovery performance of greedy pursuits with replacement is
guaranteed. Numerical simulations are performed to verify the conclusions.Comment: 27 pages, 4 figures, 5 table
The Convergence Guarantees of a Non-convex Approach for Sparse Recovery
In the area of sparse recovery, numerous researches hint that non-convex
penalties might induce better sparsity than convex ones, but up until now those
corresponding non-convex algorithms lack convergence guarantees from the
initial solution to the global optimum. This paper aims to provide performance
guarantees of a non-convex approach for sparse recovery. Specifically, the
concept of weak convexity is incorporated into a class of sparsity-inducing
penalties to characterize the non-convexity. Borrowing the idea of the
projected subgradient method, an algorithm is proposed to solve the non-convex
optimization problem. In addition, a uniform approximate projection is adopted
in the projection step to make this algorithm computationally tractable for
large scale problems. The convergence analysis is provided in the noisy
scenario. It is shown that if the non-convexity of the penalty is below a
threshold (which is in inverse proportion to the distance between the initial
solution and the sparse signal), the recovered solution has recovery error
linear in both the step size and the noise term. Numerical simulations are
implemented to test the performance of the proposed approach and verify the
theoretical analysis.Comment: 33 pages, 7 figure
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