65,939 research outputs found
A theoretical basis for the Harmonic Balance Method
The Harmonic Balance method provides a heuristic approach for finding
truncated Fourier series as an approximation to the periodic solutions of
ordinary differential equations. Another natural way for obtaining these type
of approximations consists in applying numerical methods. In this paper we
recover the pioneering results of Stokes and Urabe that provide a theoretical
basis for proving that near these truncated series, whatever is the way they
have been obtained, there are actual periodic solutions of the equation. We
will restrict our attention to one-dimensional non-autonomous ordinary
differential equations and we apply the results obtained to a couple of
concrete examples coming from planar autonomous systems
Modeling dust emission in PN IC 418
We investigated the infrared (IR) dust emission from PN IC 418, using a
detailed model controlled by a previous determination of the stellar properties
and the characteristics of the photoionized nebula, keeping as free parameters
the dust types, amounts and distributions relative to the distance of the
central star. The model includes the ionized region and the neutral region
beyond the recombination front (Photodissociation region, or PDR), where the
[OI] and [CII] IR lines are formed. We succeeded in reproducing the observed
infrared emission from 2 to 200~\mm. The global energy budget is fitted by
summing up contributions from big grains of amorphous carbon located in the
neutral region and small graphite grains located in the ionized region (closer
to the central star).
Two emission features seen at 11.5 and 30~\mm are also reproduced by assuming
them to be due to silicon carbide (SiC) and magnesium and iron sulfides
(MgFeS), respectively. For this, we needed to consider ellipsoidal
shapes for the grains to reproduce the wavelength distribution of the features.
Some elements are depleted in the gaseous phase: Mg, Si, and S have sub-solar
abundances (-0.5 dex below solar by mass), while the abundance of C+N+O+Ne by
mass is close to solar. Adding the abundances of the elements present in the
dusty and gaseous forms leads to values closer to but not higher than solar,
confirming that the identification of the feature carriers is plausible. Iron
is strongly depleted (3 dex below solar) and the small amount present in dust
in our model is far from being enough to recover the solar value. A remaining
feature is found as a residue of the fitting process, between 12 and 25~\mm,
for which we do not have identification.Comment: Accepted for publication in Astronomy & Astrophysics. V2: adding
reference
Modeling the dust emission from PN IC418
We construct a detailed model for the IR dust emission from the PN IC 418. We
succeed to reproduce the emission from 2 to 200m. We can determine the
amount of emitting dust as well as its composition, and compare to the
depletion of elements determined for the photoionized region.Comment: Poster contribution (2 pages, 1 figure) to IAU Symposium 283:
"Planetary Nebulae: An Eye to the Future" held in Puerto de la Cruz,
Tenerife, Spain in July 25th-29th 2011. Few typos correcte
- …